# tikz_tikz

folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: engines.tex
modified: 2015-10-29 00:27:14
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=red!20!white] (-1.5,2) rectangle  node{$T_{h}$} (1.5,3);
    \draw[->,line width=3,color=DarkRed] (0,2) --node[anchor=east]{$Q_{h}$}
    (0,0.5);
    \filldraw[fill=gray!20!white] (0,0) circle[radius=0.5];
    \draw[->,line width=3,color=DarkBlue] (0,-0.5) --node[anchor=east]{$Q_{c}$}
    (0,-2);
    \filldraw[fill=blue!20!white] (-1.5,-3) rectangle  node{$T_{c}$} (1.5,-2);
    \draw[->,line width=3,color=DarkGreen] (0.5,0) --node[anchor=south]{$W$}
    ++(0:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec11-prof.tex
modified: 2014-04-16 02:57:58
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[rotate=15]
      \filldraw[fill=blue!30!white] (0,0) rectangle (1,0.75);
      \draw[force] (1,0.375) -- ++(0:1) node[anchor=south]{$T$};
      \draw[force] (0.5,0.375) -- ++(-105:2) node[anchor=west]{$mg$};
      \draw[force] (0.5,0) -- ++(90:2) node[anchor=west]{$N$};
      \draw[force] (0.5,0) -- ++(180:1) node[anchor=north]{$F_{k}$};
      \draw[coord] (1.25,1.25) -- ++(0:1) node[anchor=north]{$x$};
      \draw[coord] (1.25,1.25) -- ++(90:1) node[anchor=west]{$y$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec10-prof.tex
modified: 2014-02-24 23:26:38
domain: p24
source:
  \begin{tikzpicture}[scale=1.5,>=stealth']
    \coordinate (AB) at (0,0);
    \coordinate (AC) at (2,0);
    \coordinate (BC) at (1.4,1);

    \draw[->,blue,line width=1pt] (AB) -- ($ (AB)!0.5!(AC) $) node[below] {$\mathbf{a}$} -- (AC);
    \draw[->,red,line width=1pt] (AB) -- ($ (AB)!0.5!(BC) $) node[anchor=south] {$\mathbf{b}$} -- (1.4,1);
    \draw[->,darkgray,line width=1pt] (AC) -- ($ (AC)!0.5!(BC) $)
    node[right] {$\mathbf{c = b - a}$}  -- (BC);

    % Now the arc

    \draw ($ (AB)!0.25!(AC) $) arc[ radius=0.5,start angle=0,end angle=35];
    \node at (0.67,0.2) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: engines.tex
modified: 2015-10-29 00:27:14
domain: p117
source:
  \begin{tikzpicture}[scale=1,
      heatflow/.style={line width=2,->,DarkRed},
      workflow/.style={line width=2,->,DarkGreen}
    ]
    \begin{scope}
      \filldraw[fill=red!30!white] (-1,-0.1) rectangle (1,-1);
      \node at (0.7,-0.7){$T_{h}$};
      \cylinder{(0,0)};
      \piston{(0,0.75)};
      \draw[workflow] (0,2) -- ++(90:0.85) node[anchor=south]{$W_{a}$};
      \draw[heatflow] (0,-0.5) node[anchor=east]{$Q_{h}$} -- ++(90:.85);
      \node at (0,-1.5){(a)};
    \end{scope}

    \begin{scope}[shift={(3,0)}]
      \cylinder{(0,0)};
      \piston{(0,1.5)};
      \draw[workflow] (0,2.75) -- ++(90:0.85) node[anchor=south]{$W_{b}$};
      \node at (0,-1.5){(b)};
    \end{scope}

    \begin{scope}[shift={(6,0)}]
      \filldraw[fill=blue!30!white] (-1,-0.1) rectangle (1,-1);
      \node at (0.7,-0.7){$T_{c}$};
      \cylinder{(0,0)};
      \piston{(0,2.5)};
      \draw[workflow] (0,4.5) node[anchor=east]{$W_{c}$}-- ++(-90:0.85);
      \draw[heatflow] (0,0.35) -- ++(-90:.85) node[anchor=east]{$Q_{c}$};
      \node at (0,-1.5){(c)};
    \end{scope}

    \begin{scope}[shift={(9,0)}]
      \cylinder{(0,0)};
      \piston{(0,1.5)};
      \draw[workflow] (0,3.6) node[anchor=east]{$W_{d}$} -- ++(-90:0.85);
      \node at (0,-1.5){(d)};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec25-prof.tex
modified: 2014-07-16 22:42:27
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[line width=2] (0,2) -- (0,0) -- (7,0);
    \draw[spring] (0,1) -- (2,1);
    \node at (1,1.75) {$k_{1}$};
    \draw[spring, line width=1.5] (2,1) -- (4,1);
    \node at (3,1.75) {$k_{2}$};
    \filldraw[fill=gray!40] (4,0.1) rectangle (6,2);
    \node at (5,2.5) {$m$};

    \begin{scope}[shift={(0,-3)}]
      \draw[line width=2] (0,2) -- (0,0) -- (7,0) -- (7,2);
      \draw[spring] (0,1) -- (2,1);
      \node at (1,1.75) {$k_{1}$};
      \draw[spring, line width=1.5] (4,1) -- (7,1);
      \node at (5.5,1.75) {$k_{2}$};
      \filldraw[fill=gray!40] (2,0.1) rectangle (4,2);
      \node at (3,2.5) {$m$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: vanderWaals.tex
modified: 2015-12-13 22:39:51
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=-1,
        ymax=0.5,
        xmin=0.75,
        xmax=2,
        enlargelimits=false,
        height=2.5in,
        width=2in,
        ylabel={$U(r)$},
        xlabel={$r$},
        ytick={0,1},
        xtick={1,1.25,...,2},
        xticklabels={$r_{0}$,,$1.5 r_{0}$,,$2 r_{0}$}
      ]
      \addplot[
        trace01,
        domain=0.85:2,
        samples=201,
        line width=2pt,
      ]
      {1/(x^12)-2/(x^6)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec25-prof.tex
modified: 2014-07-16 22:42:27
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=4,color=gray] (-45:4) -- (0,0) -- (225:4) ;
    \fill (-45:2) circle (0.1) node[anchor=south west]{$m$};
    \fill (225:2) circle (0.1) node[anchor=south east]{$m$};
    \draw[dashed] (-45:2) -- (225:2);
    \draw[dashed] (0,0) -- (0,-3);
    \fill (0,-1.414) circle(0.15) node[anchor = north west]{CM};
    \node at (-25:1.2) {$L/2$};
    \node at (-1,0) {$\frac{L}{2\sqrt{2}} $};
    \draw[->] (-0.55,-0.2) -- (0,-0.7);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: vanderWaals.tex
modified: 2015-12-13 22:39:51
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=3,
        ymin=0,
        ymax=2.5,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        xlabel={$V$},
        ylabel={$p$},
        %ytick={0,1},
        %xtick={0,0.5,1,1.5,2},
        xticklabel=\empty,
        yticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
      ]
      \addplot[ trace01, domain=0.45:3, samples=101, line width=2pt ]
      {8/3*0.85/(x-1/3)-3/x^2};
      \addplot[ trace02, domain=0.5:3, samples=101, line width=2pt ]
      {8/3*0.925/(x-1/3)-3/x^2};
      \addplot[ trace03, domain=0.5:3, samples=101, line width=2pt ]
      {8/3*1.0/(x-1/3)-3/x^2};
      \addplot[ trace04, domain=0.5:3, samples=101, line width=2pt ]
      {8/3*1.075/(x-1/3)-3/x^2};
      \addplot[ trace05, domain=0.55:3, samples=101, line width=2pt ]
      {8/3*1.15/(x-1/3)-3/x^2};
      %      \addplot[domain=0.5:3, samples=101] { 1/(x) };
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec25-prof.tex
modified: 2014-07-16 22:42:27
domain: p24
source:
  \begin{tikzpicture}[scale=0.8]
    \begin{axis}[xlabel={$r$},
        ylabel={$U(r)$}]
      \addplot[,domain=0.6:2.5,samples=201,]
      { 1/(3*x^3) - 1/(2*x^2)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: vanderWaals.tex
modified: 2015-12-13 22:39:51
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\temp{0.85}
    \begin{axis}[
        %no markers,
        xmin=0,
        xmax=1,
        ymin=-1,
        ymax=-0.5,
        enlargelimits=false,
        width=2.5in,
        height=2.5in,
        xlabel={$\redp$},
        ylabel={$g$},
        %ytick={0,1},
        %xtick={0,0.5,1,1.5,2},
        %xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
      ]
      % \addplot[
      % trace01,
      % domain=0.5:4,
      % samples=51,
      % line width=2pt,
      % ]
      % ( 2.6667 * \temp / (x-0.3333) - 3/x^2, -2.25/x - \temp * ln( x - 0.3333)
      % + \temp * x /(x - 0.3333) );
      \addplot+[mark indices={1,6,19,38,61,77,88}] table[x=p,y=g] {gibbs2.dat};
      %      \node[pin=0:0.1] at (0.5,-0.64) {2,6};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec16-prof.tex
modified: 2014-03-22 17:27:54
domain: p24
source:
  \begin{tikzpicture}[scale=0.5]
    \fill[fill=yellow] (3,0) circle[radius=0.2];
    \draw[color=blue] (5,0) arc[x radius=5, y radius=4, start angle=0, end angle=110];
    \draw[color=blue] (5,0) arc[x radius=5, y radius=4, start angle=0, end angle=-20];
    \draw (0,0) --node[anchor=north]{$a$} (5,0) (0,0) --node[anchor=east]{$b$}
    (0,4) --node[anchor=south west]{$a$} (3,0) --node[anchor=south]{$a\epsilon$} cycle;
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: vanderWaals.tex
modified: 2015-12-13 22:39:51
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin = 0,
        %      xmax = 6,
        ymin = 0,
        ymax = 0.9,
        enlargelimits=false,
        width=3in,
        height=2.5in,
        xlabel={$\redv$},
        ylabel={$\redp$}
      ]
      \addplot+[mark indices={1,6,19,38,61,77,88}] table[x=v,y=p] {gibbs2.dat}; %1,6,19,39,62,78,89
      %      \addplot table[x=v,y=p] {gibbs.dat};
      \draw[dashed] (0.5525,0.5046) -- (3.126,0.5046);
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec16-prof.tex
modified: 2014-03-22 17:27:54
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \fill[color=blue!50!white] (0,0) circle(0.75);
    \draw[dashed] (-10:4) arc[start angle=-10, end angle=100, radius=4];
    \draw[dashed] (0,0) circle(1);
    \fill[fill=gray] (-135:1) circle(0.1);
    \begin{scope}[rotate=45]
      \draw[color=red] (180:1) arc[
          start angle=180,
          end angle=360,
          x radius=2.5,
          y radius=2];
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: vanderWaals.tex
modified: 2015-12-13 22:39:51
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\temp{0.85}
    \begin{axis}[
        no markers,
        xmin=0,
        xmax=6,
        ymin=0,
        ymax=1.3,
        enlargelimits=false,
        width=3.75in,
        height=3in,
        xlabel={$\redv$},
        ylabel={$\redp$},
      ]
      \addplot+[dashed,color=black] table[x=vliq,y=p] {gibbs3.dat};
      \addplot+[dashed,color=black] table[x=vvap,y=p] {gibbs3.dat};
      \addplot+[color=DarkGreen!80!gray,line width=1.5] table[x=v,y=p075] {gibbs4.dat};
      \addplot+[color=DarkGreen!70!gray,line width=1.5] table[x=v,y=p080] {gibbs4.dat};
      \addplot+[solid,color=DarkGreen!60!gray,line width=1.5] table[x=v,y=p085] {gibbs4.dat};
      \addplot+[solid,color=DarkGreen!50!gray,line width=1.5] table[x=v,y=p090] {gibbs4.dat};
      \addplot+[solid,color=DarkGreen!40!gray,line width=1.5] table[x=v,y=p095] {gibbs4.dat};
      \addplot+[solid,color=DarkGreen!30!gray,line width=1.5] table[x=v,y=p100] {gibbs4.dat};
      \addplot+[solid,color=DarkGreen!20!gray,line width=1.5] table[x=v,y=p105] {gibbs4.dat};
      \addplot+[solid,color=DarkGreen!10!gray,line width=1.5] table[x=v,y=p110] {gibbs4.dat};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec01-prof.tex
modified: 2015-01-09 19:51:22
domain: p24
source:
  \begin{tikzpicture}[
      scale=0.8,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw (0,0) -- +(0:8);
    \filldraw (1,0.25) circle(0.25);
    \filldraw (5,0.25) circle(0.25);
    \filldraw[fill=gray,draw=black] (0,0.25) rectangle (6,0.75);
    \filldraw[fill=red] (5.5,0.75) rectangle (6,2.5);
    \draw[very thick,->] (6.2,0.5) -- +(0:0.75) node[anchor=west] {$
          \val{5.0}{m/s} $};
    \draw[very thick,->,draw=red] (5,1.5) -- +(180:0.75)
    node[anchor=east,color=red] {$ \val{10.0}{m/s} $};
    \node at (0.5,1) {$\val{100}{kg}$};
    \node[color=red] at (6.75,2) {$\val{80}{kg}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Mechanics MOOC
filename: vectors.tex
modified: 2014-06-17 16:32:34
domain: p24
source:
  \begin{tikzpicture}[scale=1,>=stealth']
    \draw[blue!30!white] (-1,-1) grid (6,4);
    \draw[->,line width=2,color=gray] (0,0) -- (7,0) node[anchor=north west]{east};
    \draw[->,line width=2,color=gray] (0,0) -- (0,5) node[anchor=north east]{north};
    \draw[line width=3,->,color=DarkRed] (0,0) -- node[anchor=north,fill=white]{displacement 1} (4,0);
    \draw[line width=2.5,->,color=DarkGreen] (4,0) -- (4,3);
    \node[color=DarkGreen,fill=white,rotate=-90] at (4.5,1.5) {displacement 2};
    \draw[vel] (0,0) -- (4,3) node[anchor=south east, fill=white]{$\mathbf{r}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Mechanics MOOC
filename: vectors.tex
modified: 2014-06-17 16:32:34
domain: p24
source:
  \begin{tikzpicture}[scale=1,rotate=15,>=stealth']
    \draw[blue!30!white] (-1,-1) grid (6,4);
    \draw[->,line width=2,color=gray] (0,0) -- (7,0) node[anchor=north west,fill=white]{$x$};
    \draw[->,line width=2,color=gray] (0,0) -- (0,5) node[anchor=north east,fill=white]{$y$};
    \draw[vel] (0,0) -- (4,3) node[anchor=west, fill=white]{$\mathbf{v}$};
    \draw[line width=3,->,color=DarkRed] (0,0) -- node[anchor=north,fill=white]{$\hat{\mathbf{x}}$} (1,0);
    \draw[line width=3,->,color=DarkRed] (0,0) -- (1,0);
    \draw[line width=2.5,->,color=DarkGreen] (0,0) -- node[anchor=north east,fill=white]{$\hat{\mathbf{y}}$} (0,1);
    \draw[line width=2.5,->,color=DarkGreen] (0,0) -- (0,1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: QuantumGases.tex
modified: 2015-11-10 17:07:26
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\x{4}
    \def\y{1.5}
    \draw[dashed] (0,-\y) -- (0,\y);
    \draw[line width=4pt,color=SlateGray] (0,-\y) rectangle (\x,\y);
    \draw[line width=2pt,color=SlateGray] (0,-\y/2) rectangle (-\x/3,\y/2);
    \node at (-\x/6,-\y/1.45) {system};
    \node at (\x/2,-\y*1.2) {reservoir};
    \node at (0.8*\x,0.7*\y){$T,\mu$};
    \draw[<->,color=DarkRed,line width=1.5] (-0.5,0)
    -- (0.5,0) node[anchor=north]{$\qquad\quad\Delta \nrg, \Delta N$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Mechanics MOOC/Source
filename: Flowchart.tex
modified: 2015-04-06 22:42:57
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \node[fill=yellow!20!white, text width=2.5in,draw=black] at (0,8) {Most problems are
      easier to solve using conservation laws than \( \VEC{F} = m\VEC{a} \) and \(
      \boldsymbol{\tau} = I  \boldsymbol{\alpha}  \), so your first job is to
      figure out whether you can use conservation laws.};

    \begin{scope}[shift={(7,7)}]
      \filldraw[fill=yellow!25!white,draw=DarkBlue] (-2.5,0) rectangle (2.5,-9.5);
      \node at (0,-0.5){\textbf{Conservation Laws}};

      \node[strategy] at (0,-2) {Momentum is conserved. Use \( \mathbf{p}_{0} =
        \mathbf{p}_{f} \).};
      \node[strategy] at (0, -5) {Angular momentum is conserved about this
        point. Use \( \mathbf{L}_{0} = \mathbf{L}_{f} \).};

      \node[strategy] at (0,-8) {Conserve energy using \( \displaystyle K = \frac{1}{2} MV^{2} +
        \sum_{i} \frac{1}{2} m_{i} v_{i}^{\prime 2}\) or a simplification.};

    \end{scope}
    \node[question] at (0,5) {Is there a net external force on the system?};
    \draw[flow,no] (3, 5) -- node[anchor=south]{\large No} +(0:1.25);
    \draw[flow] (0,4.25) -- node[anchor=west]{\large Yes} +(-90:1.);
    \node[question] at (0,2) {Can I choose a point in an inertial frame such that the
      sum of external torques about this point vanishes?};
    \draw[flow] (3, 2) -- node[anchor=south]{\large Yes} +(0:1.25);
    \draw[flow,no] (0, 0.75) -- node[anchor=west]{\large No} +(-90:1.);
    \node[question] at (0,-1.25) {Is mechanical energy conserved (if friction is
      present, does it do no work)?};
    \draw[flow] (3, -1.25) -- node[anchor=south]{\large Yes} +(0:1.25);
    \draw[flow,no] (0, -2.25) -- node[anchor=west]{\large No} +(-90:1.);

    \begin{scope}[shift={(0,-4)}]
      \node[strategy] (0,2.5) {Use forces and torques.};
    \end{scope}

    \begin{scope}[shift={(16.5,10)}]
      \filldraw[fill=yellow!25!white,draw=DarkBlue] (-6,0) rectangle (6,-18);
      \node at (0,-0.5){\textbf{Forces and Torques}};
      \begin{scope}[shift={(-5.5,-0.75)}]
        \filldraw[fill=white,draw=DarkBlue] (0,-.25) rectangle (11,-7.75);
        \node at (1.5,-0.5) {\textbf{Select an Origin}};
        \node[question, text width=1.6in] at (2.5,-1.85) {Is there a fixed point in the problem, such as an
          axle, that will provide reaction forces?};
        \draw[flow] (5,-1.85) --node[anchor=south]{\large Yes} +(0:1.5);
        \node[strategy, text width=1.4in] at (8.5,-1.85) {It is usually helpful to compute torques and
          angular momenta about this point.};
        \draw[flow,no] (2.5,-3) -- node[anchor=west]{\large No} +(-90:1.);
        \node[strategy, text width=1.4in] at (8.5,-4.5) {It \emph{may} be easier to
          use the point of contact to calculate torques and/or angular momentum.};
        \node[question, text width=1.6in] at (2.5,-5.2) {Is there a point of contact
          about which an object instantaneously rotates?};
        \draw[flow] (5,-4.5) --node[anchor=south] {\large Yes} +(0:1.5);
        \node[strategy, text width=1.4in] at (8.5,-6.75) {Calculate torques about
          the center of mass.};
        \draw[flow,no] (2.5,-6.5) -- ++(-90:0.5) -- node[anchor=south]{\large No}
        ++(0:4);


      \end{scope}



      \begin{scope}[shift={(-4,-9)}]
        \filldraw[fill=green!25!white, draw=DarkBlue] (0,0) rectangle (8,-8.75);
        \node[anchor=west] at (0.25,-0.35){\textbf{Apply Newton's Laws}};
        \node[strategy,text width=2.25in] at (3.25,-1.5){Isolate each object and draw a diagram of the
          forces on it.};
        \node[strategy,text width=2.25in] at (3.25,-3){Apply \( \mathbf{F} = m
          \mathbf{a} \) to each object to get 1 or more dynamical equations.};
        \node[strategy,text width=2.25in] at (3.25,-4.5){Apply \( \boldsymbol{\tau}
          = I \boldsymbol{\alpha} \) to each object to get a dynamical equation.};
        \node[strategy,text width=2.25in] at (3.25,-6.25){Develop equations of
          constraint as necessary among dynamical variables.};
        \node[strategy,text width=2.25in] at (3.25,-8){When you have as many
          equations as unknowns, \emph{solve!}};
        \draw[flow] (6.75,-1.5) -- ++(0:0.2) arc(90:-90:0.5) -- ++(180:0.2);
        \draw[flow] (6.75,-3.25) -- ++(0:0.2) arc(90:-90:0.5) -- ++(180:0.2);
        \draw[flow] (6.75,-4.75) -- ++(0:0.2) arc(90:-90:0.5) -- ++(180:0.2);
        \draw[flow] (6.75,-6.75) -- ++(0:0.2) arc(90:-90:0.5) -- ++(180:0.2);
      \end{scope}
      \draw[flow] (5,-1.85) -- (5.7,-1.85) -- ++(-90:7) -- ++(180:4.5)
      --++(-90:1);
      \draw[flow,-] (5,-5.25) -- +(0:0.7) (5,-7.5) -- ++(0:0.7);
    \end{scope}

    \draw[flow] (0, -4.5) -- ++(-90:0.5) -- ++(0:10)
    --++(90:14.75)
    --++(0:3)
    --++(-90:0.65);

    \node at (-1.5,-7.75){Peter N.\ Saeta};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: QuantumGases.tex
modified: 2015-11-10 17:07:26
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-2,
        xmax=2,
        ymin=-0.1,
        ymax=1.1,
        enlargelimits=false,
        width=3.5in,
        height=2.5in,
        xlabel={$\epsilon$},
        ylabel={$\nfd$},
        %ytick={0,1},
        xtick={-2,-1,...,2},
        xticklabels={$\mu-2\escale$,$\mu-\escale$,$\mu\vphantom{\escale}$,$\mu+\escale$,$\mu+2\escale$},
        % xticklabels{0,,$a$,,a$},
      ]
      \addplot[trace01, domain=-2:2,samples=201, line width=2pt]
      {1 / (1+exp(2*x))};
      \addplot[trace02, domain=-2:2,samples=201, line width=2pt]
      {1 / (1+exp(4*x))};
      \addplot[trace03, domain=-2:2,samples=201, line width=2pt]
      {1 / (1+exp(8*x))};
      \addplot[trace04, domain=-2:2,samples=201, line width=2pt]
      {1 / (1+exp(16*x))};
      \draw[<-,trace01] (-0.6,0.75) -- (-0.9,0.75) node[anchor=east]
      {$\kT = \frac{1}{2}\escale$};
      \draw[<-,trace02] (0.3,0.2) -- (-0.5,0.2)
      node[anchor=east]{$\kT=\frac{1}{4}\escale$};
      \draw[<-,trace03] (-0.225,0.9) -- (0.2,0.9)
      node[anchor=west]{$\kT=\frac{1}{8}\escale$};
      \draw[<-,trace04] (0.,0.7) -- (0.5,0.7)
      node[anchor=west]{$\kT=\frac{1}{16}\escale$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015
filename: math-osc-waves.tex
modified: 2015-04-27 14:51:56
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) circle[radius=2.5];
    \draw[->] (-3,0) -- (3,0) node[anchor=north]{$x$};
    \draw[->] (0,-3) -- (0,3) node[anchor=east]{$y$};
    \draw[line width=2.5,->,blue] (0,0) --node[anchor=south east]{$r$} (60:2.5);
    \draw (0:0.6) arc(0:60:0.6);
    \node at (30:0.85){$\theta$};
    \draw[color=gray,line width=2] (60:2.5) -- (1.25,0);
    \node[color=gray] at (1.8,0.6) {$r\sin\theta$};
    \draw[color=DarkRed,line width=2] (0,0) -- (1.25,0);
    \node[color=DarkRed, fill=white] at (0.625,-0.35) {$r\cos\theta$};
    \filldraw (60:2.5) circle [radius=0.1];
    \node at (60:2.9){$P$};
    \draw[color=DarkGreen,line width=3] (0:2.5) arc(0:60:2.5);
    \node[color=DarkGreen] at (30:2.75) {$s$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: QuantumGases.tex
modified: 2015-11-10 17:07:26
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-1.02,
        xmax=2,
        ymin=-0.1,
        ymax=3,
        enlargelimits=false,
        width=3.5in,
        height=2.5in,
        xlabel={$\epsilon$},
        ylabel={$\overbar{n}$},
        %ytick={0,1},
        xtick={-2,-1,...,2},
        xticklabels={$\mu-2\escale$,$\mu-\escale$,$\mu\vphantom{\escale}$,
            $\mu+\escale$,$\mu+2\escale$},
        % xticklabels{0,,$a$,,a$},
      ]
      \def\temp{4}
      \addplot[trace01, domain=-1:2,samples=201, line width=2pt]
      {1 / (exp(\temp*x))};
      \addplot[trace02, domain=-1:2,samples=201, line width=2pt]
      {1 / (1+exp(\temp*x))};
      \addplot[trace03, domain=0.05:2,samples=101, line width=2pt]
      {1 / (exp(\temp*x)-1)};
      \node[trace01] at (-0.4,2.25) {MB};
      \node[trace02] at (-0.5,1.1) {FD};
      \node[trace03] at (0.25,2.25) {BE};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015
filename: math-osc-waves.tex
modified: 2015-04-27 14:51:56
domain: p24
source:
  \begin{tikzpicture}[scale=0.6]
    \foreach \x in {-4,0,4} {
        \draw[line width=2,color=blue] (\x,0) sin(\x + 1,\am) cos(\x + 2,0)
        sin(\x + 3,-\am) cos(\x + 4,0);
      }
    \draw[->] (0,-1.5) -- (0,1.5) node[anchor=east]{$y$};
    \draw[->] (-4.5,0) -- (8.5,0) node[anchor=north]{$x$};
    \draw[<->] (1,1.2) -- node[fill=white]{$\lambda$} (5,1.2);
    \draw[dashed,color=DarkGreen] (-1.25,\am) -- (2,\am);
    \draw[<->,color=DarkGreen] (-1,0) --node[anchor=east]{$A$} (-1,\am);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: QuantumGases.tex
modified: 2015-11-10 17:07:26
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=1,
        ymin=0,
        ymax=1,
        enlargelimits=false,
        width=3in,
        height=2.25in,
        ylabel={$\spe = \hb \omega$},
        xlabel={$k$},
        ytick=\empty,
        xtick=\empty,
        xticklabel=\empty,
        yticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
        % xticklabels{0,,$a$,,a$},
      ]
      \addplot[
        trace01,
        domain=0.001:2,
        samples=201,
        line width=2pt,
      ]
      {x^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015
filename: math-osc-waves.tex
modified: 2015-04-27 14:51:56
domain: p24
source:
  \begin{tikzpicture}[scale=0.8]
    \def\am{0.5}
    \foreach \x in {0,4} {
        \draw[line width=2,color=blue] (\x,0) sin(\x + 1,\am) cos(\x + 2,0) sin(\x +
        3,-\am) cos(\x + 4,0);
        \draw[line width=2,color=blue] (\x,0) sin(\x + 1,-\am) cos(\x + 2,0) sin(\x +
        3,\am) cos(\x + 4,0);
      }
    \draw[->] (0,-1) -- (0,1) node[anchor=east]{$y$};
    \draw[->] (-0.5,0) -- (8.5,0) node[anchor=north]{$x$};
    \draw[<->] (1,0.9) -- node[fill=white]{$\lambda$} ++(0:4);
    \draw[color=DarkGreen,<-] (2,-0.1) -- ++(-90:1) node[anchor=north]{node};
    \draw[color=DarkGreen,<-] (5,-0.6) -- ++(-90:0.5) node[anchor=north]{antinode};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/hw15
filename: hw06-sol.tex
modified: 2015-01-19 18:22:12
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[accel] (-1.5,1.5) -- node[anchor=south] {\( a \)} +(0:1.5);
    \filldraw[fill=gray!20!white] (0,0) rectangle (2,1);
    \draw[force] (0,0.5) -- +(180:1.25) node[anchor=south]{\( F \)};
    \draw[force] (0.9,0.5) -- +(-90:1.5) node[anchor=east]{\( mg \)};
    \draw[force] (1,0) -- +(90:1.5) node[anchor=east]{\( N \)};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: tmp.tex
modified: 2015-11-03 06:06:25
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        %      area style,
        xmin=0,
        xmax=1.2,
        ymin=0,
        ymax=1,
        enlargelimits=false,
        width=2.5in,
        xlabel={$\varepsilon$},
        ylabel=\empty,
        ytick=\empty,
        xtick=\empty,
        xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25},
        axis on top=true,
        x label style={xshift=0.75in},
      ]
      \addplot[color=white,domain=0:0.75,samples=101,line width=0pt,fill=blue!20!white ]
      {sqrt(x)} \closedcycle;
      \addplot[domain=0:1,samples=101,line width=1pt]
      {sqrt(x)};
      \addplot[domain=0:1,samples=151,line width=1.5pt,trace02]
      {sqrt(x)/(1+exp(32*(x-0.75)))};
      \node at (0.95,0.9) {$\Omega$};
    \end{axis}
    \node at (2.95,-0.25){$\varepsilon_F$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: tmp.tex
modified: 2015-11-03 06:06:25
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        %      area style,
        xmin=0.8,
        xmax=1.2,
        ymin=0,
        ymax=1.2,
        enlargelimits=false,
        width=2.5in,
        xlabel={$\varepsilon$},
        ylabel=\empty,
        ytick=\empty,
        xtick=\empty,
        xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25},
        axis on top=true,
        x label style={xshift=0.75in},
      ]
      \addplot[color=white,domain=0.8:1,samples=101,line width=0pt,fill=blue!20!white ]
      {sqrt(x)} \closedcycle;
      \addplot[domain=0.8:1.2,samples=101,line width=1pt]
      {sqrt(x)};
      \addplot[domain=0.8:1.2,samples=151,line width=1.5pt,trace02]
      {sqrt(x)/(1+exp(32*(x-1)))};
      \node at (0.95,0.9) {$\Omega$};
    \end{axis}
    \node at (2.95,-0.25){$\varepsilon_F$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/hw15
filename: hw05-sol.tex
modified: 2015-02-04 02:38:05
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      photon/.style={line width=1.5pt,color=DarkRed,decorate,decoration={snake,post length=0.1in}},
      spring/.style={decorate,decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm}},
      traj/.style={dashed, color=gray, line width=1pt}
    ]
    % the football
    \filldraw[fill=brown] (0,-0.5) arc(-60:60:1) (0.,1.245)
    arc(120:240:1);
    \draw[force] (0,0.35) -- +(-90:1.5) node[anchor=east]{$mg$};
    \draw[coord,->] (1,0) -- +(0:0.75) node[anchor=north]{$x$};
    \draw[coord,->] (1,0) -- +(90:0.75) node[anchor=east]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/hw15
filename: hw05-sol.tex
modified: 2015-02-04 02:38:05
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      photon/.style={line width=1.5pt,color=DarkRed,decorate,decoration={snake,post length=0.1in}},
      spring/.style={decorate,decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm}},
      traj/.style={dashed, color=gray, line width=1pt}
    ]
    \shade[ball color=gray] (0,0) circle(0.25);
    \draw[force] (0,0) -- ++(-90:1.5) node[anchor=west]{$mg$};
    \draw[force] (0,0) -- ++(120:1.8) node[anchor=east]{$T$};
    \draw[accel] (-0.5,0) -- ++(180:1) node[anchor=north]{$a$};
    \draw[dashed] (0, 0.25) -- ++(90:1.5);
    \draw (0,0.75) arc (90:120:0.75);
    \node at (-0.25,1.) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Bose.tex
modified: 2015-11-20 22:55:19
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-1.02,
        xmax=1.5,
        ymin=-0.1,
        ymax=3,
        enlargelimits=false,
        width=3.5in,
        height=2.5in,
        xlabel={$\epsilon$},
        ylabel={$\overbar{n}$},
        xtick={-2,-1,...,2},
        xticklabels={$\mu-2\escale$,$\mu-\escale$,$\mu\vphantom{\escale}$,
            $\mu+\escale$,$\mu+2\escale$},
      ]
      \def\temp{2}
      \addplot[trace01, domain=-1:2,samples=201, line width=2pt]
      {1 / (exp(\temp*x))};
      \addplot[trace02, domain=-1:2,samples=201, line width=2pt]
      {1 / (1+exp(\temp*x))};
      \addplot[trace03, domain=0.05:2,samples=101, line width=2pt]
      {1 / (exp(\temp*x)-1)};
      \node[trace01] at (-0.65,1.75) {Boltzmann};
      \node[trace02] at (-0.5,0.4) {Fermi-Dirac};
      \node[trace03] at (0.75,2.25) {Bose-Einstein};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/hw15
filename: hw10-sol.tex
modified: 2015-01-19 04:46:36
domain: p24
source:
  \begin{tikzpicture}[
      scale=0.8,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      photon/.style={line width=1.5pt,color=DarkRed,decorate,decoration={snake,post length=0.1in}},
      spring/.style={decorate,decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm}},
      traj/.style={dashed, color=gray, line width=1pt}
    ]
    \draw (0,0) sin (1.57,1) cos(3.14,0) sin(4.71,-1) cos(6.28,0);
    \draw[coord,->] (0,-1.25) -- ++(90:2.5) node[anchor=east]{$F$};
    \draw[coord,->] (0,0) -- ++(0:7) node[anchor=north]{$x$};
    \draw[coord,-] (3.14,-0.15) -- ++(90:0.3)
    node[anchor=south]{$\pi/k$};
    \draw[coord,-] (6.28,-0.15) -- ++(90:0.3) node[anchor=south]{$2\pi/k$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Bose.tex
modified: 2015-11-20 22:55:19
domain: p117
source:
  \begin{tikzpicture}[scale=1.5]
    \draw[line width=2] (0,0) -- ++(0:1.5) node[anchor=west]{0};
    \draw[DarkRed,dashed,line width=1.5] (0,-0.1) node[anchor=north east]{$\mu$} -- ++(0:1.5);
    \draw (0,1) -- ++(0:1.5) node[anchor=west]{$\Delta$};
    \draw (0,2.2) -- ++(0:1.5) node[anchor=west]{$\spe_{2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/hw15
filename: hw01-sol.tex
modified: 2015-01-19 18:20:30
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[fill=blue!20] (0,0) rectangle (1,0.75) rectangle(2,0);
    \draw[very thick, ->] (2,0.375) -- (2.7,0.375) node[anchor=west]
    {$\vv_{0}$};
    \draw[fill=blue!20] (4,0) rectangle (5,0.75) rectangle (6,0)
    rectangle (7,0.75);
    \draw[dashed] (0,-0.5) -- +(0:10);
    \draw[fill=blue!20] (2,-2) rectangle (3,-1.25) rectangle(4,-2);
    \draw[very thick,->] (4,-1.625) -- +(0:0.7) node[anchor=west]
      {$\vv$};
    \draw[fill=blue!20] (6,-2) rectangle (7,-1.25) rectangle (8,-2)
    rectangle (9,-1.25);
    \draw[very thick,->] (9,-1.625) -- +(0:0.7) node[anchor=west]
      {$\vv_{0}/2$};
    \node at (3,-2.5) {$2 m \vv$};
    \node at (7.5,-2.5) {$ (3m) (\vv_{0}/2) $};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Bose.tex
modified: 2015-11-20 22:55:19
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
      xmin=0,
      xmax=1,
      ymin=0,
      ymax=1,
      enlargelimits=false,
      height=2.25in,
      width=3in,
      xlabel={$T/T_{\rm E}$},
      ylabel=\empty
      ]
      \addplot[
        trace01,
        domain=0:1,
        samples=101,
        line width=2pt,
      ]
      {1 - x^1.5};
      \addplot[
        trace02,
        domain=0:1,
        samples=101,
        line width=2pt,
      ]
      {x^1.5};
      \node[trace01,text width=1in] at (0.625,0.85) {Superfluid ($N_{0}/N$)};
      \node[trace02,text width=1.2in] at (0.3,0.3) {Normal fluid ($N_{e}/N$)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/hw15
filename: hw03-sol.tex
modified: 2017-08-26 22:35:01
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      vel/.style={->,line width=2pt,color=DarkBlue}
    ]
    \draw[line width=1.5pt] (0,-0.1) -- (10,-0.1);
    \filldraw[fill=lightgray,draw=black] (0,0) rectangle (1,0.5);
    \draw[vel] (1.2,0.25) -- node[anchor=south]{$\vv_{1}$} +(0:1);
    \filldraw[fill=lightgray,draw=black] (10,0) rectangle (9,0.5);
    \draw[vel] (8.8,0.25) -- node[anchor=south]{$\vv_{2}$} +(180:1);
    \draw[coord,<->] (0.5,0.85) -- node[fill=white]{$D =\val{1250}{m}$} +(0:9);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Solids.tex
modified: 2015-11-24 16:58:33
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin = 0,
        ymax = 1,
        xmin = 0,
        xmax = 1300,
        enlargelimits=false,
        height=2.75in,
        width=3.5in,
        xlabel={$T$ (K)},
        ylabel={$c_{p}/3R$},
      ]
      \addplot[only marks, trace01] table {
          T  Cp/3R
          222.4  0.1278
          262.4  0.1922
          283.7  0.2271
          306.4  0.2653
          331.3  0.3082
          358.5  0.3552
          413.0  0.4463
          479.2  0.5501
          520.0  0.6089
          879.7  0.8871
          1079.7  0.9034
          1258.0  0.9235
        };
      \addplot[trace02, line width=1.5,domain=0.1:1300,samples=201,opacity=0.5]
      {((0.5*1320/x/sinh(0.5*1320/x)))^2};
      % \addplot[trace03, line width=1.5,domain=1:100] {2.2e-6*x^3};
      % \node[trace02] at (50,6e-4){$\sim T$};
      % \node[trace03] at (20,0.2){$\sim T^{3}$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/hw15
filename: hw02-sol.tex
modified: 2015-01-19 03:38:39
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      vel/.style={->,line width=2pt,color=DarkBlue}
    ]
    \shadedraw[ball color=lightgray] (0,0) circle(0.5);
    \draw[vel] (0.75,0) --node[anchor=south]{$V$} +(0:1);
    \shadedraw[ball color=lightgray] (5,0) circle(0.2);
    \draw[vel] (4.6,0) -- node[anchor=south]{$\vv$} +(180:1);
    \node at (0,0.8) {$M$}; % label the hockey player
    \node at (5,0.4) {$m$}; % label the puck
    \draw[dashed] (-1,-0.75) -- +(0:6.5);
    \shadedraw[ball color=lightgray] (1,-1.5) circle(0.5);
    \draw[vel] (1.75,-1.5) --node[anchor=south]{$\vv_{f}$} +(0:1);
    \shadedraw[ball color=lightgray] (4,-1.5) circle(0.2);
    \draw[vel] (4.4,-1.5) --node[anchor=south]{$\vv'$} +(0:1);
    %  \draw (0.75,0) -- node[anchor=south]{$V$} -- +(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Solids.tex
modified: 2015-11-24 16:58:33
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{loglogaxis}[
        ymax = 1,
        enlargelimits=false,
        height=2.75in,
        width=3.5in,
        xlabel={$T$ (K)},
        ylabel={$c_{p}/3R$},
      ]
      \addplot[only marks, trace01,opacity=0.75] table {
          T  Cp/R
          1  0.000029788
          2  0.000070962
          3  0.0001
          4  0.0002
          5  0.0004
          6  0.0006
          7  0.0009
          8  0.0012
          9  0.0017
          10  0.0022
          11  0.0029
          12  0.0038
          13  0.0048
          14  0.006
          15  0.0074
          16  0.009
          17  0.011
          18  0.013
          19  0.016
          20  0.019
          25  0.039
          30  0.068
          40  0.15
          50  0.247
          55  0.296
          60  0.345
          65  0.391
          70  0.435
          80  0.515
          90  0.584
          100  0.642
          120  0.732
          140  0.797
          160  0.844
          180  0.88
          200  0.907
          240  0.946
          280  0.971
          300  0.981
        };
      \addplot[only marks, trace02] table {
          T  Cp/3R
          222.4  0.1278
          262.4  0.1922
          283.7  0.2271
          306.4  0.2653
          331.3  0.3082
          358.5  0.3552
          413.0  0.4463
          479.2  0.5501
          520.0  0.6089
          879.7  0.8871
          1079.7  0.9034
          1258.0  0.9235
        };
      \node[trace01] at (20,0.1){Cu};
      \node[trace02] at (300,0.05){diamond};
      \addplot[trace03, line width=1.5,domain=15:300,samples=201,opacity=0.5]
      {((0.5*228/x/sinh(0.5*228/x)))^2};
      \node[trace03,anchor=west] at (20,0.0003) {Einstein model};
    \end{loglogaxis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: _region_.tex
modified: 2015-08-17 04:13:58
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[color=gray, line width=3] (-0.5,2) -- (0.5,2);  % ceiling
    \draw (0,1.9) circle(0.1);
    \draw[line width=1.5] (0,1.9) --  (0,-2); % cord
    \filldraw[fill=blue!50!white] (0.4,-2) rectangle (-0.4,-4); % mass
    \node at (0.8,-3){$m$};
    \draw[accel] (2,-0.5) -- node[anchor=west]{$~~g$} ++(-90:1.5);
    \draw[dashed] (-1,-1) rectangle (1.25,-4.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Solids.tex
modified: 2015-11-24 16:58:33
domain: p117
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      decoration={coil,aspect=0.5,segment length=2mm,amplitude=2mm},
      spring/.style={line width=1.pt,color=blue,decorate},
      mass/.style={color=gray!50!white},
      coord/.style={color=DarkGreen,|->,line width=1.25},
    ]
    \foreach \x in {0,2,...,10}
      {
        \shade[ball color=gray] (\x,0) circle(0.35cm);
        \node at (\x,0.6) {$m$};
        \draw[spring] (\x,0) +(0.35,0) -- +(0:1.65) ;
        \node[color=blue] at (\x+0.9,0.45) {$\alpha$};
      }
    \draw[coord] (2,-0.75) -- node[anchor=north]{$u_{i-1}$} ++(0:1);
    \draw[coord] (4,-0.75) -- node[anchor=north]{$u_{i}$} ++(0:1);
    \draw[coord] (6,-0.75) -- node[anchor=north]{$u_{i+1}$} ++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: _region_.tex
modified: 2015-08-17 04:13:58
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[line width=1.5] (3,-2) -- (3,0) arc(0:90:1) -- (-2.4,1);
    \draw[line width=3, color=gray] (-2.5,1.5) -- (-2.5,0.5); % wall
    \draw (-2.38,1) circle(0.1);

    \filldraw[fill=gray!25!white] (2,0) circle(1) ; % pulley
    \filldraw[fill=black] (2,0) circle(0.1);
    \filldraw[fill=blue!50!white] (3.4,-2) rectangle (2.6,-4);
    \node at (3.8,-3){$m$};
    \draw[accel] (0,-2) -- node[anchor=west]{$~~g$} ++(-90:1.5);

    \draw[line width=1.25,<-] (-0.25,1) -- ++(45:1) node[anchor=south]{\textsf{here}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Solids.tex
modified: 2015-11-24 16:58:33
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin = 0,
        xmax = 1,
        ymin = 0,
        ymax = 1,
        enlargelimits=false,
        height=2.75in,
        width=3.5in,
        xlabel={$ka/\pi$},
        ylabel={$\omega/\omega_{0}$},
      ]
      \addplot+[
        only marks,
        samples=46,
        domain=0:1,
        trace02] {sin(x*90)};
    \end{axis}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: _region_.tex
modified: 2015-08-17 04:13:58
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[line width=1.5] (3,-2) -- (3,0) arc(0:90:1) -- (-2,1) arc(90:180:1)
    -- (-3,-2);
    \filldraw[fill=gray!25!white] (2,0) circle(1) (-2,0) circle(1);
    \filldraw[fill=black] (2,0) circle(0.1) (-2,0) circle(0.1);
    \filldraw[fill=blue!50!white] (3.4,-2) rectangle (2.6,-4)
    (-3.4,-2) rectangle (-2.6,-4);
    \node at (-3.8,-3){$m$};
    \node at (3.8,-3){$m$};
    \draw[accel] (0,-2) -- node[anchor=west]{$~~g$} ++(-90:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: _region_.tex
modified: 2015-08-17 04:13:58
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[color=gray, line width=3] (-1,4) -- (1,4);  % ceiling
    \draw (0,3.9) circle(0.1);
    \draw[line width=5,color=Sienna] (0,3.9) -- (0,-2); % cord
    \draw[<->] (0.75,-2) -- node[fill=white]{$L$} (0.75,4);
    \filldraw[fill=blue!50!white] (0.4,-2) rectangle (-0.4,-4); % mass
    \node at (0.8,-3){$m$};
    \draw[accel] (1.75,1.5) -- node[anchor=west]{$~~g$} ++(-90:1.5);
    \draw[coord] (-1.2,-2) -- ++(90:1.5) node[anchor=east]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Solids.tex
modified: 2015-11-24 16:58:33
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \newcommand{\freq}{60}
    \foreach \x in {0,0.5,...,12}
    \foreach \t in {0,0.25,...,4}
      {
        \pgfmathsetmacro{\y}{0.5*sin(\freq*\x-\t*90)}
        \pgfmathsetmacro{\hue}{20 + \t*15}
        \fill[color=DarkGreen!\hue!white] ( \x+\y, -1.2*\t ) circle[radius=0.1];
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: _region_.tex
modified: 2015-08-17 04:13:58
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!10!white] (0,0) circle[radius=2];
    \draw (0,0) circle[radius=0.025];
    \node at (60:1.5){$2m$};
    \foreach \ang in {90,210,330}{
        \filldraw[fill=gray] (\ang:2) circle[radius=0.25];
        \node at (\ang:2.65) {$m$};
      }
    \draw[->, line width=1.5] (140:2.75) arc(140:180:2.75) node[anchor=north
        east]{$\omega$};
    \draw[vel] (2.25,0) --++(0:1.5) node[anchor=west]{$v_{0}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Solids.tex
modified: 2015-11-24 16:58:33
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=24,
        ymin=-8,
        ymax=0,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        xlabel={$x$},
        ylabel=\empty,
        % ytick={0,1},
        xtick={0,4, 8, 12, 16, 20, 24},
        yticklabel=\empty,
        xticklabels={0,$4a$,$8a$,$12a$,$16a$,$20a$, $24a$},
      ]
      \foreach \n [count=\i] in {1,2,3,4,6,8,12} {
          \pgfmathsetmacro{\k}{360.0*\n/24}
          \addplot[trace03,domain=0:24, samples=101] {0.3*cos(x*\k)-\i};
          \addplot[trace03,mark=*,only marks, domain=0:24, samples=25] {0.3*cos(x*\k)-\i};
        }
    \end{axis}
    \foreach \n [count=\i] in {1,2,3,4,6,8,12} {
        \pgfmathsetmacro{\y}{(8.2-\i)*0.6}
        \node[anchor=west] at (2.95in,\y) {$n=\n$};
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: _region_.tex
modified: 2015-08-17 04:13:58
domain: p24
source:
  \begin{tikzpicture}[scale=1.25]
    \draw[dashed] (-1.5,0) --(1.5,0);
    \draw[dashed] (0,0) -- node[anchor=south east]{$4v_{0}$} (60:3);
    \draw (0:0.75) arc(0:60:0.75);
    \node at (30:1.1){$\dg{60}$};

    \draw[->] (60:3) -- ++(60:1.5);
    \filldraw[fill=gray] (60:3) circle[radius=0.05];

    \begin{scope}[shift={(2,0)},coord]
      \draw[->] (0,0) -- (1,0) node[anchor=north]{$\ux$};
      \draw[->] (0,0) -- (0,1) node[anchor=east]{$\uy$};
    \end{scope}
    \draw[dashed] (0,0) -- (-35:2.5);
    \filldraw[fill=gray!10!white] (-35:2.5) circle[radius=0.3];
    \begin{scope}[rotate=-35, shift=(0:2.5)]
      \foreach \ang in  {210,330}{
          \filldraw[fill=gray](\ang:0.3) circle[radius=0.05];
        }
    \end{scope}
    \draw[->] (-35:2.5) -- ++(-35:1);
    \draw[dashed,->] (-35:2.5) --node[anchor=south]{$~~v_{x}$} ++(0:.8);
    \draw[dashed,->] (2.87,-1.45) --node[anchor=west]{$v_{y}$} ++(-90:0.5);


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Solids.tex
modified: 2015-11-24 16:58:33
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=1.5,
        ymin=0,
        ymax=1.5,
        enlargelimits=false,
        area style,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25},
        height=2.75in,
        width=3.5in,
        xlabel={$\omega$},
        ylabel={$\dos(\omega)$},
        ytick={},
        xtick={0,1,1.25},
        % xticklabel=\empty,
        xticklabels={0,$\omega_{\rm D}$,$\omega_{\rm E}$}
      ]
      \addplot[
        trace01,
        fill=DarkRed!40!white,
        domain=0:1,
        samples=51,
        line width=2pt]
      {x^2} \closedcycle;
      \addplot[trace02,domain=1.24:1.26,samples=51,fill=DarkBlue!40!white]
      {1.5*exp(-10000*(x-1.25)^2)} \closedcycle;
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: _region_.tex
modified: 2015-08-17 04:13:58
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!10!white] (0,0) circle[radius=2];
    \draw (0,0) circle[radius=0.025];
    \node at (60:1.5){$2m$};
    \foreach \ang in {210,330}{
        \filldraw[fill=gray] (\ang:2) circle[radius=0.25];
        \node at (\ang:2.65) {$m$};
      }
    \draw[dashed] (0,0) --node[anchor=south east]{$R$} (210:2) (0,0) -- (330:2) ;
    \draw[dashed] (-2.5,-1) -- (2.5,-1);
    \draw (210:0.4) arc(210:330:0.4);
    \node at (-90:0.6){$\dg{120}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Solids.tex
modified: 2015-11-24 16:58:33
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{loglogaxis}[
        ymax = 1,
        enlargelimits=false,
        height=2.75in,
        width=3.5in,
        xlabel={$T$ (K)},
        ylabel={$c_{p}/3R$},
      ]
      \addplot[only marks, trace01,opacity=0.75] table {
          T  Cp/R
          0.0966  2.61984E-06
          0.0973  2.6625E-06
          0.102  2.82449E-06
          0.1065  2.97478E-06
          0.1074  3.00465E-06
          0.1166  3.31481E-06
          0.1276  3.64522E-06
          0.1451  4.10984E-06
          0.1586  4.50231E-06
          0.1735  4.9072E-06
          0.1911  5.40509E-06
          0.2118  5.99319E-06
          0.2368  6.71598E-06
          0.2661  7.52936E-06
          1  0.000029788
          2  0.000070962
          3  0.0001
          4  0.0002
          5  0.0004
          6  0.0006
          7  0.0009
          8  0.0012
          9  0.0017
          10  0.0022
          11  0.0029
          12  0.0038
          13  0.0048
          14  0.006
          15  0.0074
          16  0.009
          17  0.011
          18  0.013
          19  0.016
          20  0.019
          25  0.039
          30  0.068
          40  0.15
          50  0.247
          55  0.296
          60  0.345
          65  0.391
          70  0.435
          80  0.515
          90  0.584
          100  0.642
          120  0.732
          140  0.797
          160  0.844
          180  0.88
          200  0.907
          240  0.946
          280  0.971
          300  0.981
        };
      \addplot[trace02, line width=1.5,domain=0.1:100] {2.83e-5*x};
      \addplot[trace03, line width=1.5,domain=1:100] {2.2e-6*x^3};
      \node[trace02] at (50,6e-4){$\sim T$};
      \node[trace03] at (20,0.2){$\sim T^{3}$};
    \end{loglogaxis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-quiz1-2015-key.tex
modified: 2015-02-09 08:10:40
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!30!white] (0,0) rectangle (1,1);
    \draw[force] (0,0.5) --++(180:1) node[anchor=south]{$T$};
    \draw[force] (0.5,0.5) --++(-90:1.5) node[anchor=west]{$m_{1} g$};
    \draw[force] (0.6,0) --++(90:1.5) node[anchor=west]{$N_{1}$};
    \draw[accel] (-1.5,1) -- ++(180:1) node[anchor=south]{$a$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: throttling.tex
modified: 2015-11-03 17:02:29
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
      ymin=-1,
      ymax=0.25,
      xmin=0.8,
      xmax=2.5,
      enlargelimits=false,
      height=2.5in,
      width=3.5in,
      ylabel={$\phi(r)$},
      xlabel={$r/r_{0}$},
      ytick={0,1},
      xtick={1,1.5,...,2.5},
      %xticklabels={$r_{0}$,,$1.5 r_{0}$,,$2 r_{0}$}
      ]
      \addplot[
        trace01,
        domain=0.85:2.5,
        samples=201,
        line width=2pt,
      ]
      {1/(x^12)-2/(x^6)};
      \draw[<-] (0.9,-.2) -- (1,-0.1) node[anchor=south west]{$a$};
      \draw[<-] (1.15,-.7) -- (1.35,-0.55) node[anchor=west]{$b$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-quiz1-2015-key.tex
modified: 2015-02-09 08:10:40
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!30!white] (0,0) rectangle (1,1);
    \draw[force] (0.5,1) --++(90:1) node[anchor=west]{$T$};
    \draw[force] (0.5,0.5) --++(-90:1) node[anchor=west]{$m_{2} g$};
    \draw[accel] (-1.5,0.5) -- ++(-90:1) node[anchor=east]{$a$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: throttling.tex
modified: 2015-11-03 17:02:29
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray] (0,1) rectangle (12,1.2);
    \filldraw[fill=gray] (0,-1) rectangle (12,-1.2);
    \fill[left color=blue!40!white, right color=blue!10!white] (5,-1) rectangle (6,1);
    \draw[pattern=crosshatch dots] (5,-1) rectangle (6,1);

    \fill[fill=blue!40!white] (0,-1) rectangle (5,1);
    \fill[fill=blue!10!white] (6,-1) rectangle (12,1);

    \node at (0.5,0){$p_{1}$};
    \node at (11.5,0){$p_{2}$};

    \draw[dashed,line width=1.5,color=DarkRed] (4,-1) rectangle node {$V_{1}$} (5,1);
    %    \draw[dashed] (6,-1) rectangle node {$V_{2}$} (9,1);

    \draw[->,line width=2,DarkBlue] (2,0) -- ++(0:0.5);
    \draw[->,line width=2,DarkBlue!60!white] (9.5,0) -- ++(0:1);

    \begin{scope}[shift={(0,-3)}]
      \filldraw[fill=gray] (0,1) rectangle (12,1.2);
      \filldraw[fill=gray] (0,-1) rectangle (12,-1.2);
      \fill[left color=blue!40!white, right color=blue!10!white] (5,-1) rectangle (6,1);
      \draw[pattern=crosshatch dots] (5,-1) rectangle (6,1);

      \fill[fill=blue!40!white] (0,-1) rectangle (5,1);
      \fill[fill=blue!10!white] (6,-1) rectangle (12,1);

      \node at (0.5,0){$p_{1}$};
      \node at (11.5,0){$p_{2}$};

      %   \draw[dashed] (4,-1) rectangle node {$V_{1}$} (5,1);
      \draw[dashed,line width=1.5,color=DarkRed] (6,-1) rectangle node {$V_{2}$} (9,1);

      \draw[->,line width=2,DarkBlue] (2,0) -- ++(0:0.5);
      \draw[->,line width=2,DarkBlue!60!white] (9.5,0) -- ++(0:1);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-quiz1-2015-key.tex
modified: 2015-02-09 08:10:40
domain: p24
source:
  \begin{tikzpicture}[scale=1.25]
    \draw[color=gray] (-3,-2) rectangle (3,2);
    \filldraw (0,0) circle (0.05);
    \draw (-1.5,-0.5) -- (1.5,-0.5);
    \draw[dotted,color=gray] (0,0) -- (0,-1.5);
    \filldraw[fill=gray!70!white] (1.4,-0.6) rectangle (1.6,-0.4)
    node[anchor=west] {$m_{2}$};
    \filldraw[fill=gray!70!white] (-1.4,-0.6) rectangle (-1.6,-0.4)
    node[anchor=east] {~$m_{1}$};
    \draw[vel] (-1.5,-0.2) -- ++(90:1) node[anchor=east]{$v$};
    \draw[vel] (1.5,-0.2) -- ++(90:1) node[anchor=west]{$v$};
    \draw[<->] (-1.5,-1) -- node[fill=white]{$\frac{\ell}{2}$} (0,-1);
    \draw[<->] (1.5,-1) -- node[fill=white]{$\frac{\ell}{2}$} (0,-1);
    \node at (2.25,-1.6) {\small \textsf{top view}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-quiz1-2015-key.tex
modified: 2015-02-09 08:10:40
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!30!white] (0,0) rectangle (1,1) ;
    \draw[force] (1,0.5) -- ++(0:1.5) node[anchor=south]{$T_{1}$};
    \node at (-0.5,0.75){$m_{1}$};
    \draw[accel] (1,1.5) --++(0:1) node[anchor=south]{$a$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: throttling.tex
modified: 2015-11-03 17:02:29
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=15,
        ymin=0,
        ymax=8,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        xlabel={$p$},
        ylabel={$T$},
        %ytick={0,1},
        xtick={0,3,...,15},
        %xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
      ]
      \addplot[
        trace02,
        domain=0:9,
        samples=201,
        line width=2pt,
      ]
      {15/4 - x/12 + sqrt(9-x)};
      \addplot[
        trace02,
        domain=0:9,
        samples=201,
        line width=2pt,
      ]
      {15/4 - x/12 - sqrt(9-x)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Radiation.tex
modified: 2015-12-16 06:58:33
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=10,
        ymin=0,
        ymax=1.5,
        enlargelimits=false,
        width=3in,
        height=2.25in,
        xlabel={$\hb\omega/\kT$},
        ylabel={spectral density},
        %      ytick={0,1},
        %      xtick={0,0.5,1,1.5,2},
        %      xticklabel=\empty,
        % xticklabels{0,,$a$,,$a$},
      ]
      \addplot[
        trace01,
        domain=0.001:10,
        samples=201,
        line width=2pt,
      ]
      {x^3/(exp(x)-1)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Radiation.tex
modified: 2015-12-16 06:58:33
domain: p117
source:
  \begin{tikzpicture}[scale=2]
    \filldraw[line width=4pt,fill=gray!50!white] (0,-1) rectangle (2,1);
    \node at (0.2,0.8){\Large\textit{T}};
    \foreach \x in {70,68,...,0} {
        \pgfmathsetmacro{\myval}{0.58+0.006*\x}
        \definecolor{tempcolor}{gray}{\myval};
        \draw[line width=2.5pt,color=tempcolor] (1.98,0) -- ++(\x:1);
        \draw[line width=2.5pt,color=tempcolor] (1.98,0) -- ++(-\x:1);
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-quiz2-2015-key.tex
modified: 2015-03-06 21:45:31
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      tightspring/.style={decorate,decoration={coil,aspect=0.3,segment length=1mm,amplitude=2mm}}
    ]
    % Now the rebounding ball
    \begin{scope}[shift={(0,3.5)}]
      \draw[line width=2pt,color=gray!25!white] (0,0) -- (-150:3);
      \filldraw[fill=red!10!white,draw=gray,dashed] (-150:3) circle[radius=0.4];
      \draw[dashed] (-100:3) arc(-100:-200:3);
      \draw[->] (-90:0.75) arc(-90:-150:0.75);
      \node at (-120:1){$\theta$};
    \end{scope}


    % draw the floor and ramp
    \draw[brown!70!black, line width=2pt] (-3,0) -- (3,0) ..
    controls (5,0) and (7,1.5) .. (9,1.5) -- (13,1.5);
    \draw[dashed] (4,0) -- (13,0);

    % the two masses and the compressed spring
    \draw[line width=2pt,color=gray] (0,0.5) -- node[anchor=west]{$L$} (0,3.5);
    \draw[<-] (0.1,2.5) -- ++(45:1) node[anchor=west]{\textsf{light rod}};
    \fill (0,3.5) circle[radius=0.075];
    \node at (0.3,3.5){$P$};

    \begin{scope}[shift={(0.4,0.4)}]
      \draw[tightspring] (0,0) -- (0.65,0);
      \draw[color=brown,line width=1pt](0,0) -- (1,0);
      \node at (0.3,0.5){$k$};
    \end{scope}

    \shade[ball color=red] (0,0.5) circle[radius=0.4];
    \node at (-0.6,0.25){$ m_{1} $};
    \node at (2.1,0.25){$m_{2}$};
    \filldraw[fill=blue!60!black, rounded corners=4pt] (1,0) rectangle (1.8,0.8);


    \draw[coord,<->] (13,0) -- (13,1.5);
    \node at (13.4,0.75) {$\displaystyle\frac{L}{2}$};

    \draw[line width=4pt,color=gray] (10,1.5) -- (13,1.5);
    \draw[coord] (10,2) -- node[anchor=south]{$x$} ++(0:1.5);
    \draw[<-] (11.5,1.6) -- ++(45:1) node[anchor=west]{$\mu_{k}$};
    \draw[<-] (6,0.9) -- ++(45:1) node[anchor=south]{\textsf{no friction}};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Radiation.tex
modified: 2015-12-16 06:58:33
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[rotate=90]
      \draw[line width=2pt] (0,0.5) -- (0,2) (0,-0.5) -- (0,-2) ;
      % draw the slant cylinder
      \filldraw[color=gray,fill=yellow!60!white,dashed] (0,0.5) -- ++(150:2.5) -- ++(-90:1)
      -- ++(-30:2.5) -- cycle;
      \draw[dashed] (-2,0) -- (2,0);
      \draw[gray] (150:2.5) -- ++(-30:5);
      \draw (0:1) arc (0:-30:1);
      \node at (-15:1.25){$\theta$};
      \draw[<->,DarkGreen] (0,0.75) -- node[anchor=south,rotate=60]{$c\dop{t}$}
      ++(150:2.5);
      \draw[<-,DarkGreen] (0,0.2) -- ++(30:0.75) node[anchor=south]{$\Dop{A}$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-quiz2-2015-key.tex
modified: 2015-03-06 21:45:31
domain: p24
source:
  \begin{tikzpicture}[
      scale=0.6,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      tightspring/.style={decorate,decoration={coil,aspect=0.3,segment length=1mm,amplitude=2mm}}
    ]
    % Now the rebounding ball
    \begin{scope}[shift={(0,3.5)}]
      \draw[line width=2pt,color=gray!25!white] (0,0) -- (-150:3);
      \filldraw[fill=red!10!white,draw=gray,dashed] (-150:3) circle[radius=0.4];
      \draw[dashed] (-100:3) arc(-100:-200:3);
      \draw[->] (-90:0.75) arc(-90:-150:0.75);
      \node at (-120:1.25){$\theta$};
    \end{scope}


    % draw the floor and ramp
    \draw[brown!70!black, line width=2pt] (-3,0) -- (3,0) ..
    controls (5,0) and (7,1.5) .. (9,1.5) -- (13,1.5);
    \draw[dashed] (4,0) -- (13,0);

    % the two masses and the compressed spring
    \draw[line width=2pt,color=gray] (0,0.5) -- node[anchor=west]{$L$} (0,3.5);
    \draw[<-] (0.1,2.5) -- ++(45:1) node[anchor=west]{\textsf{light rod}};
    \fill (0,3.5) circle[radius=0.075];
    \node at (0.3,3.5){$P$};

    \begin{scope}[shift={(0.4,0.4)}]
      \draw[tightspring] (0,0) -- (0.65,0);
      \draw[color=brown,line width=1pt](0,0) -- (1,0);
      %    \node at (0.3,0.5){$k$};
    \end{scope}

    \shade[ball color=red] (0,0.5) circle[radius=0.4];
    %\node at (-0.6,0.25){$ m_{1} $};
    %  \node at (2.1,0.25){$m_{2}$};
    \filldraw[fill=blue!60!black, rounded corners=4pt] (1,0) rectangle (1.8,0.8);


    \draw[coord,<->] (13,0) -- (13,1.5);
    \node at (13.4,0.75) {$\displaystyle\frac{L}{2}$};

    \draw[line width=4pt,color=gray] (10,1.5) -- (13,1.5);
    \draw[coord] (10,2) -- node[anchor=south]{$x$} ++(0:1.5);
    \draw[<-] (11.5,1.6) -- ++(45:1) node[anchor=west]{$\mu_{k}$};
    \draw[<-] (6,0.9) -- ++(45:1) node[anchor=south]{\textsf{no friction}};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Radiation.tex
modified: 2015-12-16 06:58:33
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[color=gray!40,fill=gray!50] (0,0) rectangle (3,0.5);
    \draw[->,color=Yellow!75!black,line width=3] (1,1.5) -- ++(-90:3)
    node[anchor=east,Yellow!50!black]{$P_{\rm in}$};
    \draw[->,color=DarkRed,line width=1.5] (1.5,-1.5)
    node[anchor=north west]{$P_{\rm from\ E}$} -- ++(90:1.75);
    \draw[->,color=DarkRed!50!black, line width=1.5] (2,0.5) -- ++(90:.75)
    node[anchor=west]{$P_{\text{to space}}$};
    \draw[->,color=DarkRed!50!black, line width=1.5] (2,0) -- ++(-90:0.75)
    node[anchor=west]{$P_{\text{to E}}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-mt1-2015-key.tex
modified: 2015-02-27 21:40:04
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=blue!50!white] (0.4,-1) rectangle (-0.4,1); % mass
    \draw[force] (0,0) -- ++(-90:2) node[anchor=east]{$mg$};
    \draw[line width=2.5] (0,1) -- ++(90:1);
    \draw[force,color=blue!30!white] (0,2) -- ++(90:2) node[anchor=east]{$T$};
    \draw[accel] (1,0) -- ++(90:1) node[anchor=west]{$a$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Thermocouple.tex
modified: 2015-11-10 04:27:21
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        enlargelimits=false,
        xmax=1500,
        ymax=60,
        width=3.5in,
        height = 2.5in,
        xlabel={$T$ ($^{\circ}\mathrm{C}$},
        ylabel={$V$ (mV)},
      ]
      \addplot[trace01] table {TypeK.dat};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-mt1-2015-key.tex
modified: 2015-02-27 21:40:04
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!50!white] (0,0) rectangle (1,1);
    \draw[force] (0.55,0.5) -- ++(-90:1.5) node[anchor=east]{$mg$};
    \draw[force] (0.45,0) -- ++(90:1.5) node[anchor=east]{$N$};
    \draw[force] (0,0) -- ++(0:2) node[anchor=south]{$F_{s}$};
    \draw[accel] (2.5,0.5) --++(0:1.5) node[anchor=south]{$a$};
    \node at (-1.5,0.5){\textsf{side view}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Thermocouple.tex
modified: 2015-11-10 04:27:21
domain: p117
source:
  \begin{tikzpicture}[scale=1,fat/.style={line width=1.5}]
    \draw[->] (0,0,0) -- (2.5,0,0) node[anchor=north]{$k_{y}$};
    \draw[->] (0,0,0) -- (0,2.5,0) node[anchor=east]{$k_{z}$};
    \draw[->] (0,0,0) -- (0,0,4.5) node[anchor=east]{$k_{x}$};

    \shadedraw[ball color=gray,opacity=0.5] (0,0) circle[radius=2];
    \draw[fat, ->] (0,0) -- (1.4,1.4) node[anchor=south west]{$k\fermi$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-mt1-2015-key.tex
modified: 2015-02-27 21:40:04
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!50!white] (0,-0.25) rectangle (-0.5,0.25);
    \node at (-0.25, 0.5){$m$};
    \draw[vel] (-0.75,0) --node[anchor=south]{$u-v$} ++(180:1.5);
    \filldraw[fill=blue!50!white] (0.5,-0.5) rectangle (2.5,0.5);
    \node at (1.5,0.75){$M-m$};
    \draw[vel] (2.75,0) -- ++ (0:0.5) node[anchor=south]{$v$};
    \draw[coord,->] (0,1.5) -- node[anchor=south]{$\ux$}++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Thermocouple.tex
modified: 2015-11-10 04:27:21
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\tmp{8}
    \begin{axis}[
        xmin=0,
        xmax=2.2,
        ymin=0,
        ymax=1.2,
        enlargelimits=false,
        width=2.5in,
        xlabel={$\spe$},
        ylabel={$\nfd \; \dos(\spe)$},
        ytick=\empty,
        xtick=\empty,
        xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25},
        axis on top=true,
        x label style={xshift=0.75in},
      ]
      \fill[fill=blue!20!white] (0,0) rectangle (1,1);
      \addplot[color=black,domain=0:2,samples=101,line width=0pt,fill=white]
      {1/(1+exp(\tmp*(x-1)))} \closedcycle;
      \addplot[color=black,domain=1:2,samples=101,line width=0pt,fill=red!20!white]
      {1/(1+exp(\tmp*(x-1)))} \closedcycle;

      \draw[dashed, color=DarkSlateGray] (0,0.5) -- (2,0.5);
      \draw[dashed, color=DarkSlateGray] (1,0) -- (1,1);
      \draw[<-,color=DarkSlateGray] (0.9,0.9) -- (1.2,0.9)
      node[anchor=west]{removed};
      \draw[<-,color=DarkSlateGray] (1.1,0.1) -- (0.8,0.1) node[anchor=east]{added};
    \end{axis}
    \node at (2.25,-0.25){$\efermi$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-mt1-2015-key.tex
modified: 2015-02-27 21:40:04
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=green!70!black] (0,0) circle[radius=0.5];
    \draw[force] (0,0) -- ++(180:2) node[anchor=south]{$kv^{1/2}$};
    \draw[coord] (0,1) -- ++(0:1.5) node[anchor=south]{$x$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Thermocouple.tex
modified: 2015-11-10 04:27:21
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\tmp{4}
    \begin{axis}[
        xmin=0,
        xmax=2.2,
        ymin=0,
        ymax=1.2,
        enlargelimits=false,
        width=2.5in,
        xlabel={$\spe$},
        ylabel=\empty,
        ytick=\empty,
        xtick=\empty,
        xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25},
        axis on top=true,
        x label style={xshift=0.75in},
      ]
      \fill[fill=blue!20!white] (0,0) -- (0,0.5) -- (1,1) -- (1,0) -- cycle;
      \addplot[color=black,domain=0:2,samples=101,line width=0pt,fill=white]
      {(1+0.5*(x-1))/(1+exp(\tmp*(x-1)))} \closedcycle;
      \addplot[color=black,domain=1:2,samples=101,line width=0pt,fill=red!20!white]
      {(1+0.5*(x-1))/(1+exp(\tmp*(x-1)))} \closedcycle;
      \addplot[dashed,domain=0:2,samples=101]
      {1/(1+exp(\tmp*(x-1)))};

      \draw[dashed, color=DarkSlateGray] (0,0.5) -- (2,0.5);
      \draw[dashed, color=DarkSlateGray] (1,0) -- (1,1);
      % \addplot[domain=0:1,samples=101,line width=1pt]
      % {sqrt(x)};
      % \addplot[domain=0:1.1,samples=151,line width=1.5pt,trace02,fill=blue!30!white]
      % {sqrt(x)/(1+exp(16*(x-0.75)))} \closedcycle;
      % \node at (0.95,0.9) {$\dos$};
      % \draw (0.75,0) -- (0.75,0.5);
    \end{axis}
    \node at (2.45,-0.25){$\efermi$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-mt2-p3-2015.tex
modified: 2015-04-04 18:15:07
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=4,color=gray] (-1.5,-1.08) -- ++(0:3);
    \draw[line width=2] (0,0) circle[radius=0.3];
    \draw[line width=2] (0,0) circle[radius=1];
    \draw[line width=2,->] (180:0.3) -- ++(90:1.6);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-mt2-p3-2015.tex
modified: 2015-04-04 18:15:07
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=4,color=gray] (-1.5,-1.08) -- ++(0:3);
    \draw[line width=2] (0,0) circle[radius=0.3];
    \draw[line width=2] (0,0) circle[radius=1];
    \draw[line width=2,->] (180:0.3) -- ++(90:1.6);
    \draw[dashed, line width=1.5] (0,-1) -- ++(110:2.75);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Thermocouple.tex
modified: 2015-11-10 04:27:21
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=1.2,
        ymin=0,
        ymax=1,
        enlargelimits=false,
        width=3in,
        xlabel={$\spe$},
        ylabel={$\dos(\spe) \nfd(\spe)$},
        ytick=\empty,
        xtick=\empty,
        xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1},
        axis on top=true,
        x label style={xshift=0.75in},
      ]
      % the part showing electrons removed
      \addplot[color=black,domain=0:0.75,samples=101,line width=0pt,fill=blue!25!white ]
      {sqrt(x)} \closedcycle;
      % the density of states curve
      \addplot[domain=0:1,samples=101,line width=1pt] {sqrt(x)};
      % the states that don't change
      \addplot[domain=0:1.1,samples=151,line width=0pt,trace02,fill=gray!30!white]
      {sqrt(x)/(1+exp(16*(x-0.75)))} \closedcycle;
      % the newly filled states
      \addplot[domain=0.75:1.1,samples=51,line width=0pt,trace02,fill=red!30!white]
      {sqrt(x)/(1+exp(16*(x-0.75)))} \closedcycle;
      % the states that don't change
      \addplot[domain=0:1.1,samples=151,line width=1.5pt,trace02]
      {sqrt(x)/(1+exp(16*(x-0.75)))} \closedcycle;

      \node at (1,0.9) {$\dos(\spe)$};
      \node at (0.675,0.75){$A$};
      \node at (0.825,0.075){$B$};

    \end{axis}
    \node at (3.78,-0.28){$\efermi$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-mt2-p3-2015.tex
modified: 2015-04-04 18:15:07
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=4,color=gray] (-1.5,-1.08) -- ++(0:3);
    \draw[line width=2] (0,0) circle[radius=0.3];
    \draw[line width=2] (0,0) circle[radius=1];
    \draw[line width=2,->] (90:0.3) -- ++(0:1.6);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Thermocouple.tex
modified: 2015-11-10 04:27:21
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\newmu{0.725}
    \begin{axis}[
        xmin=0,
        xmax=1.2,
        ymin=0,
        ymax=1,
        enlargelimits=false,
        width=3in,
        xlabel={$\spe$},
        ylabel={$\dos(\spe) \nfd(\spe)$},
        ytick=\empty,
        xtick=\empty,
        xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1},
        axis on top=true,
        x label style={xshift=0.75in},
      ]
      % the part showing electrons removed, shaded blue and labeled A
      \addplot[color=black,domain=0:0.75,samples=101,line width=0pt,fill=blue!25!white ]
      {sqrt(x)} \closedcycle;

      % the density of states curve
      \addplot[domain=0:1,samples=101,line width=1pt] {sqrt(x)};

      % the old boundary, dashed gray
      \addplot[domain=0:1.1,samples=151,line width=1pt,dashed,gray]
      {sqrt(x)/(1+exp(16*(x-0.75)))} \closedcycle;

      % the states that don't change, shaded gray, now shifted to the new \mu
      \addplot[domain=0:1.1,samples=151,line width=1.5pt,trace02,fill=gray!30!white]
      {sqrt(x)/(1+exp(16*(x-\newmu)))} \closedcycle;

      % the newly filled states, shaded red, labeled B, cut back with the new \mu
      \addplot[domain=0.75:1.1,samples=51,line width=0pt,trace02,fill=red!30!white]
      {sqrt(x)/(1+exp(16*(x-\newmu)))} \closedcycle;


      \node at (1,0.9) {$\dos(\spe)$};
      \node at (0.675,0.75){$A$};
      \node at (0.825,0.075){$B$};
      \draw[<-,DarkRed,line width=1.5] (\newmu,0) -- (\newmu,0.3);
    \end{axis}
    \node[color=DarkRed] at (3.65,-0.28){$\mu$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15
filename: p24-mt2-p3-2015.tex
modified: 2015-04-04 18:15:07
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=4,color=gray] (-1.5,-1.08) -- ++(0:3);
    \draw[line width=2] (0,0) circle[radius=0.3];
    \draw[line width=2] (0,0) circle[radius=1];
    \draw[line width=2,->] (90:0.3) -- ++(0:1.6) node[anchor=south]{$T$};
    \draw[line width=2, ->] (-90:1) -- ++(180:1.2) node[anchor=south]{$F$};
    \draw[coord] (2,0) -- ++(0:1) node[anchor=north]{$x$};
    \draw[coord] (60:2.5) arc(60:30:2.5) node[anchor=south west]{+};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Thermocouple.tex
modified: 2015-11-10 04:27:21
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
      xmin=-8,
      xmax=8,
      ymin=0,
      ymax=0.26,
      enlargelimits=false,
      width=3in,
      height=2.25in,
      xlabel={$x=\beta(\spe-\mu)$},
      ylabel={$e^{x} / (1+e^{x})^{2}$},
      ]
      \addplot[
        trace01,
        domain=-10:10,
        samples=201,
        line width=2pt,
      ]
      {exp(x) / (1+ exp(x))^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15/drafts
filename: p24-mt1-2015-v2.tex
modified: 2015-02-13 01:53:16
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[color=gray, line width=3] (-0.5,2) -- (0.5,2);  % ceiling
    \draw (0,1.9) circle(0.1);
    \draw[line width=1.5] (0,1.9) -- (0,1.1) (0,0.9) -- (0,-2); % cord
    \draw (0,1.1) -- +(15:0.3) -- +(195:0.3);
    \draw (0,0.9) -- +(15:0.3) -- +(195:0.3);
    \node[text width=0.9in,font=\scriptsize] at (2.3,1) {\textsf{part of the cord
        omitted to keep diagram small}};
    \filldraw[fill=blue!50!white] (0.4,-2) rectangle (-0.4,-4); % mass
    \node at (0.8,-3){$m$};
    \draw[accel] (2,-0.5) -- node[anchor=west]{$~~g$} ++(-90:1.5);
    \draw[dashed] (-1,-1) rectangle (1.25,-4.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.25,
      coord/.style={color=green!40!black,|->},
    ]
    \shade[ball color=blue!50!white, opacity=0.3] (0,0) circle[radius=3];
    % cartesian system
    \draw[coord,->] (0,0) -- (4,0) node[anchor=west]{$y$};
    \draw[coord,->] (0,0,0) -- (0,0,6) node[anchor=north east]{$x$};
    \draw[coord,->] (0,0) -- (0,4) node[anchor=south]{$z$};
    % cover up the z axis underneath an upcoming label
    \draw[gray!35!white] (0,1.7) -- ++(90:0.25);
    % coordinate of the point
    \coordinate (A) at (1.5,2.121, 1.5);
    \draw[line width=1, ->,color=DarkRed] (0,0,0) -- node[anchor=north west]{$r$}  (A);
    % projection to the xy plane
    \draw[dashed,color=DarkBlue] (A) -- (1.5, 0, 1.5) -- (0,0);
    % circle of latitude
    \draw[dashed] (2.2,2) arc[x radius=2.2, y radius=0.5, start angle=0, end
        angle=-180];
    \draw[dashed,opacity=0.2] (2.2,2) arc[x radius=2.2, y radius=0.5, start
        angle=0, end angle=180];
    % circle of longitude
    \draw[dashed,color=black] (0,-3) arc[x radius=1.075, y radius=3, start angle=-90,
        end angle=90];
    \draw[dashed,color=gray, opacity=0.2] (0,-3) arc[x radius=1.1, y radius=3,
        start angle=-90, end angle=-270];
    % definition of phi
    \draw[->] (0,0,0.5) arc[start angle=-135, end angle=-45,
        x radius=0.35, y radius =0.25];
    \node at (0,-0.4){$\phi$};
    % theta definition
    \draw[->] (0,0.6) arc[start angle=90, end angle=50,
        y radius=0.6, x radius = 0.4];
    \node at (0.2, 0.75) {$\theta$};
    % circle of longitude at \phi + d\phi
    \draw[dashed,color=black] (0,-3) arc[x radius=1.4, y radius=3, start angle=-90,
        end angle=90];
    \draw[dashed,color=gray, opacity=0.2] (0,-3) arc[x radius=1.4, y radius=3,
        start angle=-90, end angle=-270];
    % circle of latitude at \theta + d\theta
    \draw[dashed] (2.35,1.8) arc[x radius=2.35, y radius=0.5, start angle=0, end
        angle=-180];
    \draw[dashed,opacity=0.2] (2.35,1.8) arc[x radius=2.35, y radius=0.5, start
        angle=0, end angle=180];
    % label the arcs
    \draw[<-] (1.08,1.6) -- ++(135:0.3) node[anchor=east] {$r \sin\theta
        \dd{\phi}$};
    \draw[<-] (1.28,1.45) -- ++(-30:0.3) node[anchor=west] {$r \dd{\theta}$};
    % draw dA
    \fill[fill=black,opacity=0.2] (A) -- ++(6:0.27) -- ++(-75:0.2) -- ++(186:0.28)
    -- cycle;
    % label dA
    \draw[<-] (1.08,1.48) -- ++(-50:1) node[anchor=west]{$\dd{A} = r^{2} \sin\theta
        \dd{\phi} \dd{\theta}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Thermocouple.tex
modified: 2015-11-10 04:27:21
domain: p117
source:
  \begin{tikzpicture}[scale=1]

    \draw[->] (0,-0.5) -- (0,2.5) node[anchor=east]{$y$};
    \draw[->] (6,0) --node[anchor=north]{$x$} (7,0) ;
    \begin{scope}[color=DarkSlateGray]
      \draw[->] (2.5,0) -- (3,0);
      \draw[->] (6,0.2) -- (6,0.6);
      \draw[->] (3,1) -- +(180:0.5);
      \draw[->] (-3,1) -- +(180:0.5);
      \draw[->] (-6,0.8) -- +(-90:0.4);
      \draw[->] (-3,0) -- +(0:0.4);
      \draw (0.1,0.4) -- (-0.1,0.6);
      \draw (-0.1,0.4) -- (0.1,0.6);
      \draw (-6,0) -- (6,0) -- (6,1) -- (-6,1) -- (-6,0);
    \end{scope}
    \node at (-0.5,1.2) {$2\pi i$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15/drafts
filename: p24-mt1-2015-v2.tex
modified: 2015-02-13 01:53:16
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[line width=1.5] (3,-2) -- (3,0) arc(0:90:1) -- (-1.5,1)
    (-1.7,1) -- (-2.4,1);
    \draw[line width=3, color=gray] (-2.5,1.5) -- (-2.5,0.5); % wall
    \draw (-2.38,1) circle(0.1);
    \draw (-1.5,1) -- +(75:0.3) -- +(255:0.3);
    \draw (-1.7,1) -- +(75:0.3) -- +(255:0.3); % cut

    \filldraw[fill=gray!25!white] (2,0) circle(1) ; % pulley
    \filldraw[fill=black] (2,0) circle(0.1);
    \filldraw[fill=blue!50!white] (3.4,-2) rectangle (2.6,-4);
    \node at (3.8,-3){$m$};
    \draw[accel] (0,-2) -- node[anchor=west]{$~~g$} ++(-90:1.5);

    \draw[line width=1.25,<-] (-0.25,1) -- ++(45:1) node[anchor=south]{\textsf{here}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{0.25}
    \draw[spring] (-3,\rad) -- (-1.5,\rad);
    \draw[spring] (1.5,\rad) -- (3,\rad);
    \draw[line width=1.25,color=SlateGray] (-3,-\rad) -- ++(0:6);
    \foreach \x in {-1, 1} {
        \filldraw[fill = gray] (\x,0) circle[radius=\rad];
      }
    \filldraw[fill=SlateBlue!25] (-1.5,0) rectangle node{$m$} (1.5, 2*\rad);
    \foreach \x in {-3, 3} {
        \draw[line width=1.5, color=SlateGray] (\x,-\rad) -- ++(90:1);
      }
    \foreach \x in {-2.25, 2.25}{ \node at (\x, 0.75) {$k/2$}; }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: FermiGases.tex
modified: 2015-11-01 03:21:17
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=1,
        ymin=0,
        ymax=1,
        enlargelimits=false,
        width=2.5in,
        xlabel={$\hb k$},
        ylabel={$\hb \omega$},
        ytick={0,1},
        xtick={0,0.5,1,1.5,2},
        yticklabel=\empty,
        xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25},
        % xticklabels{0,,$a$,,a$},
      ]
      \addplot[
        trace01,
        domain=0.001:2,
        samples=201,
        line width=2pt,
      ]
      {x*x};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15/drafts
filename: p24-mt1-2015-v2.tex
modified: 2015-02-13 01:53:16
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[color=gray, line width=3] (-1,4) -- (1,4);  % ceiling
    \draw (0,3.9) circle(0.1);
    \draw[line width=5,color=Sienna] (0,3.9) -- (0,-2); % cord
    \draw[<->] (0.75,-2) -- node[fill=white]{$L$} (0.75,4);
    \filldraw[fill=blue!50!white] (0.4,-2) rectangle (-0.4,-4); % mass
    \node at (0.8,-3){$m$};
    \draw[accel] (1.75,1.5) -- node[anchor=west]{$~~g$} ++(-90:1.5);
    \draw[coord] (-1.2,4) -- ++(-90:2) node[anchor=east]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{0.25}
    \draw[spring] (-3,\rad) -- (-1.5,\rad);
    \draw[spring] (1.5,\rad) -- (3,\rad);
    \draw[line width=1.25,color=SlateGray] (-3,-\rad) -- ++(0:6);
    \foreach \x in {-1, 1} {
        \filldraw[fill = gray] (\x,0) circle[radius=\rad];
      }
    \filldraw[fill=SlateBlue!25] (-1.5,0) rectangle node{$m$} (1.5, 2*\rad);
    \draw[line width=1.5, color=SlateGray] (-3,-\rad) -- ++(90:1);
    \fill (3,\rad) circle[radius=0.1];
    \draw[->,color=DarkGreen,line width=1.25] (3.25,\rad) -- ++ (0:.75)
    node[anchor=south]{$D \cos\omega t$};
    \foreach \x in {-2.25, 2.25}{ \node at (\x, 0.75) {$k/2$}; }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Extensivity.tex
modified: 2015-10-22 15:50:47
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\twelve{-12}
    \def\six{-6}
    \begin{axis}[
        xmin = 0,
        xmax = 4,
        axis lines=middle,
        ymin=-1.25,
        ymax=1,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        ylabel={$U(r)$},
        xlabel={$r$},
        %          axis x line=bottom,
        %          axis y line=left,
        %          axis line style={line width=1.25pt},
        ytick=\empty, % {0,1},
        xtick=\empty, % {0,0.5,1,1.5,2},
        %xticklabel=\empty,
      ]
      \addplot[
        trace01,
        domain=0.7:3.5,
        samples=151,
        line width=2pt
      ]% { x^2 };
      {1/(x*x*x*x*x*x) - 2/(x*x*x)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15/drafts
filename: p24-mt1-2015-v2.tex
modified: 2015-02-13 01:53:16
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    % rail
    \draw (0,0) -- (7,0);
    % wheels
    \filldraw[fill=gray!25!white] (1,0.2) circle[radius=0.2]
    (3,0.2) circle[radius=0.2];
    % car
    \filldraw[fill=gray!50!white] (0.5,0.2) rectangle (3.5,0.8);
    \node at (1,0.5){$M$};
    \draw[<->,color=DarkGreen] (0.5,1.2) --node[fill=white]{$L$}
    (3.5,1.2);
    % v
    \draw[vel] (4,0.5) -- ++(0:1) node[anchor=north]{$v_{0}$};
    % spigot
    \begin{scope}[shift={(5,1.5)}]
      \fill (0.05,0) -- (0.3,0.5) -- (0.3,0.8) -- (-0.3,0.8) -- (-0.3,0.5)
      -- (-0.05,0) -- cycle;
      \foreach \y in {-0.2, -0.4, -0.6}{
          \fill (0,\y) circle[radius=0.05];
        }
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \node at (-2.5, 2.25) {\textsf{\small top view}};
    \filldraw[fill=gray!50] (0,0) circle[radius=2];
    \draw[->,line width=1] (0,0) --node[anchor=east]{$r$} (0,-1.45);
    \fill (0,-1.5) circle[radius=0.05];
    \draw[<-] (0,-1.5) ++(-45:0.1) -- ++(-40:0.8) node[anchor=west]{landing site};
    \node[anchor=west] at (135:1.75) {$M,R$};
    \coordinate (child) at (-3, -1.5);
    \fill[color=DarkRed] (child) circle[radius=0.1];
    \node[anchor=south,shift={(90:0.2)}] at (child) {$M$};
    \draw[vel,line width=1] (child) ++(0.2,0) --node[anchor=north]{$v$} ++(0:1);
    \draw[<-,DarkGreen] (child) ++(-60:0.2) -- ++(-60:0.75) -- ++(0:0.25)
    node[anchor=west]{incoming child};
    \draw[dotted] (-1.75,-1.5) -- (0.5, -1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Extensivity.tex
modified: 2015-10-22 15:50:47
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \draw[->] (0,0) -- (6,0) node[anchor=north east]{$T$};
    \draw[->] (0,0) -- (0,4.5) node[anchor=north east]{$p$};
    \draw[trace01,line width=2] (0.5,0.5) .. controls (3,0.6) and (3.75,1.5)
    .. (5,4);
    \fill (2.48,0.89) circle[radius=0.1] node[anchor=south east]{$1$};
    \fill (3.74,1.9) circle[radius=0.1] node[anchor=south east]{$2$};
    \node at (2,3){phase B};
    \node at (2,2.5){$\mu_{A} > \mu_{B}$};
    \node at (4.5,1.){phase A};
    \node at (4.5,.5){$\mu_{A} < \mu_{B}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15/drafts
filename: p24-mt1-2015-v1.tex
modified: 2015-02-11 14:33:56
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[color=gray, line width=3] (-0.5,2) -- (0.5,2);  % ceiling
    \draw (0,1.9) circle(0.1);
    \draw[line width=1.5] (0,1.9) -- (0,1.1) (0,0.9) -- (0,-2); % cord
    \draw (0,1.1) -- +(15:0.3) -- +(195:0.3);
    \draw (0,0.9) -- +(15:0.3) -- +(195:0.3);
    \node[text width=0.9in,font=\scriptsize] at (2.3,1) {\textsf{part of the cord
        omitted to keep diagram small}};
    \filldraw[fill=blue!50!white] (0.4,-2) rectangle (-0.4,-4); % mass
    \node at (0.8,-3){$m$};
    \draw[accel] (1.25,-0.5) -- node[anchor=west]{$~~g$} ++(-90:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\peg{0.15} % the radius of the dowel

    % the ramp; corner is at (0,0), but the line width screws that up
    \draw[line width=2] (-6,3) .. controls (-3,0) and (-3,0) .. (0,0)
    -- (0, -3) -- ++(6,0);
    \coordinate (yo-yo) at (-5.25,2.5); % center of yo-yo on ramp

    \draw[coord] (0, -3.3) --node[anchor=north]{$x$} ++(0:2.5);

    %\filldraw [fill=gray] (yo-yo) circle[radius=0.15];
    % \fill[gray,opacity=0.95] (yo-yo) circle[radius=1];

    \filldraw[fill=gray!15!white] (yo-yo) circle[radius=1];
    \draw[dashed, black] (yo-yo) circle[radius=\peg];
    \draw[gray,dashed,line width=2] (-6,3) -- (-4.5,1.5);

    % Edge of the ramp
    \begin{scope}[dashed]
      \draw[line width=0.75] (0,\peg+0.05) circle[radius=\peg];
      \draw (0,\peg+0.05) circle[radius=1];
    \end{scope}

    % illustrate the radius of the dowel
    \begin{scope}[shift={(yo-yo)}]
      \draw[dashed] (-2*\peg,\peg) -- (-2, \peg)
      (-2*\peg,-\peg) -- (-2,-\peg);
      \node at (-2.3,0) {$2a$};
      \draw[coord,<-] (-2,\peg) -- +(90:0.5);
      \draw[coord,<-] (-2,-\peg) -- +(-90:0.5);
      \draw (45:0.75) -- (45:1.25) -- ++(0:0.5) node[anchor=west]{$m, R$};
    \end{scope}

    % illustrate the yo-yo ready to fly off
    \begin{scope}[shift={(5,-2+\peg/2)}]
      \draw[dashed, line width=0.75] (0,0) circle[radius=\peg];
      \draw[dashed] (0,0) circle[radius=1];
      \draw[-> ] (135:1.25)
      arc(135:45:1.25) node[anchor=south,shift={(-.4,.3)}]{$\omega$};
      \draw[vel,line width=1] (0.75,0) --node[anchor=south]{$V_{\rm f}$} ++(0:1.5);
    \end{scope}

    % Dashed level lines
    \draw[dashed,SlateBlue] (yo-yo) -- ++(0:8)
    (0,\peg+0.05) -- ++(0:4)
    (5,-2+\peg/2) -- ++(180:3);

    \draw[coord,<->] (2,\peg+0.05) --node[anchor=west]{$h$} (2,2.5);
    \draw[coord,<->] (2.25,\peg+0.05) --node[anchor=east]{$H$} (2.25,-2+\peg/2);


    % Inset showing the ramp from the right

    \begin{scope}[shift={(-8,-3.5)}]
      \filldraw[color=SlateGray,fill=gray!15,line width=2] (0,0) rectangle
      (4.5,3.25);
      % the ramp
      \shadedraw[color=black,bottom color=SlateGray!10!white,
        top color=SlateGray!50!white]
      (1.25,2.6) rectangle (1.55,0.25);

      %draw the floor
      \fill[gray!50] (0.5,0.25) rectangle (2.5,0.1);
      \draw (0.5,0.25) -- (2.5,0.25); % floor

      \node[anchor=south west] at (0,3.25) {\textsf{\small view from right}};

      % yo-yo
      \fill[gray] (1,1) rectangle (1.2,3)
      (1.6,1) rectangle (1.8,3);
      \fill[gray] (1.2,1.875) rectangle (1.6,2.125);
      \draw[dotted] (1.25,0.875) -- (1.55,0.875);

      \draw[DarkGreen,<-] (2,0.25) -- ++(45:0.4) -- ++(0:0.4)
      node[anchor=west]{floor};
      \draw[DarkGreen,<-] (1.4,1.4) -- ++(45:0.4) -- ++(0:0.4)
      node[anchor=west]{ramp};
      \draw[DarkGreen,<-] (1.6,0.875) -- ++(0:0.6) node[anchor=west]
      {end of ramp};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: temp.tex
modified: 2015-11-30 19:20:19
domain: p117
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      pathstyle/.style={line width=0.75pt,color=gray},
      dim/.style={color=green!40!black,<->},
      accel/.style={->,line width=3pt,color=gray},
      vel/.style={->,line width=2pt,color=red!50!black},
      dotted/.style={line width=0.75pt, color=gray, dashed}
    ]


    \shade[ball color=blue!30!white] (0,0) circle(0.1);
    \node at (-45:0.4){2};
    \begin{scope}[rotate=30]
      \filldraw[fill=DarkGreen!20!white,line width=0.5] (0,0) -- (4:4.5) -- (-4:4.5) --
      cycle;
      \filldraw[fill=DarkGreen!30!white, line width=0.5] (4.5,0)
      ellipse[x radius=0.1,y radius = 0.313];
      \draw[dashed] (0,0) -- (5,0);
      \node at (4.95,-0.4) {$d\Omega$};
      \draw[vel] (0:5) -- ++(0:1) node[anchor=west] {$\vector{V}$};
    \end{scope}
    \shade[left color=blue!20!white, right color=white] (-8,-2) rectangle (-3,2);
    \draw[dotted] (-8,0) -- (3,0);
    \foreach \y in {-1.75,-1.25,...,1.75} {
        \draw[vel] (-8,\y) -- ++(0:1);
      }
    \draw[line width=2] (-6.5,0.5) .. controls (-0.134,0.5) and (-0.134,0.5)
    .. (4,2.85);
    \shade[ball color=blue!30!white] (-5,0.5) circle(0.1);
    \node at (-5,0.85){1};
    \draw (1.5,0) arc (0:30:1.5);
    \node at (15:1.75) {$\theta$};
    %(-1.5,0.75) and (60:1.5) .. (60:6);

    % \shade[ball color=red!30!white] (-5,0.5) circle(0.25);
    % \shade[ball color=red!15!white] (150:1) circle(0.25);
    % \draw[pathstyle] (-5,0) -- (2,0);
    % \draw[line width=1.5] (0,0) -- (150:1);
    % \node at (-0.2,0.42) {$R + a$};
    % \draw[pathstyle] (180:0.3) arc(180:150:0.3);
    % \node at (165:0.5) {$\psi$};
    % \draw[dotted] (-5,0.5) -- +(0:4.15);
    % \draw[dotted] (150:1) -- +(120:1.5);
    % \draw[vel] (-4.75,0.5) -- +(0:0.6);
    % \draw[vel] (150:1)  +(120:1) -- +(120:1.5);
    % \draw[color=blue!70!black] (0:1.25) arc (0:120:1.825);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15/drafts
filename: p24-mt1-2015-v1.tex
modified: 2015-02-11 14:33:56
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[line width=1.5] (3,-3) -- (3,0) arc(0:90:1) -- (1,1) (-1,1) -- (-2,1) arc(90:180:1)
    -- (-3,-3);
    \draw[spring, line width=1.5] (-1,1) -- (1,1);
    \node at (0, 1.7){$k$};
    \filldraw[fill=gray!25!white] (2,0) circle(1) (-2,0) circle(1);
    \filldraw[fill=black] (2,0) circle(0.1) (-2,0) circle(0.1);
    \filldraw[fill=blue!50!white] (3.4,-3) rectangle (2.6,-5)
    (-3.4,-3) rectangle (-2.6,-5);
    \node at (-3.8,-4){$m$};
    \node at (3.8,-4){$m$};
    \draw[accel] (0,-2) -- node[anchor=west]{$~~g$} ++(-90:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \fill[gray] (0,0.2) rectangle (-0.1,-0.2);
    \fill[gray] (6,0.2) rectangle (6.1,-0.2);
    \draw (0,0.2) -- (0,-0.2) (6,0.2) -- (6,-0.2);
    \draw[dashed] (0,0) -- (6,0);
    \draw (0,0) sin (1,0.25) cos (2,0) sin (3,-0.25) cos(4,0) sin (5,0.25) cos (6,0);
    \draw[dashed] (0,0) sin (1,-0.25) cos (2,0) sin (3,0.25) cos(4,0) sin (5,-0.25)
    cos (6,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Ising.tex
modified: 2015-12-08 17:05:59
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=4,
        ymin=0,
        ymax=1.05,
        enlargelimits=false,
        height=2.75in,
        width=3.5in,
        xlabel={$\eta$},
        ylabel={$B_{S}(\eta)$}
      ]
      \addplot+[smooth,no marks,trace01,line width=1.5pt] table[x=x,
          y=B05]{Brillouin.dat};
      \addplot+[smooth,no marks,trace02,line width=1.5pt] table[x=x,
          y=B1]{Brillouin.dat};
      \addplot+[smooth,no marks,trace03,line width=1.5pt] table[x=x,
          y=B15]{Brillouin.dat};
      \addplot+[smooth,no marks,trace04,line width=1.5pt] table[x=x,
          y=B25]{Brillouin.dat};
      \addplot+[smooth,no marks,trace05,line width=1.5pt] table[x=x,
          y=B35]{Brillouin.dat};
      %      \addplot[trace01, domain=0.02:4, samples=101, line width=2pt]
      %      {2*(1/tanh(x)-0.5/tanh(x/2))};
      % \addplot[trace02, domain=0.02:4, samples=101, line width=2pt]
      % {1*(1.5/tanh(1.5*x)-0.5/tanh(x/2))};
      % \addplot[trace03, domain=0.02:4, samples=101, line width=2pt]
      % {2/3*(2/tanh(2*x)-0.5/tanh(x/2))};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=0.6,
      decoration={coil,aspect=0.3,segment
          length=3mm,amplitude=3mm},
      >=Stealth,
      beef/.style={line width=1.5}]
    \draw[line width=2] (-1,0) -- (3.5,0);
    \draw[line width=2] (-1,6) -- +(0:4.5);
    \draw[line width=2] (4.5,0) -- +(0:3) (4.5,6) -- +(0:3);
    % Draw the applied force
    \draw[->, beef] (0,3) -- (0,1.5)
    node[anchor=north]{$\vb{F}$};
    % Draw the second spring
    \draw[decorate,beef] (2,0) -- ++(90:2);
    \draw[beef] (2,2) -- (2,3);
    \node at (2.9,.8) {$k_{2}$};
    % Draw the pulley
    \filldraw[fill=blue!10!white,draw=blue] (1,3) circle(1);
    \filldraw[fill=blue!50!black] (1,3) circle(0.05);
    % Draw the first spring
    %\usetikzlibrary{decorations.pathmorphing}
    \draw[decorate,beef] (1,6) -- ++(270:2) ;
    \node at (1.9,5.2) {$k_{1}$};
    \draw[beef] (1,3) -- (1,4);
    % Draw the effective spring
    \draw[decorate,beef] (6,6) -- (6,3.5);
    \node at (6.9,4.8){$k_{\rm eff}$};
    \draw[beef,->] (6,3.5) -- (6,3) node[anchor=north]{$\vb{F}$};
    \draw[dashed] (4,-0.5) -- (4,6.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Kinetics.tex
modified: 2015-12-04 00:25:55
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \newlength{\lht}
    \setlength{\lht}{1.5cm}
    \newlength{\lwd}
    \setlength{\lwd}{2.5cm}
    \foreach \rot in {0,180} {
        \begin{scope}[rotate=\rot]
          \filldraw[fill=SlateGray!30!white] (0.1,0.05) -- (0,0.05)
          -- (0,\lht) -- (\lwd,\lht) -- (\lwd,-\lht) -- (0,-\lht)
          -- (0,-0.05) -- (0.1,-0.05)
          -- (0.1,-0.9\lht) -- (0.9\lwd,-0.9\lht) -- (0.9\lwd,0.9\lht) --
          (0.1,0.9\lht) -- cycle;
        \end{scope}
      }
    \node at (-0.65\lwd,-0.65\lht) {$T_{1}, p_{1}$};
    \node at (0.65\lwd,-0.65\lht) {$T_{2}, p_{2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=2, gray] (0,1) circle[radius=1] ; % the loop
    \draw[line width=2, gray] (1,0) -- (-1,0) .. controls (-2.5,0) and (-3,2)
    .. (-4,4);
    \fill (-3.4,3) circle[radius=0.1];
    \draw[coord] (-3.75,0) --node[anchor=east]{$h$} ++(90:3) ;
    \draw[coord,->] (0,1) -- node[anchor=south east]{$R$ } ++ (45:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15/drafts
filename: p24-quiz2-2015-v2.tex
modified: 2015-02-26 01:25:02
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      tightspring/.style={decorate,decoration={coil,aspect=0.3,segment length=1mm,amplitude=2mm}}
    ]

    % Now the rebounding ball
    \begin{scope}[shift={(0,3.5)}]
      \draw[line width=2pt,color=gray!25!white] (0,0) -- (-150:3);
      \filldraw[fill=red!10!white,draw=gray,dashed] (-150:3) circle[radius=0.4];
      \draw[dashed] (-100:3) arc(-100:-200:3);
      \draw[->] (-90:0.75) arc(-90:-150:0.75);
      \node at (-120:1){$\theta$};
    \end{scope}


    % draw the floor and ramp
    \draw[brown!70!black, line width=2pt] (-3,0) -- (3,0) ..
    controls (5,0) and (7,1.5) .. (9,1.5) -- (13,1.5);
    \draw[dashed] (4,0) -- (13,0);

    % the two masses and the compressed spring
    \draw[line width=2pt,color=gray] (0,0.5) -- node[anchor=west]{$L$} (0,3.5);
    \fill (0,3.5) circle[radius=0.075];
    \node at (0.3,3.5){$P$};

    \begin{scope}[shift={(0.4,0.4)}]
      \draw[tightspring] (0,0) -- (0.65,0);
      \draw[color=brown,line width=2pt](0,0) -- (1,0);
      \node at (0.3,0.5){$k$};
    \end{scope}

    \shade[ball color=red] (0,0.5) circle[radius=0.4];
    \node at (-0.6,0.25){$ m_{1} $};
    \node at (2.1,0.25){$m_{2}$};
    \filldraw[fill=blue!60!black, rounded corners=4pt] (1,0) rectangle (1.8,0.8);


    \draw[coord,<->] (13,0) -- (13,1.5);
    \node at (13.4,0.75) {$\displaystyle\frac{L}{2}$};

    \draw[line width=4pt,color=gray] (10,1.5) -- (13,1.5);
    \draw[coord] (10,2) -- node[anchor=south]{$x$} ++(0:1.5);
    \draw[<-] (11.5,1.6) -- ++(45:1) node[anchor=west]{$\mu_{k}$};
    \draw[<-] (6,0.9) -- ++(45:1) node[anchor=south]{\textsf{no friction}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Kinetics.tex
modified: 2015-12-04 00:25:55
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin = 0,
        ymax = 1.2,
        xmin = 0,
        xmax = 3.3,
        enlargelimits = false,
        height=2.5in,
        width=3.5in,
        ylabel={$f(v)$},
        ytick=\empty,
        xlabel={$v / \tilde{v}$},
        xtick={0,1,2,3},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25},
        xtick align=inside,
      ]
      \addplot[
        trace01,
        domain=0:3,
        samples=201,
        line width=2pt,
      ] { x^2 * exp(1-x^2) };
      \draw[color=DarkGreen] (1.128,0) -- ++(90:0.969);
      \draw[color=DarkGreen,<-] (1.128,0.969) ++(30:0.02) -- ++(30:0.2)
      node[anchor=west] {$\overline{v}$};
      \draw[DarkBlue] (1.225,0) -- (1.225,0.91);
      \draw[DarkBlue,<-] (1.28,0.91) --++(0:0.2) node[anchor=west]{$v_{\rm rms}$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm}]%,>=stealth']
    \filldraw (0,0) circle(0.1);
    \draw[decorate] (0,0) -- (30:2);
    \shade[ball color=gray] (30:2) circle(0.25) ++(-90:0.25) node[anchor=north]{
        $m$ };
    \draw[decorate] (30:2.25) -- ++(30:2);
    \shade[ball color=gray] (30:4.5) circle(0.25) ++(-90:0.25)
    node[anchor=north]{$m$};
    \draw (30:1) ++(120:0.5) node {$k$};
    \draw (30:3) ++(120:0.5) node {$k$};
    \draw[->] (24:5) arc(24:36:5) node[anchor=south]{$\omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/exams15/drafts
filename: p24-quiz2-2015-v1.tex
modified: 2015-02-25 20:21:39
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      tightspring/.style={decorate,decoration={coil,aspect=0.3,segment length=1mm,amplitude=2mm}}
    ]

    % Now the rebounding ball
    \begin{scope}[shift={(0,3.5)}]
      \draw[line width=2pt,color=gray!25!white] (0,0) -- (-150:3);
      \filldraw[fill=red!10!white,draw=gray,dashed] (-150:3) circle[radius=0.4];
      \draw[dashed] (-100:3) arc(-100:-200:3);
      \draw[->] (-90:0.75) arc(-90:-150:0.75);
      \node at (-120:1){$\theta$};
    \end{scope}


    % draw the floor and ramp
    \draw[brown!70!black, line width=2pt] (-3,0) -- (3,0) ..
    controls (5,0) and (7,1.5) .. (9,1.5) -- (13,1.5);
    \draw[dashed] (4,0) -- (13,0);

    % the two masses and the compressed spring
    \draw[line width=2pt,color=gray] (0,0.5) -- node[anchor=west]{$L$} (0,3.5);
    \fill (0,3.5) circle[radius=0.075];
    \node at (0.3,3.5){$P$};

    \begin{scope}[shift={(0.4,0.4)}]
      \draw[tightspring] (0,0) -- (0.65,0);
      \draw[color=brown,line width=2pt](0,0) -- (1,0);
      \node at (0.3,0.6){$\alpha$};
    \end{scope}

    \shade[ball color=red] (0,0.5) circle[radius=0.4];
    \node at (-0.55,0.25){$ m $};
    \node at (1.35,1.1){$M$};
    \filldraw[fill=blue!60!black] (1,0) rectangle (1.8,0.8);


    \draw[coord,<->] (13,0) -- (13,1.5);
    \node at (13.4,0.75) {$\displaystyle\frac{L}{2}$};

    \draw[line width=4pt,color=gray] (10,1.5) -- (13,1.5);
    \draw[coord] (10,2) -- node[anchor=south]{$x$} ++(0:1.5);
    \draw[<-] (11.5,1.6) -- ++(45:1) node[anchor=west]{$\mu_{k}$};
    \draw[<-] (6,0.9) -- ++(45:1) node[anchor=south]{\textsf{no friction}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Kinetics.tex
modified: 2015-12-04 00:25:55
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \shade[top color=red!30!white, bottom color=blue!50!white] (-2,-2)
    rectangle (2,2);
    \begin{scope}[color=black]
      \draw (-2,0) -- (2,0) node[anchor=west]{$z$};
      \draw[dash pattern=on 6pt off 2pt] (-2,-1.5) -- (2,-1.5)
      node[anchor=west]{$z-l$};
      \node[anchor=west] at (-1.85,1.75) {$T(z+l)$};
      \draw[dash pattern=on 6pt off 2pt] (-2,1.5) -- (2,1.5)
      node[anchor=west]{$z+l$};
      \node[anchor=west] at (-1.85,-1.75) {$T(z-l)$};
      \draw[vel] (0,1.5) -- ++(-90:0.75);
      %        node[anchor=east]{$\displaystyle\frac{n}{6}$};
      \draw[vel] (0,-1.5) -- ++(90:0.75);
      % node[anchor=east]{$\displaystyle\frac{n}{6}$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \coordinate (end) at (60:5);
    \def\wall{0.25}
    \fill[gray!50] (0,-1) -- (0,5) -- (-\wall,5) -- (-\wall,-1)
    -- (0,-1) --cycle;
    \draw (0,-1) -- (0,5);
    % the rod
    \draw[line width=3, DarkRed] (0,0) -- (end)
    node[anchor=north,shift={(-0.1,-0.8)}]{$M, \ell$};
    \fill (end) circle[radius=0.15];
    \node at ($(end) + (0.4,0)$) {$M$};
    \coordinate (spwall) at (0,{2.5*cos(30)});
    \coordinate (midpt) at (60:2.5);
    \draw[SlateGray,dashed] (spwall) -- (midpt);
    \draw[spring] (spwall) -- node[anchor=south, shift={(0,0.25)}]{$k$} (midpt);
    \filldraw[fill=white] (0,0) circle[radius=0.1];
    \fill (0,0) circle[radius=0.025];
    \draw (0,0.6) arc(90:60:0.6);
    \node at (73:0.95) {$\theta$};
    \node at (2,-1){side view};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Kinetics.tex
modified: 2015-12-04 00:25:55
domain: p117
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      pathstyle/.style={line width=0.75pt,color=gray},
      dim/.style={color=green!40!black,<->},
      accel/.style={->,line width=3pt,color=gray},
      vel/.style={->,line width=2pt,color=red!50!black},
      dotted/.style={line width=0.75pt, color=gray, dashed}
    ]

    % particle at origin
    \shade[ball color=blue!30!white] (0,0) circle(0.1);
    \node at (-45:0.4){2};
    % outgoing scattering cone
    \begin{scope}[rotate=30]
      \filldraw[fill=DarkGreen!20!white,line width=0.5] (0,0) -- (4:4.5) -- (-4:4.5) --
      cycle;
      \filldraw[fill=DarkGreen!30!white, line width=0.5] (4.5,0)
      ellipse[x radius=0.1,y radius = 0.313];
      \draw[dashed] (0,0) -- (5,0);
      \node[vel] at (4.95,-0.4) {$d\Omega$};
      \draw[vel] (0:5) -- ++(0:1) node[anchor=west] {$\vector{V}_{\rm out}$};
    \end{scope}
    % input flux
    \shade[left color=blue!20!white, right color=white] (-8,-2) rectangle (-3,2);
    \draw[dotted] (-8,0) -- (3,0);
    \foreach \y in {-1.75,-1.25,...,1.75} {
        \draw[vel] (-8,\y) -- ++(0:1);
      }
    \node[vel] at (-6.5,1.75){$\vector{J}_{1}$};
    \node[vel] at (-7.5,2.25){$\vector{V}$};
    \draw[line width=1.75,->] (-4.5,0.5) -- +(0:0.5);
    \draw[line width=2] (-6.5,0.5) .. controls (-0.134,0.5) and (-0.134,0.5)
    .. (4,2.85);

    \shade[ball color=blue!30!white] (-5,0.5) circle(0.1);
    \node at (-5,0.85){1};
    \draw[<-,color=DarkSlateGray] (-5.75,0.5) -- +(90:0.5) node[anchor=east]{$b$};
    \draw[<-,color=DarkSlateGray] (-5.75,0) -- +(-90:0.5);
    \draw (1.5,0) arc (0:30:1.5);
    \node at (15:1.75) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/rec15
filename: rec04-prof.tex
modified: 2015-01-30 17:49:01
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[color=gray, line width=3] (-0.5,2) -- (0.5,2);  % ceiling
    \draw (0,1.9) circle(0.1);
    \draw[line width=1.5] (0,1.9) -- (0,1.1) (0,0.9) -- (0,-2); % cord
    \draw (0,1.1) -- +(15:0.3) -- +(195:0.3);
    \draw (0,0.9) -- +(15:0.3) -- +(195:0.3);
    \node[text width=0.9in,font=\scriptsize] at (2.3,1) {\textsf{part of the cord
        omitted to keep diagram small}};
    \filldraw[fill=blue!50!white] (0.4,-2) rectangle (-0.4,-4); % mass
    \node at (0.8,-3){$m$};
    \draw[accel] (1.25,-0.5) -- node[anchor=west]{$~~g$} ++(-90:1.5);
    \draw (0,-1.85) circle(0.15);
    \draw[<-] (-0.2,-1.8) --++(135:0.5);
    \node at (-1.5,-1.5){\textsf{segment}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[
      decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm},
      >=stealth'
    ]
    \def\ell{2}
    \filldraw (0,0) circle(0.1);
    \draw[decorate] (0,0) -- (30:\ell);
    \shade[ball color=gray] (30:\ell) circle(0.25) ++(-90:0.25) node[anchor=north]{
        $m$ };
    \draw[decorate] (30:2.25) -- ++(30:\ell);
    \shade[ball color=gray] (30:4.5) circle(0.25) ++(-90:0.25)
    node[anchor=north]{$m$};
    \draw (30:1) ++(120:0.5) node {$k$};
    \draw (30:3) ++(120:0.5) node {$k$};
    \draw[->] (24:5) arc(24:36:5) node[anchor=south]{$\omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Kinetics.tex
modified: 2015-12-04 00:25:55
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \shade[top color=red!50!white, bottom color=blue!50!white] (-2,-2)
    rectangle (2,2);
    \begin{scope}[color=black]
      \draw (-2,0) -- (2,0) node[anchor=west]{$z$};
      \draw[dash pattern=on 6pt off 2pt] (-2,-1.5) -- (2,-1.5)
      node[anchor=west]{$z-l$};
      \node[anchor=west] at (-1.85,1.75) {$T(z+l)$};
      \draw[dash pattern=on 6pt off 2pt] (-2,1.5) -- (2,1.5)
      node[anchor=west]{$z+l$};
      \node[anchor=west] at (-1.85,-1.75) {$T(z-l)$};
      \draw[vel] (0,1.5) -- ++(-90:0.75)
      node[anchor=east]{$\displaystyle\frac{n}{6}$};
      \draw[vel] (0,-1.5) -- ++(90:0.75)
      node[anchor=east]{$\displaystyle\frac{n}{6}$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=2]
    \draw[color=DarkGreen,<->] (2,0) node[anchor=north]{$x$} -- (0,0) -- (0,2)
    node[anchor=east]{$y$};
    \draw[dashed,color=gray] (1.5,-0.5)--(1.5,2);
    \coordinate (A) at (1.5,0.5);
    \draw (0,0) --node[anchor=south]{$r$} (A);
    \fill (A) circle[radius=0.05];
    \draw[vel] (A) -- ++(90:0.5) node[anchor=east]{$v$};
    \draw (0.5,0) arc(0:20:0.5);
    \node at (10:0.85) {$\theta$};
    \node at (0.75,-0.4) {$b$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Kinetics.tex
modified: 2015-12-04 00:25:55
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \shade [top color=gray!50!white,bottom color=gray!20!white]
    (-2,0) rectangle (3,-0.5);
    \shade [top color=gray!20!white, bottom color=gray!50!white] (-2,2.25)
    rectangle (3,2.75);
    \fill[fill=red!10!white] (-2,0) rectangle (3,2.25);
    \draw[vel] (-1.75,2.5) -- ++(0:0.75) node[anchor=west]{$v_{x}$};
    \draw[color=DarkGreen,->] (0,0) -- (0,3) node[anchor=south]{$z$};
    \draw[color=DarkGreen,->] (-2,0) -- (3.25,0) node[anchor=west]{$x$};
    \draw[color=blue] (0,0) -- (2.25*0.75,2.25);
    \foreach \z in {0.5, 1, ..., 2}{
        \draw[vel] (0,\z) -- ++(0:\z*0.75);
      }
    \node at (-1.65,0.25){\textsf{gas}};
    \node at (0.5,-0.25){\textsf{fixed plate}};
    \node[anchor=west] at (0.15,2.5) {\textsf{\small{plate moving right}}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2015/rec15
filename: rec02-prof.tex
modified: 2015-01-23 17:38:53
domain: p24
source:
  \begin{tikzpicture}[scale=2]
    \draw[color=blue!50!white,->] (0,0) -- (1,0) node[anchor=south]{\( x \)};
    \draw[color=blue!50!white,->] (0,0) -- (0,0,-1) node[anchor=west]{\( y \)};
    \draw[color=blue!50!white,->] (0,0) -- (0,-2.5) node[anchor=west]{\( z \)};

    \draw[dashed, line width = 1.5] (0,0,0) -- node[anchor=east]{\( h \)} (0,-1.414,0) --
    node[anchor=south,rotate=15]{\( \ell/\sqrt{2} \)} (-1,-1.414,1);
    \draw (0,0,0) -- (1,-1.414,1) -- node[anchor=west]{\( \ell \)} (1,-1.414,-1)
    -- (-1,-1.414,-1) -- (-1, -1.414,1) -- node[anchor=north]{\( \ell \)} (1,-1.414,1)
    -- (0,0) -- (-1,-1.414,1) (0,0) -- (-1,-1.414,-1)
    (0,0) -- (1,-1.414,-1);
    % draw the right-angle symbol
    \draw (0,-1.314,0) -- (-0.1,-1.314,0.1) -- (-0.1,-1.414,0.1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \coordinate (S) at (-4,0);
    \coordinate (E) at (4,0);
    \foreach \a in {0, 15, ..., 345} \draw[yellow] (S) -- ++(\a:1);
    \fill[fill=yellow!50!white] (S) circle[radius=0.5];
    \node at (-4,-1.5) {Sun};
    \filldraw[fill=blue!20!white] (E) circle[x radius=1.5, y radius = 1.15];
    \filldraw[fill=brown!20!white] (E) circle[radius=1];
    \draw[->,line width=1.25] (S) --node[anchor=north]{$r_0$}(E);
    \draw[color=DarkGreen,->] (E) -- ++(0:1.75) node[anchor=west]{$x$};
    \draw[color=DarkGreen,->] (E) -- ++(90:1.75) node[anchor=south]{$y$};
    \draw[->,line width=1.25] (S) -- node[anchor=south]{$r$} (3.,0.88);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/lec
filename: Kinetics.tex
modified: 2015-12-04 00:25:55
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[rotate=90]
      \draw[line width=2pt] (0,0.5) -- (0,2) (0,-0.5) -- (0,-2) ;
      % draw the slant cylinder
      \filldraw[color=gray,fill=yellow!60!white,dashed] (0,0.5) -- ++(150:2.5) -- ++(-90:1)
      -- ++(-30:2.5) -- cycle;
      \draw[dashed] (-2,0) -- (2,0);
      \draw[gray] (150:2.5) -- ++(-30:5);
      \draw (0:1) arc (0:-30:1);
      \node at (-15:1.25){$\theta$};
      \draw[<->,DarkGreen] (0,0.75) -- node[anchor=south,rotate=60]{$v\dop{t}$}
      ++(150:2.5);
      \draw[<-,DarkGreen] (0,0.2) -- ++(30:0.75) node[anchor=south]{$\Dop{A}$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{2}
    \def\ang{-30}
    \draw (0,0) circle[radius=\rad];
    \draw[dashed] (0,-1.2*\rad) -- (0,1.2*\rad);
    \draw (0,0) -- (\ang:\rad);
    \fill[fill=DarkRed] (\ang:\rad) circle[radius=0.125];
    \node at (\ang:1.2*\rad) {$m$};
    \draw[->] (-90:0.75) arc (-90:\ang:0.75);
    \node at (-90-\ang:1){$\theta$};
    \draw (0,1.1*\rad) arc[start angle=-90, end angle=-240, x radius=0.5, y
        radius=0.1];
    \draw[->] (0,1.1*\rad) arc[start angle=-90, end angle=60, x radius=0.5, y
        radius=0.1];
    \node at (0.75,1.2*\rad){$\omega$};
    \draw[accel, line width=2] (10:1.4*\rad) -- node[anchor=west]{$g$}
    ++(0,-1.25);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/rec
filename: rec12-prof.tex
modified: 2015-12-15 14:59:38
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \shade [top color=gray!50!white,bottom color=gray!20!white]
    (-2,0) rectangle (3,-0.5);
    \shade [top color=gray!20!white, bottom color=gray!50!white] (-2,2.25)
    rectangle (3,2.75);
    \fill[fill=red!10!white] (-2,0) rectangle (3,2.25);
    \draw[vel] (-1.75,2.5) -- ++(0:0.75) node[anchor=west]{$u_{x}$};
    \draw[color=DarkGreen,->] (0,0) -- (0,3) node[anchor=south]{$z$};
    \draw[color=DarkGreen,->] (-2,0) -- (3.25,0) node[anchor=west]{$x$};
    \draw[color=blue] (0,0) -- (2.25*0.75,2.25);
    \foreach \z in {0.5, 1, ..., 2}{
        \draw[vel] (0,\z) -- ++(0:\z*0.75);
      }
    \node at (-1.65,0.25){\textsf{gas}};
    \node at (0.5,-0.25){\textsf{fixed plate}};
    \node[anchor=west] at (0.15,2.5) {\textsf{\small{plate moving right}}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!25] (0,0) circle[radius=2];
    \filldraw[dashed,opacity=0.5,fill=white] (0,1) circle[radius=1];
    \fill (0,0) circle[radius=0.05];
    \draw[coord, ->] (0,0) --node[anchor=north east]{$a$} (-45:2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/rec
filename: rec13-prof.tex
modified: 2015-12-14 03:41:19
domain: p117
source:
  \begin{tikzpicture}[scale=0.7]
    \fill[color=gray!50!white] (0,0) rectangle (1.5,5);
    \fill[color=gray] (0,0) rectangle(1.5,2);
    \draw (0,6) -- (0,0) -- (1.5,0) -- (1.5,6);
    \node at (0.75,-0.5){$T = \degC{-5.0}$};

    \draw (1.75,2) -- (3.75,2);
    \draw (1.75,3.5) -- (3.75,3.5);
    \draw[<->] (2.75,2) --node[anchor=east]{$x$} (2.75,3.5);
    \node at (2.75,0.5) {solid};
    \node at (2.75,4) {liquid};

    \begin{scope}[shift={(4,0)}]
      \fill[color=gray!50!white] (0,0) rectangle (1.5,4.5);
      \fill[color=gray] (0,0) rectangle(1.5,3.5);
      \draw (0,6) -- (0,0) -- (1.5,0) -- (1.5,6);
      \node at (0.75,-0.5){$T = \degC{-5.2}$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \def\fat{0.25}
    \fill[gray!50] (-2,0) -- (1,0) -- ++(0,-\fat) -- (-2,-\fat) -- cycle;
    \draw (-2,0) -- (1,0);


    \fill (-2,1) circle[radius=0.1] node[anchor=north,shift={(0,-0.15)}] {$m$};

    \draw[vel,line width=1] (-1.8,1) -- node[anchor=south]{$v$} ++(0:0.5);

    \filldraw[fill=gray!15] (0,0) -- (-1, 0) -- (-1, 1) -- (0,1) -- cycle;

    \node at (-0.5,0.5) {$m$};
    \node[anchor=south] at (-0.5,1) {$\ell$};
    \filldraw[fill=white] (0,0) circle[radius=0.05];
    \draw[line width=0.75,<-] (0.1,0.1) -- (45:0.5) node[anchor=west]{hinge};


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{0.25}
    \draw[spring] (-3,\rad) -- (-1.5,\rad);
    \draw[spring] (1.5,\rad) -- (3,\rad);
    \draw[line width=1.25,color=SlateGray] (-3,-\rad) -- ++(0:6);
    \foreach \x in {-1, 1} {
        \filldraw[fill = gray] (\x,0) circle[radius=\rad];
      }
    \filldraw[fill=SlateBlue!25] (-1.5,0) rectangle node{$m$} (1.5, 2*\rad);
    \draw[line width=1.5, color=SlateGray] (-3,-\rad) -- ++(90:1);
    \fill (3,\rad) circle[radius=0.1];
    \draw[->,color=DarkGreen,line width=1.25] (3.25,\rad) -- ++ (0:.75)
    node[anchor=south]{$D e^{i\omega t}$};
    \foreach \x in {-2.25, 2.25}{ \node at (\x, 0.75) {$k/2$}; }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/rec
filename: rec13-prof.tex
modified: 2015-12-14 03:41:19
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
      xmin=0.9,
      xmax=1.15,
      ymin=-1.1,
      ymax=-0.5,
      enlargelimits=false,
      height=2.25in,
      width=3in,
      xlabel={$r/a$},
      ylabel={$U/U_{0}$},
      ]
      \addplot[ trace01, domain=0.9:1.15, samples=101, line width=2pt ]
      {(1/x)^12-2*(1/x)^6};
      \addplot[ trace02, domain=0.9:1.15, samples=101, line width=1.5pt, dashed ]
      {-1+36*(x-1)^2};
      \addplot[ trace03, domain=0.9:1.15, samples=101, line width=2pt ]
      {-1+36*(x-1)^2-252*(x-1)^3};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\fat{0.25}
    \fill[gray!50] (0,0) -- (2,0) -- (2,-\fat) -- (-\fat,-\fat)
    -- (-\fat,3) -- (0,3) -- cycle;
    \draw[line width=1] (0,3) -- (0,0) -- (2, 0);
    \draw[line width=2,DarkRed] (0.05,2.5) -- (1.5,0.03);
    \draw (1.2,0) arc(180:125:0.3);
    \node at (1.1,0.25) {$\theta$};
    \node[anchor=south west] at (1.5, 0){$\mu$};
    \node[anchor=south west] at (0, 2.5){$\mu$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/rec
filename: rec14-prof.tex
modified: 2015-12-17 04:16:31
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=3pt,color=DarkRed] (0,0) -- (0,4);
    \draw[line width=3pt, color=DarkBlue!50!white] (2,0) -- (2,4);
    \begin{scope}[shift={(1,3.5)}]
      \def\x{0.8}
      \def\y{0}
      \draw[->,line width=1.5,DarkRed] (180:\x) --node[anchor=south]{$P_{1}$}
      (0:\x);

      %      \pgfmathsetlength{\x}{\x-0.2}
      %      \pgfmathsetlength{\y}{-0.8}
      \def\x{0.6}
      \def\y{-0.8}
      \draw[->,line width=1.5,DarkRed] (\x,\y) --node[anchor=south]{$P_{1}R_{B}$}
      ++(180:\x*2);
      \def\x{0.45} \def\y{-1.6}
      \draw[->,line width=1.5,DarkRed] (-\x,\y) --node[anchor=south]{$P_{1}R_{B}R_{A}$}
      ++(0:\x*2);
      \def\x{0.35} \def\y{-2.4}
      \draw[->,line width=1.5,DarkRed] (\x,\y) --node[anchor=south]{$P_{1}R^{2}_{B}R_{A}$}
      ++(180:\x*2);

    \end{scope}
    \node at (0,-0.5) {$T_{A}, R_{A}$};
    \node at (2,-0.5) {$T_{B}, R_{B}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\fat{0.25}
    \fill[gray!50] (0,0) -- (3,0) -- ++(0,-\fat) -- (\fat,-\fat) --
    (\fat,-1.5) -- (0,-1.5) -- cycle;
    \draw (0,-1.5) -- (0,0) -- (3,0);

    \draw[line width=1.5pt, DarkGreen] (2,0.05) -- ++(180:3);
    \fill (1.95,0.18) circle[radius=0.1];
    \fill (-0.95,0.18) circle[radius=0.1];
    \draw[vel,line width=1] (-1.25,0.5) -- node[anchor=east] {$v_{0}$}
    ++(-90:0.6);
    \node[anchor=south] at (1.95,0.28) {$m$};
    \node[anchor=south] at (-0.95,0.28) {$m$};
    \node[anchor=south] at (-0.5,0.05) {$a$};
    \node[anchor=south] at (1,0.05) {$b$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/rec
filename: rec07-prof.tex
modified: 2015-10-17 23:28:29
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \fill[fill=gray!20!white] (0,0) rectangle (2.5,1.5);
    \draw[line width=1.25pt] (3.25,0) -- (0,0) -- (0,1.5) -- (3.25,1.5)
    (2.5,-0.25) -- (2.5,1.75);
    \draw[<->] (-0.5,0) --node[anchor=east]{$l$} (-0.5,1.5);
    \draw[->] (0,-0.5) --node[anchor=south]{$x$} ++(0:2.5);
    \node at (2.95,0.75){$2\sigma l$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\dx{0.75} \def\dy{0.25}
    \filldraw[fill=gray!20] (-\dx,-\dy) rectangle (\dx,\dy);
    \draw[force] (-\dx,0) -- node[anchor=south]{$\frac{k}{2} x$}
    ++ (180:2) coordinate(A);
    \draw[force] (A) -- node[anchor=south]{$\frac{k}{2} (x - D\cos\omega)$}
    ++(180:3) coordinate (B);
    \draw[force] (B) -- node[anchor=south]{$b \xd$} ++(180:1);
    \draw[coord] (0,0.5) -- node[anchor=south]{$x$} ++(0:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/exam
filename: phys-117-2015-mt1-key.tex
modified: 2015-10-01 15:05:16
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=0,
        ymax=1.2,
        xmin=0,
        xmax=1.2,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        xlabel={$E$},
        ylabel={$S$},
        axis x line=bottom,
        axis y line=left,
        ytick=\empty,
        xtick=\empty,
        axis line style={line width=1.25}
      ]
      \addplot[trace01,
        domain=0:1,
        samples=101,
        line width=2pt
      ]
      {x^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (0,0) -- (0,-3);
    \draw[dashed] (0,-2.382) circle[x radius=1.375,y radius=0.15];
    \draw (0,0) -- ++(-60:2.75) coordinate (M);
    \filldraw[fill=gray] (M) circle[radius=0.1];
    \draw[force] (M) -- ++(-90:1.25) node[anchor=east]{$Mg$};
    \draw[force] (M) --node[anchor=west]{$T$} ++(120:1.35);
    \fill (0,-2.382) coordinate(O) circle[radius=0.05];
    \draw[dashed] (O) --node[anchor=north]{$\rho$} (M);

    \begin{scope}[shift={(4,0)}]
      \draw[dashed] (0,0) -- (0,-3);
      \draw[dashed] (0,-2.382) circle[x radius=1.375,y radius=0.15];
      \draw (0,0) -- ++(-60:2.75) coordinate (M);
      \filldraw[fill=gray] (M) circle[radius=0.1];
      \draw[force] (M) -- ++(-90:1.25) node[anchor=east]{$Mg$};
      \draw[force] (M) --node[anchor=west]{$T$} ++(120:1.35);
      \fill (0,0) coordinate(O) circle[radius=0.05];
      \draw[force,Red] (M) -- ++(30:1.25) node[anchor=south]{$L$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/exam
filename: phys-117-2015-mt1-key.tex
modified: 2015-10-01 15:05:16
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=0,
        ymax=1.2,
        xmin=0,
        xmax=1.2,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        xlabel={$E_{1}$},
        ylabel={$S$},
        axis x line=bottom,
        axis y line=left,
        ytick=\empty,
        xtick=\empty,
        axis line style={line width=1.25}
      ]
      \addplot[trace01,
        domain=0:1,
        samples=101,
        line width=2pt
      ]
      {x^2};
      \addplot[trace02,
        domain=0:1,
        samples=101,
        line width=2pt]
      {(1-x)^2};
      \addplot[trace03,
        domain=0:1,
        samples=101,
        line width=2pt]
      {x^2+(1-x)^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[DarkRed,line width=3] (0,0) -- (60:4) ;
    \draw[force] (60:2) -- ++(180:2) node[anchor=east]{$F$};
    \draw[force] (60:2) -- ++(-90:2) node[anchor=north]{$M g$};
    \draw[force] (60:4) -- ++(-90:2) node[anchor=north]{$M g$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/exam
filename: phys-117-2015-mt1-key.tex
modified: 2015-10-01 15:05:16
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=0,
        ymax=1.2,
        xmin=0,
        xmax=3.2,
        enlargelimits=false,
        height=2in,
        width=2.5in,
        xlabel={$\kb T/\epsilon$},
        ylabel={$E/\epsilon$},
        axis x line=bottom,
        axis y line=left,
        ytick={0,1},
        xtick={0,0.5,1,1.5,2,2.5,3},
        axis line style={line width=1.25}
      ]
      \addplot[trace01,
        domain=0.01:3,
        samples=101,
        line width=2pt
      ]
      {2/(exp(1/x)+1)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[DarkGreen,->] (0,0) -- (4,0) ;
    \draw[DarkGreen,->] (0,0) -- (0,3) ;
    \draw[DarkGreen,->] (0,0) -- (230:1.5);
    \foreach \x/\y in {1/2.5, 2/1.5, 2/-1} {
        \fill[gray] (\x,\y) circle[radius=0.1];
      }
    \coordinate (A) at (3, -0.5);
    \coordinate (CM) at (1.5,1.5);
    \fill[gray] (A) circle[radius=0.1];

    \draw[line width=1.25,->] (0,0) --node[anchor=south east]{$\vb{R}$} (CM);
    \draw[line width=1.25,->] (CM) --node[anchor=west]{$\vb{r}_{i}'$} (A)
    node[anchor=north]{$m_{i}$};
    \draw[line width=1.25,->] (0,0) -- node[anchor=north]{$\vb{r}_{i}$} (A);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/exam
filename: phys-117-2015-mt1-key.tex
modified: 2015-10-01 15:05:16
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=0,
        ymax=1.2,
        xmin=0,
        xmax=3.2,
        enlargelimits=false,
        height=2in,
        width=2.5in,
        xlabel={$\kb T/\epsilon$},
        ylabel={$C/\kb$},
        axis x line=bottom,
        axis y line=left,
        ytick={0,1},
        xtick={0,0.5,1,1.5,2,2.5,3},
        axis line style={line width=1.25}
      ]
      \addplot[trace01,
        domain=0.01:3,
        samples=101,
        line width=2pt
      ]
      {2/x^2*exp(1/x)/(exp(1/x)+1)^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1,
      coord/.style={color=green!40!black,|->},
    ]
    \shade[ball color=blue!50!white, opacity=0.3] (0,0) circle[radius=3];
    % cartesian system
    \draw[coord,->] (0,0) -- (4,0) node[anchor=west]{$y$};
    \draw[coord,->] (0,0,0) -- (0,0,6) node[anchor=north east]{$x$};
    \draw[coord,->] (0,0) -- (0,4) node[anchor=south]{$z$};
    % cover up the z axis underneath an upcoming label
    \draw[gray!35!white] (0,1.7) -- ++(90:0.25);
    % coordinate of the point
    \coordinate (A) at (1.5,2.121, 1.5);
    \draw[line width=1, ->,color=DarkRed] (0,0,0) -- node[anchor=north west]{$r$}  (A);
    % projection to the xy plane
    \draw[dashed,color=DarkBlue] (A) -- (1.5, 0, 1.5) -- (0,0);
    % circle of latitude
    \draw[dashed] (2.2,2) arc[x radius=2.2, y radius=0.5, start angle=0, end
        angle=-180];
    \draw[dashed,opacity=0.2] (2.2,2) arc[x radius=2.2, y radius=0.5, start
        angle=0, end angle=180];
    % circle of longitude
    \draw[dashed,color=black] (0,-3) arc[x radius=1.075, y radius=3, start angle=-90,
        end angle=90];
    \draw[dashed,color=gray, opacity=0.2] (0,-3) arc[x radius=1.1, y radius=3,
        start angle=-90, end angle=-270];
    % definition of phi
    \draw[->] (0,0,0.5) arc[start angle=-135, end angle=-45,
        x radius=0.35, y radius =0.25];
    \node at (0,-0.5){$\phi$};
    % theta definition
    \draw[->] (0,0.6) arc[start angle=90, end angle=50,
        y radius=0.6, x radius = 0.4];
    \node at (0.2, 0.85) {$\theta$};
    % circle of longitude at \phi + d\phi
    \draw[dashed,color=black] (0,-3) arc[x radius=1.4, y radius=3, start angle=-90,
        end angle=90];
    \draw[dashed,color=gray, opacity=0.2] (0,-3) arc[x radius=1.4, y radius=3,
        start angle=-90, end angle=-270];
    % circle of latitude at \theta + d\theta
    \draw[dashed] (2.35,1.8) arc[x radius=2.35, y radius=0.5, start angle=0, end
        angle=-180];
    \draw[dashed,opacity=0.2] (2.35,1.8) arc[x radius=2.35, y radius=0.5, start
        angle=0, end angle=180];
    % label the arcs
    \draw[<-] (1.08,1.6) -- ++(135:0.3) node[anchor=east] {$r \sin\theta
        \dd\phi$};
    \draw[<-] (1.28,1.45) -- ++(-30:0.3) node[anchor=west] {$r \dd\theta$};
    % draw dA
    \fill[fill=black,opacity=0.2] (A) -- ++(6:0.27) -- ++(-75:0.2) -- ++(186:0.28)
    -- cycle;
    % label dA
    \draw[<-] (1.08,1.48) -- ++(-50:1) node[anchor=west]{$\dd{A} = r^{2} \sin\theta
        \dd{\phi} \dd{\theta}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/exam
filename: phys-117-2015-final-v1.tex
modified: 2015-12-18 00:17:25
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=1.5,
        ymin=0,
        ymax=1,
        enlargelimits=false,
        height=3.25in,
        width=4.5in,
        xlabel={$T$},
        ylabel={$C$},
      ]
      \addplot[trace01, domain=0.001:1.5, samples=101, line width=1.5pt]
      {(1 / (2*x*sinh(0.5/x)))^2};
      \addplot[trace02, domain=0.001:1.5, samples=101, line width=1.5pt]
      {1 / (2*x * cosh(0.5/x))^2};
      \addplot[trace03,line width=1.5pt] table {CDebye.dat};
      \node[trace01] at (0.7,0.78){(a)};
      \node[trace02] at (1.,0.27){(b)};
      \node[trace03] at (0.2,0.6){(c)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=0.75]
    \draw (0,0) circle[radius=3];
    \draw (0,0) -- (3.5,0) node[anchor=north]{$x$};
    \draw[->] (3,0) -- ++(90:3.5);
    \draw (0,0) -- node[anchor=south]{$r$}  (3,2);
    \draw[vel] (3,2) -- ++ (90:0.75) node[anchor=east]{$v$};
    \fill (3,2) circle[radius=0.05];
    \draw (0:0.8) arc(0:32:0.8);
    \node at (16:1.1) {$\theta$};
    \node at (1.5,-0.25) {$b$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/exam
filename: phys-117-2015-final-v1.tex
modified: 2015-12-18 00:17:25
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \draw[->] (0,0) -- (9,0) node[anchor=north]{$T$};
    \draw[->] (0,0) -- (0,6) node[anchor=east]{$E$};
    \node[anchor=east] at (0,0) {$0$};
    \node[anchor=east] at (0,1.25) {$\frac{1}{4}\mnrg$};
    \node[anchor=east] at (0,2.5) {$\frac{1}{2}\mnrg$};
    \node[anchor=east] at (0,3.75) {$\frac{3}{4} \mnrg$};
    \node[anchor=east] at (0,5) {$\mnrg$};
    \foreach \y in {1.25,2.5,3.75,5}{
        \draw[color=SlateGray,dashed] (0,\y) -- ++(9,0);
      }
    \foreach \x in {1,2,3,4} {
        \draw[color=SlateGray,dashed] (\x*2,0) -- ++(0,6);
      }
    \node[anchor=north] at (2,0) {$\displaystyle\frac{\mnrg}{\kb}$};
    \node[anchor=north] at (4,0) {$\displaystyle 2 \frac{\mnrg}{\kb}$};
    \node[anchor=north] at (6,0) {$\displaystyle 3 \frac{\mnrg}{\kb}$};
    \node[anchor=north] at (8,0) {$\displaystyle 4 \frac{\mnrg}{\kb}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[red, line width=2,shift={(0.05,0)}] (-0.1,-0.1) -- (0.1,0.1)
    (-0.1,0.1) -- (0.1,-0.1);
    \fill[fill=gray] (0,-2.5) rectangle (0.1,-4);
    \draw (0,0) rectangle (0.1,-4);
    \draw[coord,<->] (1,0) -- node[fill=white]{$d$} ++(-90:4);
    \draw[coord,<->] (0.5,0) -- node[fill=white]{$\alpha d$} ++(-90:2.5);
    \draw[coord] (-0.5,0) -- node[fill=white]{$x$} ++(-90:3.25);
    \draw[force] (-1.,-3.25) --node[anchor=north]{$\vb{\Delta P}$} ++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/exam
filename: phys-117-2015-mt2-v2.tex
modified: 2015-11-12 17:22:02
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \draw[<->] (6,0) node[anchor=north]{$T$} -- (0,0) -- (0,5)
    node[anchor=east]{$G$};
    % liquid
    \draw (0.5,4.5) .. controls (2,4) and (2.5,3.5) .. (5,1);
    \node at (1,4.75){Liquid};
    % solid
    \draw (0.75,4) .. controls (2.5,3.75) and (3.5,3.25) .. (5,2);
    \node at (0.75,3.5){Solid};
    % gas
    \draw (2,4.5) .. controls (3.25,4) and (3.6,3) .. (4,0.5);
    \node at (3.4,4) {Gas};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\radius{6}
    \draw[dashed] (0,0) arc(0:15:\radius) coordinate (A);
    \draw[DarkSlateBlue,dashed] (0,0) -- ++(180:1.5);
    \draw[DarkSlateBlue,dashed] (A) -- ++(195:1.5);
    \draw[vel] (0,0) -- ++(0:2) node[anchor=north]{$\ur(\theta)$};
    \draw[vel] (A) -- ++(15:2)
    node[anchor=west]{$\ur(\theta+\Delta\theta)$};
    \draw[vel,opacity=0.5] (0,0) -- ++(15:2) coordinate(B)
    node[anchor=south west]{$\ur(\theta + \Delta\theta)$};
    \draw[vel,DarkRed] (2,0) -- node[anchor=west]{$\Delta\ur$} (B);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \fill[fill=DarkRed] (0,0) circle[radius=0.1];
    \draw[force] (0,0) -- ++(-90:1.5) node[anchor=west]{$mg$};
    \draw[force] (0,0) -- ++(150:1.75) node[anchor=south]{$N$};
    \draw[accel] (-1,0) -- ++(180:1) node[anchor=south]{$a$};
    \draw[dashed] (0,0) -- (90:1.25);
    \draw[->] (0,1) arc(90:150:1);
    \node at (120:1.3){$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/exam
filename: phys-117-2015-mt1-v1.tex
modified: 2015-09-29 00:33:31
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \draw[->] (0,0) -- (4,0) node[anchor=north]{$T$};
    \draw[->] (0,0) -- (0,3) node[anchor=east]{$E$};
    \begin{scope}[shift={(8,0)}]
      \draw[->] (0,0) -- (4,0) node[anchor=north]{$T$};
      \draw[->] (0,0) -- (0,3) node[anchor=east]{$C$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) circle[radius=2];
    \draw (0,0) -- (-90:2);
    \draw (0,0) --node[anchor=south west]{$R$} (-30:2);
    \draw (-90:0.5) arc (-90:-30:0.5);
    \node at (-60:0.75) {$\theta$};
    \begin{scope}[shift={(-30:2)},rotate=60]
      \filldraw (-0.1,0) rectangle (0.1,0.1);
    \end{scope}

    \begin{scope}[shift={(4,0)},rotate=60]
      \draw (-0.3,-0.2) rectangle (0.3,0.2);
      \draw[force] (0,0) -- ++(-150:1.5) node[anchor=north]{$mg$};
      \draw[force] (0,-0.2) -- ++(90:1.5) node[anchor=east]{$N$};
      \draw[force] (0,-0.2) -- ++(180:1.5) node[anchor=north]{$f$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[DarkRed,line width=2] (0,3) -- (2,0);
    \draw[force] (1,1.5) --node[anchor=east]{$mg$} ++(-90:2);
    \draw[force] (2,0) -- ++(0,1.5) node[anchor=west]{$N_{1}$};
    \draw[force] (2,0) -- node[anchor=north]{$\mu N_{1}$} ++(-0.8,0);
    \draw[force] (0,3) -- ++(0:0.5) node[anchor=west]{$N_{2}$};
    \draw[force] (0,3) -- ++(90:0.5) node[anchor=east]{$\mu N_{2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (-1.5,0) -- (2.5,0) node[anchor=north]{$x$} ;
    \draw[dashed] (0, -1.5) -- (0, 1.5) node[anchor=east]{$y$};
    \foreach \y in {-1.2,1.2} {
        \filldraw[fill=white] (0,\y) circle[radius=0.15];
        \node at (0.4,\y) {$M$};
        \node at (0.25,\y/2) {$a$};
        \draw[line width=1.5] (-2,0) -- (1.5,0);
        \filldraw[fill=white] (-1.5,0) circle[radius=0.1];
        \node at (-1.5,0.35){$m$};
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm},>=stealth']
    \filldraw (0,0) circle(0.1);
    \draw[decorate] (0,0) -- (30:2);
    \shade[ball color=gray] (30:2) circle(0.25) ++(-90:0.25) node[anchor=north]{
        $m$ };
    \draw[decorate] (30:2.25) -- ++(30:2);
    \shade[ball color=gray] (30:4.5) circle(0.25) ++(-90:0.25)
    node[anchor=north]{$m$};
    \draw (30:1) ++(120:0.5) node {$k$};
    \draw (30:3) ++(120:0.5) node {$k$};
    \draw[->] (24:5) arc(24:36:5) node[anchor=south]{$\omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed,<-] (0,2.7) node[anchor=south]{$z$} -- (0,-2);
    \draw[dashed,->] (-1.5,0) -- (1.5,0) node[anchor=west]{$x$};
    \draw[->] (-0.25,2.4) arc[x radius=0.5,y radius=0.2,start angle=120,end angle=420];
    \draw[line width=2,color=gray] (2,1.5) --node[anchor=south]{$a$} (0,1.5)
    --node[anchor=east]{$b$} (0,0)
    -- node[anchor=west]{$b$} (0,-1.5)
    -- node[anchor=north]{$a$} (-2,-1.5) ;
    \shade[ball color=red] (2,1.5) circle[radius=0.25];
    \shade[ball color=red] (-2,-1.5) circle[radius=0.25];
    \node at (2.4,1.9) {$m$};
    \node at (-2.4,-1.9) {$m$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (-3,0) circle[radius=0.2];
    \node[anchor=south] at (-3, 0.2) {$m$};
    \draw[vel] (-2.8,0) -- ++(0:1) node[anchor=north]{$v_{0}$};
    \draw[dashed] (-1.7,0) -- (-0.2,0);
    \filldraw[color=black,fill=gray] (0,0) rectangle (0.3,4);
    \node[anchor=east] at (0,2) {$M$};
    \draw[coord,<->] (0.5,0) --node[anchor=west]{$\ell$} (0.5,4);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \coordinate (S) at (-4,0);
    \coordinate (E) at (4,0);
    \filldraw[fill=gray!20!white] (S) circle[radius=0.5];
    \node at (-4,-1) {Sun};
    \filldraw[fill=blue!20!white] (E) circle[x radius=1.5, y radius = 1.15];
    \filldraw[fill=brown!20!white] (E) circle[radius=1];
    \draw[->,line width=1.5] (S) --node[anchor=north]{$r_0$}(E);
    \draw[color=DarkGreen,->] (E) -- ++(0:1.75) node[anchor=west]{$x$};
    \draw[color=DarkGreen,->] (E) -- ++(90:1.75) node[anchor=south]{$y$};
    \draw[->,line width=1.5] (S) -- node[anchor=south]{$r$} (3.,0.88);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (-2,0) -- (2,0) (0,-1) -- (0,2);
    \draw[->,line width=1.25pt] (-1.5,0) -- ++(0:1) node[anchor=north]{$v$};
    \shade[shading=ball] (-1.5,0) circle[radius=0.25] node[anchor=south,shift={(0,0.25)}] {$2m$};
    \draw[->,line width=1.25pt] (0,1.5) -- ++(-90:1) node[anchor=west]{$v$};
    \shade[shading=ball] (0,1.5) circle[radius=0.15] node[anchor=west,shift={(0.25,0)}] {$m$};

    \begin{scope}[shift={(0,-3.5)}]
      \draw (-2,0) -- (2,0) (0,-2) -- (0,2);
      \coordinate (A) at (45:0.5);
      \draw[dashed] (A) -- ++(0:1);
      \draw[vel] (A) -- ++(30:1.5) node[anchor=south]{$U$};
      \draw (A) ++(0.5,0) arc(0:30:0.5);
      \node at ($(A) + (15:0.8)$) {$\theta$};
      \shade[shading=ball] (45:0.5) circle[radius=0.15]
      node[anchor=south,shift={(0,0.25)}] {$m$};
      \coordinate (B) at (0,-0.5);
      \draw[->,line width=1.25pt] (B) -- ++(-90:1) node[anchor=west]{$v$};
      \shade[shading=ball] (B) circle[radius=0.25] node[anchor=east,shift={(-0.25,0)}] {$2m$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\radius{3}
    \def\L{4}
    \def\rot{15}

    \draw (\radius,0) arc[radius=\radius,start angle=0, end angle=180]; % drum
    \draw[dashed] (0,0) -- (0,\radius); % show the original point of contact
    \draw (0,0) -- (90-\rot:\radius);

    % illustrate \theta
    \draw[<-] (90:2) arc(90:105:2);
    \draw[<-] (90-\rot:2) arc(90-\rot:75-\rot:2);
    \node at (90-\rot/2:2) {$\theta$};

    \begin{scope}[shift={(0,\radius)}]
      \draw[dashed] (\L/2, 0) rectangle (-\L/2,\L);
      \draw (0, \L/2) circle[radius=0.05];
    \end{scope}
    \begin{scope}[shift={(90-\rot:\radius)}, rotate=-\rot]
      \pgfmathsetmacro{\dx}{\radius * rad(\rot)}
      \fill (0,0) circle[radius=0.05]; % show the point of contact
      \draw[dotted] (0,0) -- ++(90+\rot:\L*1.2); % show a vertical line
      \draw (\L/2-\dx, 0) rectangle (-\L/2-\dx,\L);
      \draw[force] (-\dx,\L/2) --++ (-90+\rot:1) node[anchor=north]{$mg$};
      \fill (-\dx,\L/2) circle[radius=0.05];
    \end{scope}

    \draw[coord,<->] (-0.75*\radius,1) node[anchor=west]{$y$} -- ++(0,-1)
    -- ++(1,0) node[anchor=north]{$x$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
      xmin=0, xmax=120, ymin=0.95, ymax=1.4, enlargelimits=false,
      width=\columnwidth, height=0.67\columnwidth,
      xlabel={$\theta_{0} (^{\circ})$}, ylabel={$T/T_{0}$},
      ytick={1,1.1,1.2,1.3,1.4},
      xtick={0,30,...,120},
      % xticklabel=\empty, xticklabels{0,,$a$,,a$},
      % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0:120, samples=100, line width=2pt,]
      { 1 + (0.5 * sin(x/2))^2 + (3/8 * sin(x/2)^2)^2 +
        (5/16 * sin(x/2)^3)^2 + (35/128 * sin(x/2)^4)^2
        + (63/256 * sin(x/2)^5)^2 +
        (231/1024 * sin(x/2)^6)^2 +
        (429/2048 * sin(x/2)^7)^2 +
        (6435/32768 * sin(x/2)^8)^2
      };
    \end{axis}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \node[fill=yellow!20!white, text width=2.5in,draw=black] at (0,8) {Most problems are
      easier to solve using conservation laws than \( \vb{F} = m\vb{a} \) and \(
      \boldsymbol{\tau} = I  \boldsymbol{\alpha}  \), so your first job is to
      figure out whether you can use conservation laws.};

    \begin{scope}[shift={(7,7)}]
      \filldraw[fill=yellow!25!white,draw=DarkBlue] (-2.5,0) rectangle (2.5,-9.5);
      \node at (0,-0.5){\textbf{Conservation Laws}};

      \node[strategy] at (0,-2) {Momentum is conserved. Use \( \mathbf{p}_{0} =
        \mathbf{p}_{f} \).};
      \node[strategy] at (0, -5) {Angular momentum is conserved about this
        point. Use \( \mathbf{L}_{0} = \mathbf{L}_{f} \).};

      \node[strategy] at (0,-8) {Conserve energy using \( \displaystyle K = \frac{1}{2} MV^{2} +
        \sum_{i} \frac{1}{2} m_{i} v_{i}^{\prime 2}\) or a simplification.};

    \end{scope}
    \node[question] at (0,5) {Is there a net external force on the system?};
    \draw[flow,no] (3, 5) -- node[anchor=south]{\large No} +(0:1.25);
    \draw[flow] (0,4.25) -- node[anchor=west]{\large Yes} +(-90:1.);
    \node[question] at (0,2) {Can I choose a point in an inertial frame such that the
      sum of external torques about this point vanishes?};
    \draw[flow] (3, 2) -- node[anchor=south]{\large Yes} +(0:1.25);
    \draw[flow,no] (0, 0.75) -- node[anchor=west]{\large No} +(-90:1.);
    \node[question] at (0,-1.25) {Is mechanical energy conserved (if friction is
      present, does it do no work)?};
    \draw[flow] (3, -1.25) -- node[anchor=south]{\large Yes} +(0:1.25);
    \draw[flow,no] (0, -2.25) -- node[anchor=west]{\large No} +(-90:1.);

    \begin{scope}[shift={(0,-6.5)}]
      \node[strategy] at (0,2.5) {Use forces and torques.};
    \end{scope}



    \begin{scope}[shift={(16.5,10)}]
      \filldraw[fill=yellow!25!white,draw=DarkBlue] (-6,0) rectangle (6,-18);
      \node at (0,-0.5){\textbf{Forces and Torques}};
      \begin{scope}[shift={(-5.5,-0.75)}]
        \filldraw[fill=white,draw=DarkBlue] (0,-.25) rectangle (11,-7.75);
        \node at (1.5,-0.5) {\textbf{Select an Origin}};
        \node[question, text width=1.6in] at (2.5,-1.85) {Is there a fixed point in the problem, such as an
          axle, that will provide reaction forces?};
        \draw[flow] (5,-1.85) --node[anchor=south]{\large Yes} +(0:1.5);
        \node[strategy, text width=1.4in] at (8.5,-1.85) {It is usually helpful to compute torques and
          angular momenta about this point.};
        \draw[flow,no] (2.5,-3) -- node[anchor=west]{\large No} +(-90:1.);
        \node[strategy, text width=1.4in] at (8.5,-4.5) {It \emph{may} be easier to
          use the point of contact to calculate torques and/or angular momentum.};
        \node[question, text width=1.6in] at (2.5,-5.2) {Is there a point of contact
          about which an object instantaneously rotates?};
        \draw[flow] (5,-4.5) --node[anchor=south] {\large Yes} +(0:1.5);
        \node[strategy, text width=1.4in] at (8.5,-6.75) {Calculate torques about
          the center of mass.};
        \draw[flow,no] (2.5,-6.5) -- ++(-90:0.5) -- node[anchor=south]{\large No}
        ++(0:4);


      \end{scope}



      \begin{scope}[shift={(-4,-9)}]
        \filldraw[fill=green!25!white, draw=DarkBlue] (0,0) rectangle (8,-8.75);
        \node[anchor=west] at (0.25,-0.35){\textbf{Apply Newton's Laws}};
        \node[strategy,text width=2.25in] at (3.25,-1.5){Isolate each object and draw a diagram of the
          forces on it.};
        \node[strategy,text width=2.25in] at (3.25,-3){Apply \( \mathbf{F} = m
          \mathbf{a} \) to each object to get one or more dynamical equations.};
        \node[strategy,text width=2.25in] at (3.25,-4.5){Apply \( \boldsymbol{\tau}
          = I \boldsymbol{\alpha} \) to each object to get a dynamical equation.};
        \node[strategy,text width=2.25in] at (3.25,-6.25){Develop equations of
          constraint as necessary among dynamical variables.};
        \node[strategy,text width=2.25in] at (3.25,-8){When you have as many
          equations as unknowns, \emph{solve!}};
        \draw[flow] (6.75,-1.5) -- ++(0:0.2) arc(90:-90:0.5) -- ++(180:0.2);
        \draw[flow] (6.75,-3.25) -- ++(0:0.2) arc(90:-90:0.5) -- ++(180:0.2);
        \draw[flow] (6.75,-4.75) -- ++(0:0.2) arc(90:-90:0.5) -- ++(180:0.2);
        \draw[flow] (6.75,-6.75) -- ++(0:0.2) arc(90:-90:0.5) -- ++(180:0.2);
      \end{scope}
      \draw[flow] (5,-1.85) -- (5.7,-1.85) -- ++(-90:7) -- ++(180:4.5)
      --++(-90:1);
      \draw[flow,-] (5,-5.25) -- +(0:0.7) (5,-7.5) -- ++(0:0.7);
    \end{scope}

    % \draw[flow] (0, -4.5) -- ++(-90:0.5) -- ++(0:10) 
    % --++(90:14.75)
    % --++(0:3)
    % --++(-90:0.65);


    % flow line connecting the left side and the right
    \draw[flow] (2.5, -4) -- ++(0:7.5)
    --++(90:13.75)
    --++(0:3)
    --++(-90:0.65);

    \node at (-1.5,-7.75){Peter N.\ Saeta};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=1.5] (0,0) -- (0,3.5);
    \draw[line width=5,color=gray] (1,-0.15) -- (-1,-0.15);
    \fill (0,0) circle[radius=0.1];
    \draw[->] (0.5,2.5) arc(90:45:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[
      scale=2,
      >=Stealth,
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw [fill=gray!50!white] (0,0) -- (1,0) arc(0:90:1) -- cycle;
    \node at (0.5,-0.2) {$R$};
    \draw [fill=blue!50!white] (-2,0.4) circle (0.1);
    \node at (-2, 0.2) {$m$};
    \draw [->,line width=1.5pt,red!50!black] (-1.8,0.4) -- ++(0:0.5)
    node[anchor=north]{$\vv_{0}$};
    \node at (-1,-0.2) {top view};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[
      scale=1.25,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=1.5pt,color=blue,->},
    ]
    \draw[DarkSlateGray, line width=3] (0:2) arc(0:180:2);
    \draw[DarkSlateGray,->] (0,0) -- node[anchor=north west]{$R$} (45:2);
    \draw[dashed,->] (-2.25,0) -- (2.25,0) node[anchor=north]{$x$};
    \draw[dashed,->] (0,-0.25) -- (0, 2.25) node[anchor=south]{$y$};
    \fill (90:1) circle[radius=0.05];
    \node at (115:0.8) {$P$};

    \draw[dashed,line width=1.5pt,DarkSlateBlue] (-1.732,0) -- ++(90:1) --
    (1.732,1) -- (1.732,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[
      scale=1.25,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=1.5pt,color=blue,->},
    ]
    \draw[DarkSlateGray, line width=3] (0:2) arc(0:180:2);
    \draw[DarkSlateGray,->] (0,0) -- node[anchor=north west]{$R$} (45:2);
    \draw[dashed,->] (-2.25,0) -- (2.25,0) node[anchor=north]{$x$};
    \draw[dashed,->] (0,-0.25) -- (0, 2.25) node[anchor=south]{$y$};
    \fill (90:1) circle[radius=0.05];
    \node at (105:1) {$P$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (-2,0) -- (3,0) node[anchor=north]{$x$};
    \draw[dashed] (0,-2) -- (0,2) node[anchor=east]{$y$};
    % thick horizontal line
    \draw[line width=1.5] (-2,0) -- (2,0);
    % m
    \filldraw[fill=white] (-1.5,0) circle[radius=0.1]
    node[anchor=south,shift={(0,0.2)}]{$m$};
    \filldraw[fill=white] (0,1.5) circle[radius=0.2]
    node[anchor=west, shift={(0.2,0)}]{$M$};
    \filldraw[fill=white] (0,-1.5) circle[radius=0.2]
    node[anchor=west, shift={(0.2,0)}]{$M$};
    \foreach \y in {-0.75,0.75} {
        \node at (0.2,\y) {$a$};
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    % attempt to draw three-d rod
    \shade[left color=black!50, right color=black!30, middle color=black!10]  (-0.2,3) rectangle
    (0.2,-3);
    \draw[line width=1,->] (-0.4,2.7) arc[start angle=140,delta angle=280, x
        radius = 0.5, y radius = 0.1];
    \node at (0.75,2.7) {$\omega$};
    % upper string
    \draw (-0.21,2) arc[x radius=0.21, y radius=0.04, start angle=160,
        end angle=380];
    \draw (-0.21,-2) arc[x radius=0.21, y radius=0.04, start angle=160,
        end angle=380];
    \draw (0.2,-2) --node[below]{$l$} (2,0) --node[above]{$l$} (0.2,2);
    \shade[ball color=NavyBlue!70] (2,0) circle[radius=0.3];
    \node at (2.6,0){$m$};
    % arcs
    \draw (0.2,-2+0.65) arc(90:47:0.65);
    \node at (0.55,-1.1){$\dg{45}$};
    \draw (0.2,2-0.65) arc (-90:-47:0.65);
    \node at (0.55,1.1){$\dg{45}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (1.5,2.98) -- (0,0);
    \draw (-1.5,2.98) -- (0,0);
    \filldraw[fill=\background] (0,3) circle[x radius=1.5, y radius = 0.3];
    \draw (0,2) circle[x radius=1, y radius = 0.2];
    \draw[dashed, line width=1.5, ->] (0.5,2.175) -- ++(165:1.25)
    node[anchor=east]{$v_{0}$};
    \fill (0.5,2.175) circle[radius=0.075] node[anchor=south west]{$m$};
    \draw[dashed] (0,0) -- ++(0,1.75);
    \draw (0,1) arc(90:64:1);
    \node at (77:1.25){$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=8, ymin=0, ymax=8, enlargelimits=false,
        width=2.5in, height=2in,
        xlabel={$x$}, ylabel={$U(x)$}, ytick={0,2,...,8}, xtick={0,2,...,8},
        % xticklabel=\empty, xticklabels{0,,$a$,,a$},
        % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0.25:8, samples=100, line width=2pt,]
      {x + 2/x};
      \draw[dashed,DarkRed] (0,6) -- (8,6);
      \draw[DarkRed,<->] (1.414, 2.828) -- node[anchor=west]{$K_0$}
      (1.414,6);
    \end{axis}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=2] (0,0) circle[radius=2];
    \draw[force] (0,0) -- (-90:1.5) node[anchor=west] {$Mg$};
    \draw[force] (0,2) -- ++(90:1) node[anchor=west]{$T$};
    \foreach \theta in {60,120} {
        \fill[fill=gray,opacity=0.5] (\theta:2) circle[radius=0.2];
        \draw[force] (\theta:2) -- ++(\theta:1) node[anchor=south]{$N$};
      }

    \begin{scope}[shift={(0,-4)}]
      \fill[fill=gray!50] (0,0) circle[radius=0.5];
      \draw[force] (0,0) -- ++(-90:1.5) node[anchor=north]{$mg$};
      \draw[force] (0,0) -- ++(240:1.25) node[anchor=north east]{$N$};
      \draw[accel] (60:2) -- node[anchor=south east]{$a$}++(240:1);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=6,color=gray] (0,0) -- (2,0);
    \draw[force] (0,0) -- ++(90:1) node[anchor=south]{$F_{\rm v}$};
    \draw[force] (1,0) -- ++(-90:2) node[anchor=north]{$M g$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \def\background{white}
    \begin{scope}[rotate=-10]
      \fill [fill=gray!70] (2,0) rectangle (-2,-0.3);
      \draw (0,.75) circle[radius=.75];
      \draw[->] (0, 1.7) arc(90:60:0.9);
      \node at (0.25,1.8) {$\alpha$} ;
      \draw[coord,<->] (0,0.75) -- node[fill=\background] {$R$} ++(135:0.75);
      \draw[vel] (0,0.75)  node[anchor=north]{$a$} -- ++(0:0.6);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[force] (1,0) -- ++(105:1.5) node[anchor=south]{$T$};
    \draw[line width=2] (1,0) -- (3,0);
    \draw[force] (3,0) -- ++(-90:2) node[anchor=north]{$Mg$};
    \draw[dashed] (0,-2) -- (0,2);
    \draw[line width=2,color=DarkRed] (0.1,0.1) -- (-0.1,-0.1) (0.1,-0.1) -- (-0.1,0.1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \def\background{blue!10!white}
    \begin{scope}[rotate=-10]
      \fill [fill=gray!70] (2,0) rectangle (-2,-0.3);
      \draw (0,.75) circle[radius=.75];
      \draw[->] (0, 1.7) arc(90:60:0.9);
      \node at (0.25,1.8) {$\alpha$} ;
      \draw[coord,<->] (0,0.75) -- node[fill=\background] {$R$} ++(135:0.75);
      \draw[vel] (0,0.75)  node[anchor=north]{$a$} -- ++(0:0.6);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=2] (-2.5,-0.5) -- (2.5,-0.5);
    \filldraw[fill=gray] (-1.5,0) circle[radius=0.5];
    \filldraw[fill=gray] (1.5,0) circle[radius=0.5];
    \filldraw[fill=gray!25!white] (-2.5,0) rectangle (2.5,1.5);
    \draw[line width=2,color=DarkRed] (-0.1,0.5) -- (0.1,0.7) (0.1,0.5) --
    (-0.1,0.7);
    \draw[coord,<->] (-1.5,-1.25) --node[anchor=north]{$w$} (1.5,-1.25);
    \draw[->,line width=2] (2.75,0.75) -- ++(0:1) node[anchor=west] {$A$};

    \draw[force] (0,0.6) -- ++(-90:1.5) node[anchor=west]{$M g$};
    \draw[->,line width=2,dashed] (0,0.6) -- ++(180:1) node[anchor=east] {$MA$};
    \draw[dashed, line width=1.5] (0,0.6) -- (-2.25,-1.05);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) rectangle (4,0.25);
    \draw[force] (0.5,0) -- ++(90:1.2) node[anchor=south]{$N_{1}$};
    \draw[force] (3,0) -- ++(90:1.5) node[anchor=south]{$N_{2}$};
    \filldraw[fill=gray,opacity=0.2] (0.5,-0.5) circle[radius=0.5];
    \draw[force] (0.5,0) -- ++(0:0.9) node[anchor=north]{$F_{1}$};
    \filldraw[fill=gray,opacity=0.2] (3,-0.5) circle[radius=0.5];
    \draw[force] (3,0) -- ++(180:1.) node[anchor=north]{$F_{2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \foreach \x in {0, 1.5, 3} {
        \draw[spring] (\x,0) -- ++(0:1.5);
        \node at (\x+0.75, -0.5) {$k$};
      }
    \foreach \x in {1,2,3,4} {
        \filldraw[fill=gray] (1.5*\x-1.5,0) circle[radius=0.15];
        \node at (1.5*\x-1.5,-0.5) {$m$};
        \draw[coord] (1.5*\x-1.5,0.4) -- node[anchor=south]{$x_{\x}$} ++ (0:0.5);
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \shade[ball color=yellow] (30:3) circle[radius=0.5];
    \draw[force] (30:3) -- ++(210:1.25) node[anchor=south east]{$F$};
    \draw[accel] (30:1) --node[anchor=south east]{$a$} ++(210:1.25);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=0.75]
    \def\rad{2cm}
    \draw[dashed] (0,0) -- (-45:\rad)
    (0,0) -- (-135:\rad);
    \draw[dashed, <->] (-45:\rad/2) arc(-45:225:\rad/2);
    \node at (0,0.75*\rad){$\theta$};
    % now the rope 
    \draw[gray,line width=3] (-45:\rad+1.5pt) -- ++(-135:4)
    (-45:\rad+1.5pt) arc(-45:225:\rad+1.5pt) -- ++(-45:3);
    \begin{scope}[shift={(-45:\rad+1.5pt)}]
      \draw[force] (-135:4.2) -- ++(-135:1) node[anchor=north east]{$T_{A}$};
    \end{scope}
    \begin{scope}[shift={(-135:\rad+1.5pt)}]
      \draw[force] (-45:3.2) -- ++(-45:1) node[anchor=north east]{$T_{B}$};
    \end{scope}
    \begin{scope}[shift={(-135:\rad)}, rotate=-45]
      \fill[fill=white] (\rad-0.5pt,0.5pt) rectangle ++(4pt,1pt);
      \fill[fill=white] (\rad-0.5pt,-3.5pt) rectangle ++(4pt,-1pt);
    \end{scope}
    \draw (0,0) circle[radius=\rad];
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[SlateGray, fill=SlateGray!25] (0,0) -- (0,-2) -- (5, -2)
    coordinate (P) -- cycle;
    \draw (P) ++(180:1) arc(180:158.2:1);
    \draw (P) ++(168:1.05) node[anchor=east]{$\theta$};
    \node at (0.25,-1.75){$M$};
    \begin{scope}[rotate=-21.8]
      \filldraw[DarkSlateBlue, fill=SlateBlue!33](0.25, 0) rectangle (0.75,
      0.5);
      \node[rotate=-21.8] at (0.5, 0.25) {$m$};
    \end{scope}

    \draw[SlateGray, line width=3] (-1, -2.07) -- ++(7,0);


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \foreach \x in {1, 2, 3, 4} {
        \filldraw[fill=gray] (3*\x,0) rectangle ++(0.5,0.5);
        \node[anchor=south] at (3*\x+0.2,0.5) {$m_{\x}$};
      }
    \draw[line width=2] (2.5,-0.075) -- ++(0:11);
    \draw[vel] (3.7,0.25) -- node[anchor=south]{$v_{1}$} ++(0:1.25);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \fill[fill=gray] (-3,0) rectangle (3,-0.2);
    \draw (-1, 1.82) -- (-0.24, 1.82);
    \draw (-0.1,1.675) -- ++(-90:0.5);
    \coordinate (A) at (-0.25,1.675);
    \fill[fill=gray!50!white] (A) circle[radius=0.15];

    \draw[fill=gray!20!white] (-2,0) -- ++(90:1.5)
    -- ++(0:1.5) --  ++(45:0.2914) arc(135:-45:0.05)
    -- ++(-135:0.35) -- ++(-90:1) -- ++(0:0.6)
    -- ++(90:1.1) -- ++(0:1) --++(-90:1.48) -- cycle;
    \fill (A) circle[radius=0.025];
    \draw[fill=gray!15!white] (-1.75,1.5) rectangle node{$M_{2}$} (-1,2);
    \draw[fill=gray!15!white] (-0.45,1.25) rectangle node{$M_{3}$} (0.1,0.75);
    \node at (-1.5, 0.25) {$M_{1}$};
    \draw[force] (-3,0.75) -- node[anchor=south]{$F$} (-2,0.75);

    %      \draw[coord] (-3,0.25) -- node[anchor=south]{$x_{1}$} ++(0:1);
    %      \draw[coord] (-2,2) --node[anchor=south]{$x_{2}$} (-1.75,2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\a{2}
    \def\b{1.5}
    \pgfmathsetmacro{\c}{sqrt(\a*\a-\b*\b)};
    \draw[->] (0,-2) -- (0,2.5) node[anchor=east]{$y$};
    \draw[->] (-2,0) -- (4,0) node[anchor=north]{$x$};
    \draw[line width=2] (\c,0) circle[x radius=\a, y radius=\b];

    \draw[dashed] (\c,-2) -- ++(90:4); % vertical through center
    \draw[DarkGreen,<->] (\c,-1.75) -- node[anchor=north]{$a$} ++(\a,0);
    \draw[DarkGreen,<->] (\c+2.25,0) -- node[anchor=west]{$b$} ++(-90:\b);
    \draw[DarkGreen,<->] (0,-0.25) --node[anchor=north]{$c$} ++(\c,0);

    % show the foci
    \foreach \x in {0,2*\c}{
        \fill (\x,0) circle[radius=0.05];
      }
    % show a point on the ellipse

    \draw[DarkRed] (0,0) --node[anchor=south]{$r$}
    ++(30:2.6) -- (2*\c,0);
    \draw (0.5,0) arc[start angle=0,end angle=30,radius=0.5];
    \node at (15:0.8) {$\theta$};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!50!white] (-0.5,0.5) --
    ++(0:0.75) % top
    arc(90:-90:0.5) % right arc
    -- ++(180:0.75) % bottom
    -- cycle;
    \draw[force] (-1.5,0) node[anchor=east]{$N_{h}$} -- (-0.5,0);
    \draw[force] (0,0) -- ++(-90:1) node[anchor=north]{$Mg$};
    \draw[force,<-] (0.25,0) ++(-30:0.5) --node[anchor=south west]{$F$} ++(-30:1.5)
    coordinate (A);
    \draw[dashed] (A) -- ++(180:1.);
    \draw (A) ++(180:0.5) arc(180:150:0.5);
    \draw (A) ++(165:1) node {$\theta$};


    \node at (0, -2.25){\begin{minipage}{2in}
        \begin{align}
          N_{h}     & = F\cos\theta\label{eq:1}       \\
          M\ddot{y} & = F\sin\theta - Mg \label{eq:2}
        \end{align}
      \end{minipage}
    };

    \begin{scope}[shift={(6,0)}]
      \filldraw[fill=gray!50!white] (-0.5,-0.5) --
      ++(90:0.75)
      arc(180:0:0.5)
      -- ++(-90:0.75)
      -- cycle;
      \draw[force] (-0.1,0) -- ++(-90:1.25) node[anchor=north]{$Mg$};
      \draw[force] (0.1,-0.5) -- ++(90:2) node[anchor=south] {$N_{v}$};
      \draw[force,<-] (0,0.25) ++(150:0.5) coordinate (B)
      -- node[anchor=south]{$F$} ++(150:1.5);
      \draw[force] (0,-0.5) -- ++(180:1) node[anchor=south]{$F_{f}$};
      \draw[dashed] (B) -- ++(180:1.5);
      \draw (B) ++(180:0.5) arc(180:150:0.5);
      \draw (B) ++(165:1) node {$\theta$};

      \node at (0, -2.25) {
        \begin{minipage}{2in}
          \begin{align}
            N_{v}     & = Mg + F\sin\theta \label{eq:3}    \\
            M\ddot{x} & = F\cos\theta - F_{f} \label{eq:4}
          \end{align}
        \end{minipage}
      };
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!50] (0,0) circle[radius=3];
    \fill (0,0) circle[radius=0.05];
    \draw[coord,->] (30:3.5) arc(30:60:3.5);
    \node[coord] at (45:3.7) {$\omega$};
    \foreach \q/\r in {30/1,90/1.5,240/2,150/2.5, 330/1.75, 180/0.75} {
        \fill[gray] (\q:\r) circle[radius=0.1];
        \draw[vel] (\q:\r) ++(\q+90:.15) -- ++(\q+90:\r) node[shift={(\q:.25)}]{$v$};
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \def\fat{0.25}
    \fill[gray!50] (0,0) -- (3,0) -- ++(0,-\fat) -- (\fat,-\fat) --
    (\fat,-1.5) -- (0,-1.5) -- cycle;
    \draw (0,-1.5) -- (0,0) -- (3,0);

    \draw[line width=1.5pt, DarkGreen] (2,0.05) -- ++(180:3);
    \fill (1.95,0.18) circle[radius=0.1];
    \fill (-0.95,0.18) circle[radius=0.1];
    \draw[vel,line width=1] (-1.25,0.5) -- node[anchor=east] {$v_{0}$}
    ++(-90:0.6);
    \node[anchor=south] at (1.95,0.28) {$m$};
    \node[anchor=south] at (-0.95,0.28) {$m$};
    \node[anchor=south] at (-0.5,0.05) {$a$};
    \node[anchor=south] at (1,0.05) {$b$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \node[fill=yellow!20!white, text width=2.5in,draw=black] at (0,8) {Most problems are
      easier to solve using conservation laws than \( \vb{F} = m\vb{a} \) and \(
      \boldsymbol{\tau} = I  \boldsymbol{\alpha}  \), so your first job is to
      figure out whether you can use conservation laws.};

    \begin{scope}[shift={(7,7)}]
      \filldraw[fill=yellow!25!white,draw=DarkBlue] (-2.5,0) rectangle (2.5,-9.5);
      \node at (0,-0.5){\textbf{Conservation Laws}};

      \node[strategy] at (0,-2) {Momentum is conserved. Use \( \mathbf{p}_{0} =
        \mathbf{p}_{f} \).};
      \node[strategy] at (0, -5) {Angular momentum is conserved about this
        point. Use \( \mathbf{L}_{0} = \mathbf{L}_{f} \).};

      \node[strategy] at (0,-8) {Conserve energy using \( \displaystyle K = \frac{1}{2} MV^{2} +
        \sum_{i} \frac{1}{2} m_{i} v_{i}^{\prime 2}\) or a simplification.};

    \end{scope}
    \node[question] at (0,5) {Is there a net external force on the system?};
    \draw[flow,no] (3, 5) -- node[anchor=south]{\large No} +(0:1.25);
    \draw[flow] (0,4.25) -- node[anchor=west]{\large Yes} +(-90:1.);
    \node[question] at (0,2) {Can I choose a point in an inertial frame such that the
      sum of external torques about this point vanishes?};
    \draw[flow] (3, 2) -- node[anchor=south]{\large Yes} +(0:1.25);
    \draw[flow,no] (0, 0.75) -- node[anchor=west]{\large No} +(-90:1.);
    \node[question] at (0,-1.25) {Is mechanical energy conserved (if friction is
      present, does it do no work)?};
    \draw[flow] (3, -1.25) -- node[anchor=south]{\large Yes} +(0:1.25);
    \draw[flow,no] (0, -2.25) -- node[anchor=west]{\large No} +(-90:1.);

    \begin{scope}[shift={(0,-6.5)}]
      \node[strategy] at (0,2.5) {Use forces and torques.};
    \end{scope}



    \begin{scope}[shift={(16.5,10)}]
      \filldraw[fill=yellow!25!white,draw=DarkBlue] (-6,0) rectangle (6,-18);
      \node at (0,-0.5){\textbf{Forces and Torques}};
      \begin{scope}[shift={(-5.5,-0.75)}]
        \filldraw[fill=white,draw=DarkBlue] (0,-.25) rectangle (11,-7.75);
        \node at (1.5,-0.5) {\textbf{Select an Origin}};
        \node[question, text width=1.6in] at (2.5,-1.85) {Is there a fixed point in the problem, such as an
          axle, that will provide reaction forces?};
        \draw[flow] (5,-1.85) --node[anchor=south]{\large Yes} +(0:1.5);
        \node[strategy, text width=1.4in] at (8.5,-1.85) {It is usually helpful to compute torques and
          angular momenta about this point.};
        \draw[flow,no] (2.5,-3) -- node[anchor=west]{\large No} +(-90:1.);
        \node[strategy, text width=1.4in] at (8.5,-4.5) {It \emph{may} be easier to
          use the point of contact to calculate torques and/or angular momentum.};
        \node[question, text width=1.6in] at (2.5,-5.2) {Is there a point of contact
          about which an object instantaneously rotates?};
        \draw[flow] (5,-4.5) --node[anchor=south] {\large Yes} +(0:1.5);
        \node[strategy, text width=1.4in] at (8.5,-6.75) {Calculate torques about
          the center of mass.};
        \draw[flow,no] (2.5,-6.5) -- ++(-90:0.5) -- node[anchor=south]{\large No}
        ++(0:4);


      \end{scope}



      \begin{scope}[shift={(-4.5,-9)}]
        \filldraw[fill=green!25!white, draw=DarkBlue] (0,0) rectangle (9,-8.75);
        \node[anchor=west] at (0.25,-0.35){\textbf{Apply Newton's Laws}};

        \node[strategy,text width=2.25in] at (3.75,-1.5){Isolate each object and
          draw a diagram of the forces on it.};
        \node[strategy,text width=2.25in] at (5,-3){Apply \( \mathbf{F} = m
          \mathbf{a} \) to each object to get one or more dynamical equations.};
        \node[strategy,text width=2.25in] at (3.75,-4.5){Apply \( \boldsymbol{\tau}
          = I \boldsymbol{\alpha} \) to each object to get a dynamical equation.};
        \node[strategy,text width=2.25in] at (5,-6.25){Develop equations of
          constraint as necessary among dynamical variables.};
        \node[strategy,text width=2.25in] at (3.75,-8){When you have as many
          equations as unknowns, \emph{solve!}};

        \draw[flow] (7.0,-1.5) -- ++(0:0.25)  arc(90:0:0.5) -- ++(-90:0.2);
        \draw[flow] (1.75,-3) -- ++(180:0.25) arc(90:180:0.5) -- ++(-90:0.2);

        \draw[flow] (7.,-4.5) -- ++(0:0.25) arc(90:0:0.5) -- ++(-90:0.2);

        \draw[flow] (1.75,-6.5) -- ++(180:0.25) arc(90:180:0.5) -- ++(-90:0.2);
      \end{scope}
      \draw[flow] (5,-1.85) -- (5.7,-1.85) -- ++(-90:7) -- ++(180:4.5)
      --++(-90:1);
      \draw[flow,-] (5,-5.25) -- +(0:0.7) (5,-7.5) -- ++(0:0.7);
    \end{scope}

    % \draw[flow] (0, -4.5) -- ++(-90:0.5) -- ++(0:10) 
    % --++(90:14.75)
    % --++(0:3)
    % --++(-90:0.65);


    % flow line connecting the left side and the right
    \draw[flow] (2.5, -4) -- ++(0:7.5)
    --++(90:13.75)
    --++(0:3)
    --++(-90:0.65);

    \node at (-1.5,-7.75){Peter N.\ Saeta};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!15] (-2,-0.05) rectangle (2, 0.05) ;
    \fill (0,0) circle[radius=0.02];
    \draw[coord] (0,0.15) -- ++(0:1) node[anchor=south]{$x$};
    \fill[DarkSlateGray] (0.95,-0.05) rectangle (1.05,0.05);
    \node[anchor=north] at (1,-0.15) {$\dd{m} = \frac{M}{\ell} \dd{x} $};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.25]
    \def\a{1.5}
    \def\b{2}
    \draw[dashed] (0,\b+0.5) -- (0,-\b-0.5);
    \draw[line width=2] (\a,\b) --node[anchor=south]{$b$} (0,\b)
    -- (0,-\b) -- node[anchor=north]{$b$} (-\a,-\b);

    \foreach \x/\y in {\a/\b, -\a/-\b}{
        \draw[dashed, gray] (0,\y) circle[x radius=\a, y radius=0.25];
        \shade[ball color=SlateGray] (\x,\y) circle[radius=0.25];
        \node at (1.4*\x,\y) {$m$};
        \foreach \q in {0,180}{
            \fill[Red] (0,0.925*\y) ++(\q-45:0.08) rectangle ++(\q+45:0.16);
          }}
    \draw[DarkGreen,->] (0.4,2.65) arc[start angle=45,
        end angle=300,x radius=0.5, y radius=0.15];
    \node[DarkGreen] at (-0.65,2.6){$\omega$};
    \fill[yellow] (0,0) circle[radius=0.05];
    \draw[DarkGreen,<->] (-0.5,0) -- node[anchor=east]{$c$} ++(90:\b);
    \draw[DarkGreen,<->] (-0.5,0) -- node[anchor=east]{$c$} ++(-90:\b);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\a{1.5}
    \def\b{2}
    \draw[dashed] (0,\b+0.5) -- (0,-\b-0.5);
    \draw[line width=2] (\a,\b) --node[anchor=south]{$b$} (0,\b)
    -- (0,-\b) -- node[anchor=north]{$b$} (-\a,-\b);

    \foreach \x/\y in {\a/\b, -\a/-\b}{
        \draw[dashed, gray] (0,\y) circle[x radius=\a, y radius=0.25];
        \shade[ball color=DarkSlateBlue] (\x,\y) circle[radius=0.25];
        \node at (1.4*\x,\y) {$m$};
        \foreach \q in {0,180}{
            \fill[Red] (0,0.925*\y) ++(\q-45:0.08) rectangle ++(\q+45:0.16);
          }}
    \draw[DarkGreen,->] (0.4,2.65) arc[start angle=45,
        end angle=300,x radius=0.5, y radius=0.15];
    \node[DarkGreen] at (-0.65,2.6){$\omega$};
    \fill[yellow] (0,0) circle[radius=0.05];
    \draw[DarkGreen,<->] (-0.5,0) -- node[anchor=east]{$c$} ++(90:\b);
    \draw[DarkGreen,<->] (-0.5,0) -- node[anchor=east]{$c$} ++(-90:\b);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[dashed] (-0.5,0) -- (5,0);
    \draw[dashed] (3.5,0) coordinate(A) ++(45:0.25)-- ++(45:2)
    coordinate(B);
    \draw[vel] (B) ++(45:0.25) -- ++(45:1) node[anchor=south]{$v_{1}$};
    \shade[ball color=DarkRed,opacity=0.5] (B) circle[radius=0.2];
    \shade[ball color=DarkRed]  (0,0) circle[radius=0.2]
    node[anchor=south,shift={(0,0.2)}] {$m_{1}$};
    \shade[ball color=DarkGreen]  (A) circle[radius=0.2]
    node[anchor=south,shift={(0,0.2)}] {$m_{2}$};
    \draw[vel] (0.3,0) -- ++(0:1) node[anchor=south]{$v_{0}$};
    \draw (A) ++(0:1) arc(0:45:1);
    \begin{scope}[shift={(3.5,0)}]
      \node[anchor=west] at (27.5:1) {$\theta$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=0.6]
    \node at (-2.5, 2.25) {\textsf{\small top view}};
    \filldraw[fill=gray!50] (0,0) circle[radius=2];
    \draw[->,line width=1] (0,0) --node[anchor=east]{$r$} (0,-1.45);
    \fill (0,-1.5) circle[radius=0.05];
    \draw[<-] (0,-1.5) ++(-45:0.1) -- ++(-40:0.8) node[anchor=west]{landing site};
    \node[anchor=west] at (135:1.75) {$M,R$};
    \coordinate (child) at (-3, -1.5);
    \fill[color=DarkRed] (child) circle[radius=0.1];
    \node[anchor=south,shift={(90:0.2)}] at (child) {$M$};
    \draw[vel,line width=1] (child) ++(0.2,0) --node[anchor=north]{$v$} ++(0:1);
    \draw[<-,DarkGreen] (child) ++(-60:0.2) -- ++(-60:0.95) -- ++(0:0.25)
    node[anchor=west]{incoming child};
    \draw[dotted] (-1.75,-1.5) -- (0.5, -1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[color=SlateBlue!50!white,line width=1.5] (0,0) sin (3,2) cos (6,0);
    \draw[color=SlateGray,->] (0,0) -- (7,0) node[anchor=north]{$t$};
    \draw[color=SlateGray,->] (0,0) -- (0,3) node[anchor=east]{$y$};
    \draw[color=DarkRed] (0,0) -- ++(46.3:4.5);
    \fill[color=DarkGreen] (0,0) circle[radius=0.05] node[anchor=east]{$A$};
    \draw[color=DarkGreen] (46.3:1) circle[radius=0.05] node[anchor=south
        east]{$B$} -- ++(-90:.705);
    \draw[color=DarkGreen] (46.3:4) circle[radius=0.05] node[anchor=south
        east]{$C$} -- ++ (-90:2.87);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=0.6,
      decoration={coil,aspect=0.3,segment
          length=3mm,amplitude=3mm},
      >=stealth',
      beef/.style={line width=1.5}]
    \draw[line width=2] (-1,0) -- (3.5,0);
    \draw[line width=2] (-1,6) -- +(0:4.5);
    \draw[line width=2] (4.5,0) -- +(0:3) (4.5,6) -- +(0:3);
    % Draw the applied force
    \draw[->, beef] (0,3) -- (0,1.5)
    node[anchor=north]{$\VEC{F}$};
    % Draw the second spring
    \draw[decorate,beef] (2,0) -- ++(90:2);
    \draw[beef] (2,2) -- (2,3);
    \node at (2.9,.8) {$k_{2}$};
    % Draw the pulley
    \filldraw[fill=blue!10!white,draw=blue] (1,3) circle(1);
    \filldraw[fill=blue!50!black] (1,3) circle(0.05);
    % Draw the first spring
    %\usetikzlibrary{decorations.pathmorphing}
    \draw[decorate,beef] (1,6) -- ++(270:2) ;
    \node at (1.9,5.2) {$k_{1}$};
    \draw[beef] (1,3) -- (1,4);
    % Draw the effective spring
    \draw[decorate,beef] (6,6) -- (6,3.5);
    \node at (6.9,4.8){$k_{\rm eff}$};
    \draw[beef,->] (6,3.5) -- (6,3) node[anchor=north]{$\VEC{F}$};
    \draw[dashed] (4,-0.5) -- (4,6.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.25,
      coord/.style={color=green!40!black,|->},
    ]
    \shade[ball color=blue!50!white, opacity=0.3] (0,0) circle[radius=3];
    % cartesian system
    \draw[coord,->] (0,0) -- (4,0) node[anchor=west]{$y$};
    \draw[coord,->] (0,0,0) -- (0,0,6) node[anchor=north east]{$x$};
    \draw[coord,->] (0,0) -- (0,4) node[anchor=south]{$z$};
    % cover up the z axis underneath an upcoming label
    \draw[gray!35!white] (0,1.7) -- ++(90:0.25);
    % coordinate of the point
    \coordinate (A) at (1.5,2.121, 1.5);
    \draw[line width=1, ->,color=DarkRed] (0,0,0) -- node[anchor=north west]{$r$}  (A);
    % projection to the xy plane
    \draw[dashed,color=DarkBlue] (A) -- (1.5, 0, 1.5) -- (0,0);
    % circle of latitude
    \draw[dashed] (2.2,2) arc[x radius=2.2, y radius=0.5, start angle=0, end
        angle=-180];
    \draw[dashed,opacity=0.2] (2.2,2) arc[x radius=2.2, y radius=0.5, start
        angle=0, end angle=180];
    % circle of longitude
    \draw[dashed,color=black] (0,-3) arc[x radius=1.075, y radius=3, start angle=-90,
        end angle=90];
    \draw[dashed,color=gray, opacity=0.2] (0,-3) arc[x radius=1.1, y radius=3,
        start angle=-90, end angle=-270];
    % definition of phi
    \draw[->] (0,0,0.5) arc[start angle=-135, end angle=-45,
        x radius=0.35, y radius =0.25];
    \node at (0,-0.4){$\phi$};
    % theta definition
    \draw[->] (0,0.6) arc[start angle=90, end angle=50,
        y radius=0.6, x radius = 0.4];
    \node at (0.2, 0.75) {$\theta$};
    % circle of longitude at \phi + d\phi
    \draw[dashed,color=black] (0,-3) arc[x radius=1.4, y radius=3, start angle=-90,
        end angle=90];
    \draw[dashed,color=gray, opacity=0.2] (0,-3) arc[x radius=1.4, y radius=3,
        start angle=-90, end angle=-270];
    % circle of latitude at \theta + d\theta
    \draw[dashed] (2.35,1.8) arc[x radius=2.35, y radius=0.5, start angle=0, end
        angle=-180];
    \draw[dashed,opacity=0.2] (2.35,1.8) arc[x radius=2.35, y radius=0.5, start
        angle=0, end angle=180];
    % label the arcs
    \draw[<-] (1.08,1.6) -- ++(135:0.3) node[anchor=east] {$r \sin\theta
        \dd\phi$};
    \draw[<-] (1.28,1.45) -- ++(-30:0.3) node[anchor=west] {$r \dd\theta$};
    % draw dA
    \fill[fill=black,opacity=0.2] (A) -- ++(6:0.27) -- ++(-75:0.2) -- ++(186:0.28)
    -- cycle;
    % label dA
    \draw[<-] (1.08,1.48) -- ++(-50:1) node[anchor=west]{$\DD A = r^{2} \sin\theta
        \dd \phi \dd \theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.25]
    \shade[ball color=blue!50!white, opacity=0.3] (0,0) circle[radius=3];
    % cartesian system
    \draw[coord,->] (0,0) -- (4,0) node[anchor=west]{$y$};
    \draw[coord,->] (0,0,0) -- (0,0,6) node[anchor=north east]{$x$};
    \draw[coord,->] (0,0) -- (0,4) node[anchor=south]{$z$};
    % cover up the z axis underneath an upcoming label
    \draw[gray!35!white] (0,1.7) -- ++(90:0.25);
    % coordinate of the point
    \coordinate (A) at (1.5,2.121, 1.5);
    \draw[line width=1, ->,color=DarkRed] (0,0,0) -- node[anchor=north west]{$r$}  (A);
    % projection to the xy plane
    \draw[dashed,color=DarkBlue] (A) -- (1.5, 0, 1.5) -- (0,0);
    % circle of latitude
    \draw[dashed] (2.2,2) arc[x radius=2.2, y radius=0.5, start angle=0, end
        angle=-180];
    \draw[dashed,opacity=0.2] (2.2,2) arc[x radius=2.2, y radius=0.5, start
        angle=0, end angle=180];
    % circle of longitude
    \draw[dashed,color=black] (0,-3) arc[x radius=1.075, y radius=3, start angle=-90,
        end angle=90];
    \draw[dashed,color=gray, opacity=0.2] (0,-3) arc[x radius=1.1, y radius=3,
        start angle=-90, end angle=-270];
    % definition of phi
    \draw[->] (0,0,0.5) arc[start angle=-135, end angle=-45,
        x radius=0.35, y radius =0.25];
    \node at (0,-0.4){$\phi$};
    % theta definition
    \draw[->] (0,0.6) arc[start angle=90, end angle=50,
        y radius=0.6, x radius = 0.4];
    \node at (0.2, 0.75) {$\theta$};
    % circle of longitude at \phi + d\phi
    \draw[dashed,color=black] (0,-3) arc[x radius=1.4, y radius=3, start angle=-90,
        end angle=90];
    \draw[dashed,color=gray, opacity=0.2] (0,-3) arc[x radius=1.4, y radius=3,
        start angle=-90, end angle=-270];
    % circle of latitude at \theta + d\theta
    \draw[dashed] (2.35,1.8) arc[x radius=2.35, y radius=0.5, start angle=0, end
        angle=-180];
    \draw[dashed,opacity=0.2] (2.35,1.8) arc[x radius=2.35, y radius=0.5, start
        angle=0, end angle=180];
    % label the arcs
    \draw[<-] (1.08,1.6) -- ++(135:0.3) node[anchor=east] {$r \sin\theta
        \dd\phi$};
    \draw[<-] (1.28,1.45) -- ++(-30:0.3) node[anchor=west] {$r \dd\theta$};
    % draw dA
    \fill[fill=black,opacity=0.2] (A) -- ++(6:0.27) -- ++(-75:0.2) -- ++(186:0.28)
    -- cycle;
    % label dA
    \draw[<-] (1.08,1.48) -- ++(-50:1) node[anchor=west]{$\DD A = r^{2} \sin\theta
        \dd \phi \dd \theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=1.5] (0,0) -- (0,3.5);
    \draw[line width=5,color=gray] (1,-0.1) -- (-1,-0.1);
    \fill (0,0) circle[radius=0.1];
    \draw[->] (0.5,2.5) arc(90:45:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (1.5,2.98) -- (0,0);
    \draw (-1.5,2.98) -- (0,0);
    \filldraw[fill=white] (0,3) circle[x radius=1.5, y radius = 0.3];
    \draw (0,2) circle[x radius=1, y radius = 0.2];
    \draw[dashed, line width=1.5, ->] (0.5,2.175) -- ++(165:1.25)
    node[anchor=east]{$v_{0}$};
    \fill (0.5,2.175) circle[radius=0.075] node[anchor=south west]{$m$};
    \draw[dashed] (0,0) -- ++(0,1.75);
    \draw (0,1) arc(90:64:1);
    \node at (77:1.25){$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) rectangle node {$m$} (2,1);
    \draw[vel] (2.2,0.5) -- ++(0:1) node[anchor=west]{$v$};
    \draw[->,line width=3,color=DarkRed] (-1.5,0.5) --
    node[anchor=south]{$\Delta p$} ++(0:1.25);
    \node[anchor=west] at (-2,0) {$t$};

    \draw[dashed] (-2, -0.5) -- ++(0:5.5);

    \begin{scope}[shift={(0,-2)}]
      \draw (0,0) rectangle node {$m + \Delta m$} (2,1);
      \draw[vel] (2.2,0.5) -- ++(0:1.2) node[anchor=west]{$v + \Delta v$};
      \node[anchor=west] at (-2,1) {$t + \Delta t$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \shade [ball color=blue!50] (0,0) circle[radius=1];
    \node at (-0.7,1.1) {$m$};
    \draw (0,0) -- node[anchor=south west]{$R$} ++(135:1);
    \draw[vel] (0,0) -- ++(0:2) node[anchor=south]{$v_{0}$};

    \draw[line width=1.5] (-1,-1) -- (14,-1);
    \draw[<-] (4.5,-0.9) -- ++(45:1) node[anchor=west]{\small \textsf{frictionless ice}};

    \begin{scope}[shift={(12,-1)}]
      \draw[line width=3,color=DarkRed,opacity=0.3] (0,3) -- ++(-65:2.9);
      \draw[->] (0,2) arc(-90:-65:1);
      \node at (0.3,1.7){$\theta$};
      \draw[line width=3,color=DarkRed] (0,0.1) -- (0,3);
      \fill (0,3) circle[radius=0.1];
      \draw[<-] (0.1,3.1) -- ++(45:0.5) node[anchor=west]{\textsf{\small
          frictionless pivot}};
      \node at (-0.5,3.3) {$3m$};
      \draw[<->] (-0.75,0.1) --node[anchor=east]{$d$} (-0.75,3);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\lim{2}
    \begin{axis}[
        xmin=-\lim,
        xmax=\lim,
        ymin=-\lim,
        ymax=\lim,
        enlargelimits=false,
        width=4.5in,
        height=4.5in,
        xlabel={xlabel},
        ylabel={ylabel},
        %ytick={0,1},
        %xtick={0,0.5,1,1.5,2},
        xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
      ]
      \addplot[
        trace01,
        domain=0:1080,
        samples=201,
        line width=2pt,
        data cs=polar,
      ]
      {x/(3.141592*180)};

      % \tikzmath{
      %   int \qdeg;
      %   real \theta, \r, \ar, \aq, \amag, \aangle;
      %   for \qdeg in {60, 180, ..., 540}{
      %     \node at (1,1) {$\qdeg$};
      %   }
      % };
      %     \tikzmath{
      %         int \qdeg;
      %         real \theta, \r, \ar, \aq, \amag, \aangle;
      %         for \qdeg in {60, 180, ..., 540}{

      %       \theta = \qdeg * 3.1415927 / 180.0;
      %       \r = \qdeg / 180.0;
      %       \ar = 1 - 2 * \theta * \theta;
      %       \aq = 5 * \theta;
      % %      \amag = sqrt(\ar*\ar + \aq*\aq);
      % %      \aangle = atan(\aq / \ar);

      %       % \pgfmathsetmacro{\theta}{\qdeg/180.0*3.1415927}
      %       % \pgfmathsetmacro{\r}{\qdeg/180.0}
      %       % \pgfmathsetmacro{\ar}{1-2*\theta*\theta}
      %       % \pgfmathsetmacro{\aq}{5*\theta}

      %       % \pgfmathsetmacro{\amag}{sqrt(\ar*\ar+\aq*\aq)}
      %       % \pgfmathsetmacro{\aangle}{\qdeg+atan(\aq/\ar)}
      %       %\draw[->] (\qdeg:\r) -- ++(\aangle:\amag);
      %       \draw[->] (30:1.5) -- ++(120:0.75);
      %       %\node at (\qdeg:1.5) {\aangle, \amag};
      %       }
      %     }
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \shade[ball color=yellow] (30:3) circle[radius=0.5];
    \node at (30:3.75){$m$};
    \shade[ball color=red] (210:2) circle[radius=0.75];
    \node at (210:3){$M$};
    \draw[->,line width=1.5,DarkSlateBlue] (0,0) --node[anchor=north west]{$r_{1}$}
    (30:3);
    \draw[->,line width=1.5,DarkSlateBlue] (0,0) --node[anchor=north west]{$r_{2}$} (210:2);
    \draw[SlateGray,->] (-0.5,0) -- (3.5,0) node[anchor=north]{$x$};
    \draw[SlateGray,->] (0,-0.5) -- (0,2) node[anchor=east]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\myang{30}
    \draw[dashed] (0,-2) -- (0,2.5);
    \draw (0,0) circle[radius=2];
    \draw[->,line width=1] (0,0) -- ++(0.75,0) node[anchor=north] {$\ux$};
    \draw[->,line width=1] (0,0) -- ++(0,0.75) node[anchor=east]{$\uy$};
    \draw[dashed] (0,0) -- node[anchor=north]{$l$} ++(\myang:2) coordinate (a);
    \fill (a) circle[radius=0.05];
    \node[anchor=south west] at (a) {$a$};
    \draw[coord,->](\myang+15:1.5) node[anchor=south east]{$\omega$}
    arc(\myang+15:\myang-15:1.5);

    \draw[dashed] (0,0) -- node[anchor=north]{$l$} ++(180-\myang:2) coordinate (a);
    \fill (a) circle[radius=0.05];
    \node[anchor=south east] at (a) {$b$};
    \draw[coord,->](180-\myang-15:1.5) node[anchor=south west]{$\omega$}
    arc(180-\myang-15:180-\myang+15:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \coordinate (B) at (0,0);
    \coordinate (A) at (0,3);
    \draw (A) -- node[anchor=east]{$l$} (B);
    \filldraw[fill=gray!20] (B) circle[radius=0.2] (A) circle[radius=0.2] ;
    \node[anchor=east,shift={(-0.2, 0)}] at (B) {$m_{b}$};
    \node[anchor=east,shift={(-0.2, 0)}] at (A) {$m_{a}$};
    \draw[vel] (B) ++(0.3,0) -- ++ (0:1) node[anchor=west] {$v_{0}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=blue!25!white] (0,0) -- (0,0.5) -- (3,0.5) -- (3.5,0) -- (3,-0.5)
    -- (0,-0.5) -- cycle;
    \node at (1.5,0) {$M_{R}+M_{F}$};
    \draw[<->] (-0.5,-0.5) -- node[anchor=east] {$2R$}  (-0.5,0.5);
    \draw[vel] (2,-1) --node[anchor=north]{$v_{0}$} ++(0:1.5);

    %  \node at (8,1.5) {$v_{i} = 0$};
    \node [cloud, draw, cloud puffs=10, cloud puff arc=120, aspect=2, inner
      ysep=1em,minimum width=7cm,minimum height=4cm,fill=gray!15,
      text width=1.5in,align=center] at (10,0) {$N$ particles/m$^{3}$\\ $v_{i} = 0$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[vel] (0,0) -- ++(0:1.25) node[anchor=south]{$v_{0}$};
    \draw[fill=white] (0,0) circle[radius=0.1] node[anchor=east]{$m$};
    \draw[vel] (4,0) -- ++(180:1.75) ;
    \draw[fill=white] (4,0) circle[radius=0.2];
    \node at (4.4,0) {$M$};
    \node at (2,-0.5) {\textsf{Before}};

    \begin{scope}[shift={(0,-3)}]
      \draw (2.25,0) arc(0:45:0.75);
      \node at (2.6, 0.35){$\dg{45}$};
      \draw[dashed] (0,0) -- (4,0);
      \draw[vel] (1.5, -0.25) -- ++(-90:0.75) node[anchor=west]{$v_{0}/2$};
      \draw[fill=white] (1.5, -0.25) circle[radius=0.1]
      node[anchor=east]{$m$};
      \draw[dashed] (1.5,0) -- ++(45:1.5);
      \draw[vel] (2.5,1) -- ++(45:1.5);
      \draw[fill=white] (2.5, 1) circle[radius=0.2];
      \node at (2, -1.75){\textsf{After}};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \fill[gray] (0,0) -- (2,0) -- (2,-0.15) -- (-0.15,-0.15) --
    (-0.15,2) -- (0,2) -- cycle;
    \draw (0,2) -- (0,0) -- (2,0);
    \draw (1.2, 0) -- (0, 1.6) -- ++(36.87:0.075) --
    node[anchor=south west] {$2L$}
    ++(-53.13:2) -- cycle;
    \draw (0.8,0) arc(180:127.87:0.4);
    \node at (0.7,0.25) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \filldraw[SlateGray, fill=SlateGray!10!white] (0,0) rectangle (0.5,0.4);
    \draw[spring] (0.5,0.2) -- ++(2,0);
    \filldraw[SlateGray, fill=SlateGray!10!white] (2.5,0) rectangle
    ++(0.5,0.4);
    \node at (0.25,0.2) {$m_{1}$};
    \node at (2.75,0.2) {$m_{2}$};

    \fill[gray!25] (0,0) -- ++(0, 1.25) -- ++(-0.2,0)
    -- ++(0,-1.45) -- ++(3.7, 0) -- ++(0, 0.2)
    -- cycle;
    \draw (0,1.25) -- (0,0) -- (3.5,0);
    \draw[coord] (3.6, 0) --  node[anchor=north]{$x$} ++(0:0.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\WW{0.2}

    % floor and wall
    \fill[gray!50] (0,0) -- (3,0) -- ++(0, -\WW)
    -- (-\WW,-\WW) -- ++(0, 4.5+\WW) -- ++(\WW, 0) -- cycle;
    \draw (0,4.5) -- (0,0) --(3,0);

    % draw the rod
    \draw (2.5, 0.2) coordinate (B) circle[radius=0.05];
    \draw (2.5, 0.2) ++ (125:4) coordinate (T) circle[radius=0.05];
    \begin{scope}[shift={(2.5, 0.2)},rotate = 35]
      \filldraw[black, fill=SlateGray!33!white] (-0.05, 0) rectangle (0.05, 4);
      \node[anchor=west] at (0.2, 2) {$L$};
    \end{scope}

    % draw the masses
    \filldraw[DarkSlateGray,fill=gray!25] (2.2, 0) arc[x radius=0.3, y
        radius=0.5, start angle=180, end angle=0] -- cycle;
    \fill (B) circle[radius=0.05];
    \draw (B) ++(0.2,0.3) node[anchor=south]{$M$};

    \filldraw[DarkSlateGray, fill=gray!25] (T) ++(-0.2,0.3) arc[x radius=0.5, y
        radius=0.3, start angle=90, end angle=-90] -- cycle;
    \fill (T) circle[radius=0.05];
    \draw (T) ++(0.3,0.2) node[anchor=west]{$M$};

    % labels
    \draw[coord,<->] (-0.35, 0) --node[anchor=east]{$b$} ++(0, 3.5);
    \draw[coord] (2,-0.4) -- ++(0:1) node[anchor=north]{$x$};
    \draw[coord] (-0.5,3.75) -- ++(90:1) node[anchor=east]{$y$};
    \begin{scope}[shift={(2.6,0)}]
      \draw[coord,-] (-0.6,0) arc(180:125:0.6);
      \node at (150:0.8) {$\theta$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \fill[fill=gray] (-3,0) rectangle (3,-0.2);
    \draw (-1, 1.82) -- (-0.24, 1.82);
    \draw (-0.1,1.675) -- ++(-90:0.5);
    \coordinate (A) at (-0.25,1.675);
    \fill[fill=gray!50!white] (A) circle[radius=0.15];

    \draw[fill=gray!20!white] (-2,0) -- ++(90:1.5)
    -- ++(0:1.5) --  ++(45:0.2914) arc(135:-45:0.05)
    -- ++(-135:0.35) -- ++(-90:1) -- ++(0:0.6)
    -- ++(90:1.1) -- ++(0:1) --++(-90:1.48) -- cycle;
    \fill (A) circle[radius=0.025];
    \draw[fill=gray!15!white] (-1.75,1.5) rectangle node{$M_{2}$} (-1,2);
    \draw[fill=gray!15!white] (-0.45,1.25) rectangle node{$M_{3}$} (0.1,0.75);
    \node at (-1.5, 0.25) {$M_{1}$};
    \draw[force] (-3,0.75) -- node[anchor=south]{$F$} (-2,0.75);

    %      \draw[coord] (-3,0.25) -- node[anchor=south]{$x_{1}$} ++(0:1);
    %      \draw[coord] (-2,2) --node[anchor=south]{$x_{2}$} (-1.75,2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) -- (1,1) -- (1.5,1) -- (1.5,-0.5) --
    (-1.5,-0.5) -- (-1.5,1) -- (-1,1) --
    cycle;
    \draw (0,1) circle[radius=0.707];
    \draw[dashed] (-1,0) -- (1,0);
    \draw (0.5,0) arc(0:45:0.5);
    \draw (-0.5,0) arc(180:135:0.5);
    \node at (17.5:0.85) {$\dg{45}$};
    \node at (162.5:0.8) {$\dg{45}$};
    \draw[->] (0,1) ++(45:0.5) arc(45:150:0.5) node[anchor=west]{$\omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
      xmin=0, xmax=2, ymin=-1.1, ymax=1.1, enlargelimits=false,
      width=3.5in, height=2.5in,
      xlabel={$t$}, ylabel={$a$ or $\dot{a}$},
      ytick={-1,0,1}, xtick={0,1,2},
      xticklabels={0,$T$,$2T$},
      yticklabels={\textcolor{DarkGreen}{$-a_{m}$},\textcolor{DarkGreen}{$0$},\textcolor{DarkGreen}{$a_{m}$}}
      % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0:1, samples=40, line width=1.5pt,]
      {sin(180*x)^2};
      \addplot[DarkGreen, domain=1:2, samples=40, line width=1.5pt,]
      {-sin(180*x)^2};
      \addplot[DarkRed, domain=0:1, samples=40, line width=2pt]
      {sin(360*x)};
      \addplot[DarkRed, domain=1:2, samples=40, line width=2pt]
      {-sin(360*x)};

      \draw[DarkGreen, line width=1.5pt] (0.1,-0.8) -- (0.3,-0.8)
      node[anchor=west] {$a$};
      \draw[DarkRed, line width=2pt] (0.1,-0.95) -- (0.3,-0.95) node[anchor=west] {$\dot{a}$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\RR{3}
    \def\QQ{30}
    \draw[dashed] (0, 0) ++ (-30:\RR) arc(-30:90:\RR);
    \draw[vel] (0,0) --node[anchor=south] {$\vb{r}$} (\QQ:\RR) coordinate (P);
    \fill (P) circle[radius=0.05];
    \draw[vel, DarkRed] (P) -- ++(\QQ+90:1.5) node[anchor=south]{$\vb{v}$};
    \draw[vel, DarkGreen] (P) ++(-90+\QQ:0.15) -- node[anchor=north]{$\vb{a}$}
    ++(180+\QQ:2);
    \draw[vel,SlateGray] (P) -- ++(-90+\QQ:1.5) node[anchor=north]{$\dot{\vb{a}}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[fill=black] (0,0) rectangle (0.25, 0.25);
    \draw[force] (0,0.125) -- ++(180:1.25) node[anchor=east]{$T$};
    \draw[coord] (-3.5,0.125) -- ++(0:1) node[anchor=west]{$r$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1,
      acc/.style={->,DarkRed,line width=1.5}
    ]
    \begin{axis}[
        axis equal,
        xmin=-1.75,
        xmax=2.25,
        ymin=-2.5,
        ymax=1.5,
        width=3.5in,
        height=3.5in]
      \def\accel{4*pi}
      \def\radv{1/pi}

      \def\xth{}
      \def\xr{}
      \def\vth{}
      \def\vr{}
      \def\ath{}
      \def\ar{}
      \def\dth{}
      \def\domega{}
      \def\dalpha{}

      \addplot[
        DarkGreen,
        domain=0:2*pi,
        data cs=polarrad,
        samples=100,
        line width=2pt]
      {\radv * x};

      \newcommand*{\setuv}[1]{%
        \coordinate (ur) at (#1:0.75cm);
        \coordinate (uth) at (#1+90:0.75cm);
      }

      \setuv{45}
      \coordinate (d) at (45:0.25);
      \coordinate (v) at ($(ur) + pi/4*(uth)$);
      \coordinate (a) at ($-0.02337*(ur) +.3927*(uth)$);
      \draw[vel] (d) -- ++(v);
      \draw[acc] (d) --  ++(a);

      \setuv{90}
      \coordinate (d) at (90:0.5);
      \coordinate (v) at ($(ur) + pi/2*(uth)$);
      \coordinate (a) at ($-.3935*(ur) +.7854*(uth)$);
      \draw[vel] (d) -- ++(v);% node[anchor=south]{$v$};
      \draw[acc] (d) --  ++(a);% node[anchor=south east]{$a$};

      \setuv{135}
      \coordinate (d) at (135:0.75);
      \coordinate (v) at ($(ur) + 0.75*pi*(uth)$);
      \coordinate (a) at ($-1.010*(ur) +1.178*(uth)$);
      \draw[vel] (d) -- ++(v);% node[anchor=south]{$v$};
      \draw[acc] (d) --  ++(a);% node[anchor=south east]{$a$};

    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1, arrows = {-Stealth[scale width=0.5]}, line width=2pt]
    \draw[coord,<->] (0,2) node[anchor=east]{$y_{A}$} -- (0,0) -- (3,0)
    node[anchor=north]{$x_{A}$};
    \coordinate (B) at (-1,-3);
    \coordinate (P) at (2.5,1);
    \fill[fill=DarkRed!70!white] (P) circle[radius=0.1]
    node[anchor=west,color=DarkRed]{$P$};

    \begin{scope}[shift={(B)}]
      \draw[coord,<->] (0,2) node[anchor=east]{$y_{B}$} -- (0,0) -- (3,0)
      node[anchor=north]{$x_{B}$};
    \end{scope}

    % draw vector to point P
    \draw (0,0) -- node[anchor=south]{$r_{A}$} (P);
    \draw (0,0) -- node[anchor=south west]{$R$} (B);
    \draw (B) -- node[anchor=west]{$r_{B}$} (P);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) rectangle (1.5,1);
    \draw[force] (0.75,0) -- ++(180:1.5) node[anchor=east]{$f$};
    \draw[force] (0, 0.5) -- ++(180:1.5) node[anchor=east]{$k x$};
    \draw[force] (0.75,0) -- ++(90:1.5) node[anchor=south]{$N$};
    \draw[force] (0.8,0.5) -- ++(-90:1.5) node[anchor=north]{$Mg$};
    \draw[coord] (-1, -1) -- ++(0:1) node[anchor=north]{$x$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (0,0) -- (0,3);
    \draw(0,1) arc(90:60:1);
    \node at (75:1.4){$\phi$};
    \draw[line width=3,opacity=0.5] (0,0) -- (60:4);
    \draw[force] (60:3) -- ++(-90:1.5) node[anchor=west]{$M g$};
    \draw[line width=2,color=DarkRed] (0.1,0.1) -- (-0.1,-0.1) (0.1,-0.1) --
    (-0.1,0.1);
    \draw[line width=3,color=DarkGreen,->] (4.2,0.2) -- ++(60:3.5)
    node[anchor=south west]{$I_{0} \omega_{s}$};
    \draw[line width=1.5] (4,0) circle[radius=0.2];
    \draw (4.14,0.14)--(3.86,-0.14)
    (4.14,-0.14) -- (3.86,0.14);
    \node at (3.7,0.2){$\tau$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[coord,<->] (0,1.5) node[anchor=south]{$z$} -- (0,0)
    -- (1.5,0) node[anchor=west]{$x$};
    \filldraw[color=DarkGreen, fill=white] (0,0) circle[radius=0.15];
    \node[color=DarkGreen] at (45:0.35){$y$};
    \draw[color=DarkGreen] (45:0.15) -- (225:0.15) (-45:0.15) -- (135:0.15);
    \draw[line width=2] (0,0) --node[anchor=south east]{$l$} (-120:2.5);
    \fill (-120:2.5) circle[radius=0.25];
    \draw[dashed] (0,0) -- (0,-2.5);
    \draw[->] (0,-1) arc(-90:-120:1);
    \node at (-105:1.35){$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed,gray] (-120:1.5) coordinate (A) --++(150:1.5);
    \draw[dashed,gray] (-120:1.5) coordinate (A) --++(-30:3.5)
    coordinate (B);
    \draw (B) -- ++(180:1.5);
    \draw (B) ++(180:0.75) arc(180:150:0.75);
    \draw (B) ++(180:0.75) node[anchor=south east] {$\theta$};
    \draw[line width=2,gray,opacity=0.5] (0,0) circle[radius=1.5];
    \draw[force] (A) -- ++(150:0.5) node[anchor=north east]{$F$};
    \draw[force] (0,0) -- ++(-90:1) node[anchor=west]{$Mg$};
    \draw[force] (A) -- ++(60:1) node[anchor=east]{$N$};
    \draw[coord,->] (-30:2) --node[anchor=south]{$x$} ++(-30:2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=2,color=SlateGray] (-2,1) parabola bend (0,0) (2,1);
    \draw[fill=gray,rotate=36] (1.6,-0.4) rectangle (2,-0.2);
    \draw[force,rotate=36] (1.8,-0.4) -- ++(90:1.25) node[anchor=south]{$N$};
    \draw[force,rotate=36] (1.8,-0.3) -- ++(-126:1.25) node[anchor=north]{$mg$};
    \draw[coord,->] (0,0) -- (2,0) node[anchor=west]{$r$};
    \draw[coord,->] (0,0) -- (0,2) node[anchor=south]{$z$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    % the ground
    \fill[SlateGray] (-1.5,0) rectangle (1.5,-0.15);
    \draw[line width=1.25,color=gray] (-0.5,3) -- (-0.5,2.25)
    (0.5,3) -- (0.5, 1.5)
    (0,0) -- (0,1.5)
    (1,1.5) -- (1,0.75);
    \filldraw[fill=gray!25!white] (0,3) circle[radius=0.5];
    \filldraw[fill=gray!25!white] (0.5,1.5) circle[radius=0.5];
    \draw[line width=1.25,color=gray] (0.5,1.5) -- (0.5,2);
    \fill (0,3) circle[radius=0.05] (0.5,1.5) circle[radius=0.05];
    \node[draw] at (-0.5,2) {$M_{1}$};
    \node[draw] at (1,0.5) {$M_{2}$};
    \draw[coord] (-1,0) -- node[anchor=east]{$x_{1}$} (-1,2);
    \draw[coord] (-0.25,0) -- node[anchor=east]{$x_{3}$} (-0.25,1.5);
    \draw[coord] (0.55,0) -- node[anchor=east]{$x_{2}$} (0.55,0.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \draw (0,0) -- (0,-4);
    \draw (0,-1) arc(-90:-70:1);
    \node at (-80:1.35){$\alpha$};
    \begin{scope}[shift={(0,-3)}, rotate=10]
      \draw[line width=2] circle[x radius=1, y radius=0.2];
      \coordinate (A) at (1,0);
      \draw (0,0) -- (-1.5,0);
      \draw (0,0) -- (170:1.5);
      \draw (-1.35,0) arc(180:170:1.35);
      \node at (175:1.6) {$\beta$};
    \end{scope}
    \draw[line width=1,opacity=0.5] (0,0) -- (A);
    \draw[force] (A) -- ++(110:1) node[anchor=west]{$T$};
    \draw[force] (0,-3) -- ++(-90:1) node[anchor=north]{$M g$};
    \draw[line width=2.5,color=DarkRed,->] (0,-3) -- ++ (100:2)
    node[anchor=south]{$L$};


    \begin{scope}[shift={(2,-3)},color=DarkGreen,scale=1.5]
      \draw[->] (0,0) -- (0,1.5) node[anchor=south]{$\uz$};
      \draw[->] (0,0) -- (1.5,0) node[anchor=west]{$\urho$};
      \draw[dashed,->,line width=1.5] (0,0) -- (10:1.5) node[anchor=south west]{$\urho'$};
      \draw[dashed,->, line width=1.5] (0,0) -- (100:1.5) node[anchor=south]{$\uz'$};
      \draw (1,0) arc(0:10:1);
      \node at (5:1.2) {$\beta$};
      \draw[force] (10:1.25) -- ++ (110:1) node[anchor=south]{$T$};

      \draw[dashed] (10:1.25) -- ++(100:1.25);
      \begin{scope}[shift={(10:1.25)}]
        \draw (110:0.6) arc (110:100:0.6);
        \node[anchor=west] at (90:0.6) {$\alpha-\beta$};
      \end{scope}
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \draw (-2,0) -- (1,0) ; % the ground
    \begin{scope}[color=DarkGreen,shift={(-2,1.5)}]
      \draw[->] (0,0) -- (0.5,0) node[anchor=west]{$\rho$};
      \draw[->] (0,0) -- (0,0.5) node[anchor=south]{$z$};
      \filldraw[fill=white] (0,0) circle[radius=0.1];
      \draw (45:0.1) -- (225:0.1) (-45:0.1)--(135:0.1);
      \node at (-0.2,-0.2) {$\phi$};
    \end{scope}
    \begin{scope}[rotate=15]
      \draw (-0.05,0) rectangle (0.05,2);
      \draw[force] (0,1) --node[anchor=east]{$Mg$} ++(-105:0.75);
      \draw[vel] (0,1) -- ++(180:1.5) node[anchor=east]{$L_{s}$};
      \draw (0,1) -- ++(165:1);
      \draw (-0.5,1) arc(180:165:0.5);
      \node at (-0.3,1.25){$\alpha$};
    \end{scope}
    \draw[force] (0,0) -- ++(90:1) node[anchor=west]{$N$};
    \draw[force] (0,0) -- ++(180:0.5) node[anchor=north]{$f$};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) -- (3,0);
    \draw (3,2) parabola (0,0);
    \draw (0.5,0) arc[start angle=0, end angle=45, radius=0.5];
    \node at (23:0.75){$\theta$};
    \draw[<->,color=DarkGreen] (3.2,0) --node[anchor=east]{$h$} ++(90:2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[color=gray,line width=1.5] (0,0) -- (150:4);
    \begin{scope}[rotate=-30]
      \fill[fill=gray!25!white] (-2.5,0) rectangle (-3.5,0.5);
      \draw[force] (-3,0) -- (-3,1.5) node[anchor=south east]{$N$};
      \draw[force] (-3,0.25) -- ++(-60:1.25) node[anchor=east] {$mg$};
      \draw[force] (-3,0) -- ++(180:1.5) node[anchor=south]{$F$};
      \draw[force,color=DarkRed] (-3,0.25) -- node[anchor=north]{$ma$} ++(210:1.25);
    \end{scope}

    \draw[accel] (-1,2) -- node[anchor=south] {$a$} ++(0:1.75);
    \draw (-1,0) arc (180:150:1);
    \node at (165:1.4){$\theta$};
    \draw (-3,0) -- (0,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[fill=gray!15!white] (0,0) rectangle node{$M_{2}$} (1.5,1) ;
    \draw[force] (1.5,0.5) -- ++(0:1.25) node[anchor=west]{$T$};
    \draw[force] (0.75,0.25) -- ++(-90:1.25) node[anchor=north]{$M_{2}g$};
    \draw[force] (1.25,0) -- ++(90:1.25) node[anchor=south]{$N_{2}$};
    \draw[coord] (-1.5,0.5) -- node[anchor=south]{$x_{1} + x_{2}$}++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \fill (0,0) circle[radius=0.25];
    \draw[force] (0,0) -- (154:1.5) node[anchor=south]{$N$};
    \draw[force] (0,0) -- (0,-2.5) node[anchor=west]{$mg$};
    \draw[dashed,color=gray] (0,0) -- (180:2);
    \draw (-1,0) arc(180:154:1);
    \node at (167:1.4){$\theta$};
    \draw[accel] (-1,0) -- ++(180:1.5) node[anchor=north]{$a$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a
filename: tikz.tex
modified: 2021-02-15 21:09:00
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!50!white] (-0.5,0.5) --
    ++(0:0.75) % top
    arc(90:-90:0.5) % right arc
    -- ++(180:0.75) % bottom
    -- cycle;
    \draw[force] (-0.5,-0.1) -- ++(1.5,0) node[anchor=west]{$N_{h}$};
    \draw[force] (0,0) -- ++(-90:1) node[anchor=north]{$Mg$};
    \draw[force,->] (0,0) coordinate (A) -- ++(120:1.5)  node[anchor=south east]{$F$};

    \draw[dashed] (A) -- ++(180:1.);
    \draw (A) ++(180:0.65) arc(180:120:0.65);
    \draw (A) ++(150:1) node {$\theta$};

    \draw[coord] (0,-1) -- (90:1) node[anchor=east]{$y$};

    \node at (0, -2.25){\begin{minipage}{2in}
        \begin{align}
          N_{h}     & = F\cos\theta\label{eq:1}       \\
          M\ddot{y} & = F\sin\theta - Mg \label{eq:2}
        \end{align}
      \end{minipage}
    };

    \begin{scope}[shift={(6,0)}]
      \filldraw[fill=gray!50!white] (-0.5,-0.5) --
      ++(90:0.75)
      arc(180:0:0.5)
      -- ++(-90:0.75)
      -- cycle;
      \draw[force] (0,0) -- ++(-90:1.25) node[anchor=north]{$Mg$};
      \draw[force] (0.1,-0.5) -- ++(90:2) node[anchor=south] {$N_{v}$};
      \draw[force,->] (0,0.25) ++(120:0.5) coordinate (B)
      -- ++(-60:1.5) node[anchor=north]{$F$};

      \draw[dashed] (B) -- ++(180:1.5) (B) -- ++(120:1);
      \draw (B) ++(180:0.5) arc(180:120:0.5);
      \draw (B) ++(150:.8) node {$\theta$};

      \node at (0, -2.25) {
        \begin{minipage}{2in}
          \begin{align}
            N_{v}     & = Mg + F\sin\theta \label{eq:3} \\
            M\ddot{x} & = F\cos\theta \label{eq:4}
          \end{align}
        \end{minipage}
      };
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/hw
filename: hw07-sol.tex
modified: 2022-03-07 21:24:57.133135
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}
      \node at (2,1.5) {$L$};
      \filldraw[fill=gray] (0,0) circle[radius=0.1]
      node[anchor=north,shift={(0,-0.1)}] {$m$};
      \draw[vel] (0,0) -- node[anchor=south]{$v_{0}$} ++(0:2.5);
      \filldraw[fill=gray] (4,0) circle[radius=0.125]
      node[anchor=north,shift={(0,-0.1)}] {$M$};
    \end{scope}

    \draw[dashed] (4.5, -0.5) -- ++(90:2);

    \begin{scope}[shift={(5,0)}]
      \node at (2,1.5) {$C$};
      \filldraw[fill=gray] (0,0) circle[radius=0.1]
      node[anchor=north,shift={(0,-0.1)}] {$m$};
      \draw[vel] (0.4,0) -- node[anchor=south]{$v$} ++(0:1.25);
      \filldraw[fill=gray] (4,0) coordinate (M) circle[radius=0.125]
      node[anchor=north,shift={(0,-0.1)}] {$M$} ;
      \draw[vel] (M) ++(-0.2,0) -- node[anchor=south]{$V$} ++(180:1);

      \draw[dashed,->] (1.5,0) -- (2.5,0) (2,0) coordinate (col)-- ++(45:1.5);
      \draw (col) ++(0.4,0) arc(0:45:0.4);
      \draw (col) ++(20:0.65) node {$\Theta$};

      \draw[coord,<->] (6,0) node[anchor=north] {$\ux$} -- ++(180:0.75)
      -- ++(90:0.75) node[anchor=east] {$\uy$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220322-orbits.tex
modified: 2022-03-21 14:16:16.015546
domain: p24a
source:
  \begin{tikzpicture}[scale=1,
      posi/.style={line width=1pt, color=SlateBlue,->},
      thecm/.style={line width=1.25pt, color=SlateGray,->},
      relpos/.style={line width=1.25pt, color=DarkRed,->}
    ]
    \draw[coord,<->] (5,0) node[anchor=north] {$x$} -- (0,0)
    -- (0,5) node[anchor=east]{$y$};

    % masses
    \fill[gray] (15:4.5) coordinate(m1) circle[radius=0.05]
    (30:5.5) coordinate(m2) circle[radius=0.05]
    (60:5) coordinate(m3) circle[radius=0.05];

    \coordinate (CM) at (40:4.75);
    \draw[thecm] (0,0) -- node[anchor=south]{$R$} (CM);


    \dopoint{(m1)}{1}{north}{west}
    \dopoint{(m2)}{2}{north}{south}
    \dopoint{(m3)}{3}{east}{east}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220322-orbits.tex
modified: 2022-03-21 14:16:16.015546
domain: p24a
source:
  \begin{tikzpicture}[scale=0.8]
    \def\aa{3} \def\ee{0.6}
    \pgfmathsetmacro{\bb}{\aa*sqrt(1-\ee*\ee)}
    \draw[SlateBlue] (0,0) circle[x radius=\aa, y radius=\bb];

    \filldraw[fill=yellow] (1.8,0) coordinate (O) circle[radius=0.2];
    \draw[coord] (1.8,-3) -- (1.8,3) node[anchor=east] {$y$};
    \draw[coord] (-3.5,0) -- (3.5,0) node[anchor=north] {$x$};

    % planet
    \fill[brown] (2.5,1.33) coordinate (P) circle[radius=0.1];
    \draw[coord] (O) -- node[anchor=west] {$r$} (P);
    \begin{scope}[shift={(1.8,0)}]
      \draw (0:0.4) arc(0:63:0.4);
      \node at (25:0.55) {$\theta$};
    \end{scope}

    % ellipse properties
    \begin{scope}[DarkRed,line width=1.5]
      \draw (0,0) -- node[anchor=north] {$\varepsilon a$} (\aa*\ee,0);
      \filldraw[fill=gray,draw=black,line width=0.5pt] (-\aa*\ee,0)
      coordinate (f2) circle[radius=0.05];
      \draw (0,0) -- node[anchor=north] {$\varepsilon a$} (f2);
      \draw[dashed,line width=0.75,gray] (f2) --node[anchor=south]{$s$} (P);
    \end{scope}
    \draw[coord,DarkRed,<->] (0,-0.5) -- node[anchor=north]{$a$} (-\aa,-0.5);
    \draw[coord,DarkRed,<->] (0,-0.5) -- node[anchor=north]{$a$} (\aa,-0.5);
    \draw[coord,DarkRed,<->] (0,0) -- node[anchor=east]{$b$} (0,\bb);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220322-orbits.tex
modified: 2022-03-21 14:16:16.015546
domain: p24a
source:
  \begin{tikzpicture}[scale=0.75]
    \fill[gray] (210:2) coordinate(m1) circle[radius=0.1]
    node[anchor=north,shift={(0,-0.1)}] {$m_{1}$};
    \fill[gray] (30:4) coordinate(m2) circle[radius=0.05]
    node[anchor=north,shift={(0,-0.1)}] {$m_{2}$};
    \fill[DarkRed] (0,0) circle[radius=0.05] node[anchor=south east] {CM};
    \draw[coord] (0,0) -- node[anchor=north] {$r_{1}$} (m1);
    \draw[coord] (0,0) -- node[anchor=north]{$r_{2}$} (m2);

    \begin{scope}[shift={(-60:0.65)}]
      \draw[vel,line width=1.25] (210:2) -- node[anchor=north] {$r$} (30:4);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220322-orbits.tex
modified: 2022-03-21 14:16:16.015546
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\angmom{0.004} \def\grav{0.1}
    \def\xlim{0.5}
    \begin{axis}[
        xmin=0, xmax=0.5, ymin=-1, ymax=1, enlargelimits=false,
        width=2.5in, height=2.5in,
        xlabel={$r$}, ylabel={}, ytick={0}, xtick=\empty,
        axis x line=middle, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0.01:0.45, samples=100, line width=1pt,]
      {\angmom / (x*x)};
      \addplot[DarkRed,domain=0.01:\xlim,samples=100,line width=1pt]
      {-\grav/x};
      \addplot[DarkBlue,domain=0.01:\xlim,samples=100,line width=1.5pt]
      {\angmom/(x*x) - \grav/x};
      \draw (0,0) -- (\xlim,0);
      \node[DarkGreen,anchor=south] at (0.2,0.15) {$\frac{L^2}{2\mu r^2}$};
      \node[DarkRed,anchor=west] at (0.15,-0.7) {$- \frac{G m_1 m_2}{r}$};
      \node[DarkBlue] at (0.05,-0.7) {$U_{\rm eff}$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220322-orbits.tex
modified: 2022-03-21 14:16:16.015546
domain: p24a
source:
  \begin{tikzpicture}[scale=0.8]
    \def\aa{3} \def\ee{0.6}
    \pgfmathsetmacro{\bb}{\aa*sqrt(1-\ee*\ee)}
    \draw[SlateBlue] (0,0) circle[x radius=\aa, y radius=\bb];

    \filldraw[fill=yellow] (1.8,0) coordinate (O) circle[radius=0.2];
    \draw[coord] (1.8,-3) -- (1.8,3) node[anchor=east] {$y$};
    \draw[coord] (-3.5,0) -- (3.5,0) node[anchor=north] {$x$};

    % planet
    \fill[brown] (2.5,1.33) coordinate (P) circle[radius=0.1];
    \draw[coord] (O) -- node[anchor=west] {$r$} (P);
    \begin{scope}[shift={(1.8,0)}]
      \draw (0:0.4) arc(0:63:0.4);
      \node at (25:0.6) {$\theta$};
    \end{scope}

    % ellipse properties
    \begin{scope}[DarkRed,line width=1.5]
      \draw (0,0) -- node[anchor=north] {$\varepsilon a$} (\aa*\ee,0);
      \filldraw[fill=gray,draw=black,line width=0.5pt] (-\aa*\ee,0)
      coordinate (f2) circle[radius=0.05];
      \draw (0,0) -- node[anchor=north] {$\varepsilon a$} (f2);
      \draw[dashed,line width=0.75,gray] (f2) --node[anchor=south]{$s$} (P);
    \end{scope}
    \draw[coord,DarkRed,<->] (0,-0.5) -- node[anchor=north]{$a$} (-\aa,-0.5);
    \draw[coord,DarkRed,<->] (0,-0.5) -- node[anchor=north]{$a$} (\aa,-0.5);
    \draw[coord,DarkRed,<->] (0,0) -- node[anchor=east]{$b$} (0,\bb);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220419-lec12.tex
modified: 2022-04-19 04:25:58.736145
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!50] (0,0) circle[radius=3];
    \fill (0,0) circle[radius=0.05];
    \draw[coord,->] (30:3.5) arc(30:60:3.5);
    \node[coord] at (45:3.7) {$\omega$};
    \foreach \q/\r in {30/1,90/1.5,240/2,150/2.5, 330/1.75, 180/0.75} {
        \draw[gray] (0,0) --node[shift={(\q+90:0.2)}]{$r$} (\q:\r);
        \fill[gray] (\q:\r) circle[radius=0.1];
        \draw[vel] (\q:\r) ++(\q+90:.15) -- ++(\q+90:\r) node[shift={(\q:.25)}]{$v$};
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220419-lec12.tex
modified: 2022-04-19 04:25:58.736145
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \xyzframe
    \draw[force] (1,1.5) coordinate (A) -- ++(0,-1.5) node[anchor=north]{$F$};
    \draw[force] (2,1)  coordinate (B)-- ++(0,1.5) node[anchor=south]{$F$};
    \draw[->] (0,0) --node[anchor=south east]{$r_{1}$} (A);
    \draw[->] (0,0) -- (B) node[anchor=north]{$r_{2}$};
    \draw[coord,<->] (1,1.5) -- node[anchor=south]{$b$} ++(1,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220419-lec12.tex
modified: 2022-04-19 04:25:58.736145
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\a{1.5}
    \def\b{2}
    \draw[dashed] (0,\b+0.5) -- (0,-\b-0.5);
    \draw[line width=2] (\a,\b) --node[anchor=south]{$b$} (0,\b)
    -- (0,-\b) -- node[anchor=north]{$b$} (-\a,-\b);

    \draw[coord] (-2,0) coordinate (O) -- ++ (0.51,0) node[anchor=north]{$\ux$};
    \draw[coord] (O) -- ++ (0,0.5) node[anchor=east]{$\uz$};

    \foreach \x/\y in {\a/\b, -\a/-\b}{
        \draw[dashed, gray] (0,\y) circle[x radius=\a, y radius=0.25];
        \shade[ball color=DarkSlateBlue] (\x,\y) circle[radius=0.25];
        \node at (1.4*\x,\y) {$m$};
        \foreach \q in {0,180}{
            \fill[Red] (0,0.925*\y) ++(\q-45:0.08) rectangle ++(\q+45:0.16);
          }}
    \draw[DarkGreen,->] (0.4,2.65) arc[start angle=45,
        end angle=300,x radius=0.5, y radius=0.15];
    \node[DarkGreen] at (-0.65,2.6){$\omega$};
    \fill[yellow] (0,0) circle[radius=0.05];
    \draw[DarkGreen,<->] (-0.5,0) -- node[anchor=east]{$a$} ++(90:\b);
    \draw[DarkGreen,<->] (-0.5,0) -- node[anchor=east]{$a$} ++(-90:\b);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220419-lec12.tex
modified: 2022-04-19 04:25:58.736145
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[coord] (0,0) -- ++(4,0) node[anchor=north]{$x$};
    \draw[coord] (0,0) -- ++(0,4) node[anchor=east]{$y$};
    \draw[vel] (0,0) --node[anchor=north west]{$\vb{R}(t)$} (2.5,1) coordinate (O);
    \begin{scope}[shift={(O)},rotate=15]
      \draw[coord] (0,0) -- ++(4,0) node[anchor=north]{$x'$};
      \draw[coord] (0,0) -- ++(0,4) node[anchor=east]{$y'$};
      \fill (2,2) coordinate (P) circle[radius=0.05] node[anchor=west]{$m$};
      \draw[vel] (0,0) --node[anchor=north west]{$\vb{r}'$} (P);
    \end{scope}
    \draw[DarkRed,line width=2,->] (0,0) -- node[anchor=south]{$\vb{r}$} (P);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220118-lec01.tex
modified: 2022-01-17 02:19:52.406883
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[vector] (0,0) --node[anchor=south east]{$\vb{C}$} ++(30:3) ;
    \onslide<2-3|handout:0>{
      \draw[accel] (0,0) --node[anchor=north]{$\vb{A}$} (4,-1) coordinate
      (A);
      \draw[accel] (A) -- node[anchor=west]{$\vb{B}$} (30:3);
    }
    \onslide<2|handout:0>{
      \node at (2,-1.5){$\vb{A + B = C}$};
    }
    \onslide<3|handout:0>{
      \node at (2,-1.5){$|\vb{C}| = C \ne A + B$};
    }
    \onslide<4->{
      \draw[coord,->] (0,-0.5) -- ++(90:2.5) node[anchor=east]{$y$};
      \draw[coord,->] (-0.5,0) -- (0:3.25) node[anchor=north]{$x$};
      \draw[component] (0,0) -- node[anchor=north]{$C_{x}$} (2.598076211,0)
      coordinate (B);
      \draw[component] (B) -- node[anchor=west]{$C_{y}$} (30:3);

      \node at (2,-1.5) {$\vb{C} = C_{x}\ux + C_{y} \uy$};
    }

    \onslide<5->{
      \node[component] at (2,-2.5) {
        $C_{x} = \vb{C} \vdot \ux$};
      \node[component] at (2,-3) {
        $C_{y} = \vb{C} \vdot \uy$};
    }

    \onslide<6>{
      \node[DarkGreen,
        text width=4cm,
        anchor=north,
        rounded corners,
        draw,
        fill=yellow!15] at (2,-4)
      {In general, is $C_{x}$ the magnitude of the $x$ component
        of $\vb{C}$?};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220118-lec01.tex
modified: 2022-01-17 02:19:52.406883
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\sd{4}
    \foreach \z in {0,\sd} {
        \draw[opacity=0.5] (0,0,\z) -- (0,\sd,\z) -- (\sd,\sd,\z) -- (\sd,0,\z) --
        cycle;
      }
    \foreach \x/\y in {0/0, 0/\sd, \sd/\sd, \sd/0} {
        \draw[opacity=0.5] (\x,\y,0) -- (\x,\y,\sd);
      }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220118-lec01.tex
modified: 2022-01-17 02:19:52.406883
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[vector] (0,0) -- node[anchor=north]{$A$} (-15:3);
    \draw[vector] (0,0) -- node[anchor=south]{$B$} (15:4);
    \draw[coord] (-15:1.1) arc[x radius=1.5,y radius=0.5, start angle=-45,
        end angle=30];
    \node[DarkGreen] at (0:1.7) {$\theta$};
    \draw[vector,DarkRed] (0,0) -- node[anchor=east]{$\vb{A}\times\vb{B}$} (100:3)
    node[anchor=south,font=\scriptsize\sffamily,text width=2cm] {direction from right-hand rule};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220118-lec01.tex
modified: 2022-01-17 02:19:52.406883
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \xyzframe
    \def\brad{0.125}
    \onslide<2->{
      \shade[ball color=DarkRed!50] (2.5,1.5,1.5) coordinate (b) circle[radius=\brad];
    }

    \onslide<3->{
      \draw[vel,DarkRed,line width=1.5] (0,0,0) -- node[anchor=south]{$\vb{r}$} (b);
    }
    \onslide<4->{
      \shade[ball color=DarkRed!25,opacity=0.75] (3,0,1) coordinate (c)
      circle[radius=\brad];
      \draw[vel,DarkRed!50!white,line width=1.5] (0,0,0)
      --node[anchor=north]{$\vb{r}(t+\Delta t)$} (c);
      \draw[vector] (b) --node[anchor=south west]{$\vb{v} \Delta t$} (c);
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220118-lec01.tex
modified: 2022-01-17 02:19:52.406883
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[coord,<->] (3,0) node[anchor=north]{$x$} -- (0,0) -- (0,3)
    node[anchor=east]{$y$};
    \draw[vector] (0,0) -- node[anchor=east]{\vb{r}} (120:2.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220118-lec01.tex
modified: 2022-01-17 02:19:52.406883
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[coord,<->] (3,0) node[anchor=north]{$x$} -- (0,0)
    -- (0,3) node[anchor=east]{$y$};
    \draw[vector] (0,0) -- node[anchor=south]{$\vb{r}$} (30:2.5) coordinate
    (p);
    \draw[coord] (0:1) arc(0:30:1);
    \draw[DarkGreen] (15:1.25) node {$\theta$};
    \draw[coord] (p) -- ++(30:1) node[anchor=north]{$\ur$};
    \draw[coord] (p) -- ++(120:1) node[anchor=east]{$\uth$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220125-lec02.tex
modified: 2022-01-23 22:36:21.593897
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[SlateGray, fill=SlateGray!25] (0,0) -- (0,-2) -- (-5, -2)
    coordinate (P) -- cycle;
    \draw (P) ++(0:1) arc(0:21.8:1); % 180:158.2:1);
    \draw (P) ++(12:1.05) node[anchor=west]{$\theta$};
    \node at (-0.25,-1.75){$M$};
    \begin{scope}[rotate=21.8]
      \filldraw[DarkSlateBlue, fill=SlateBlue!33](-0.25, 0) rectangle (-0.75,
      0.5);
      \node[rotate=21.8] at (-0.5, 0.25) {$m$};
    \end{scope}

    \draw[SlateGray, line width=3] (1, -2.07) -- ++(-7,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220125-lec02.tex
modified: 2022-01-23 22:36:21.593897
domain: p24a
source:
  \begin{tikzpicture}[scale=0.75,
      string/.style={SlateGray,line width=2pt},
      mass/.style={DarkSlateGray, fill=SlateGray!25},
      ceiling/.style={gray!50,line width=4pt},
      pulley/.style={fill=SlateBlue!50!white},
    ]
    \onslide<1>{\begin{scope}[shift={(0,0)}]
        \draw[mass] (-0.2, 0) rectangle (0.2, 1);
        \node[anchor=west] at (0.2,0.5) {$M$};
        \draw[string] (0,1) -- (0,4);
        \draw[ceiling] (-0.5,4) -- (0.5,4);
        \draw[<-,DarkGreen] (-0.1,2.5) -- ++(180:0.5);
        \node at (0,-0.4) {(a)};
      \end{scope}}
    \onslide<2->{
      \begin{scope}[shift={(0,0)},opacity=0.25]
        \draw[mass] (-0.2, 0) rectangle (0.2, 1);
        \node[anchor=west] at (0.2,0.5) {$M$};
        \draw[string] (0,1) -- (0,4);
        \draw[ceiling] (-0.5,4) -- (0.5,4);
        \draw[<-,DarkGreen] (-0.1,2.5) -- ++(180:0.5);
        \node at (0,-0.4) {(a)};
      \end{scope}
    }

    \onslide<2>{\begin{scope}[shift={(2,0)}]
        \draw[mass] (-0.2, 0) rectangle (0.2, 1);
        \node[anchor=west] at (0.2,0.5) {$M$};
        \draw[spring] (0,2) -- (0,3);
        \draw[string] (0,1) -- (0,2) (0,3) -- (0,4);
        \draw[ceiling] (-0.5,4) -- (0.5,4);
        \node[anchor=west] at (0.2,2.5) {$k$};
        \node at (0,-0.4) {(b)};
      \end{scope}
    }
    \onslide<3->{\begin{scope}[shift={(2,0)},opacity=0.25]
        \draw[mass] (-0.2, 0) rectangle (0.2, 1);
        \node[anchor=west] at (0.2,0.5) {$M$};
        \draw[spring] (0,2) -- (0,3);
        \draw[string] (0,1) -- (0,2) (0,3) -- (0,4);
        \draw[ceiling] (-0.5,4) -- (0.5,4);
        \node[anchor=west] at (0.2,2.5) {$k$};
        \node at (0,-0.4) {(b)};
      \end{scope}
    }

    \onslide<3>{\begin{scope}[shift={(7,0)}]
        \draw[mass] (-0.2, 0) rectangle (0.2, 1);
        \node[anchor=west] at (0.2,0.5) {$M$};

        \draw[string] (0,1) -- (0,2.5) arc(0:90:0.5) -- ++(-1,0) coordinate (R);
        \draw[spring] (R) -- ++(-1,0) coordinate (L);
        \draw (R) ++(-0.5, -0.2) node[anchor=north] {$k$};
        \draw[string] (L) -- ++(-1,0) coordinate (W);
        \filldraw[pulley] (-0.5,2.5) coordinate (C) circle[radius=0.5];
        \fill (C) circle[radius=0.05];
        \draw[ceiling] (W) ++(0,0.5) -- ++(0,-1);
        \node at (-2,-0.4) {(c)};
      \end{scope}
    }
    \onslide<4->{\begin{scope}[shift={(7,0)},opacity=0.25]
        \draw[mass] (-0.2, 0) rectangle (0.2, 1);
        \node[anchor=west] at (0.2,0.5) {$M$};

        \draw[string] (0,1) -- (0,2.5) arc(0:90:0.5) -- ++(-1,0) coordinate (R);
        \draw[spring] (R) -- ++(-1,0) coordinate (L);
        \draw (R) ++(-0.5, -0.2) node[anchor=north] {$k$};
        \draw[string] (L) -- ++(-1,0) coordinate (W);
        \filldraw[pulley] (-0.5,2.5) coordinate (C) circle[radius=0.5];
        \fill (C) circle[radius=0.05];
        \draw[ceiling] (W) ++(0,0.5) -- ++(0,-1);
        \node at (-2,-0.4) {(c)};
      \end{scope}
    }

    \onslide<4>{\begin{scope}[shift={(5,-4.25)}]
        \draw[mass] (-0.2, 0) rectangle (0.2, 1);
        \node[anchor=west] at (0.2,0.5) {$M$};

        \draw[string] (0,1) -- (0,2.5) arc(0:90:0.5) -- ++(-0.75,0) coordinate (R);
        \draw[spring] (R) -- ++(-1,0) coordinate (L);
        \draw (R) ++(-0.5, -0.2) node[anchor=north] {$k$};
        \draw[string] (L) -- ++(-0.75,0) arc(90:180:0.5) -- ++(0,-1)
        coordinate (E);
        \foreach \x in {-0.5, -3}{
            \filldraw[pulley] (\x,2.5) circle[radius=0.5];
            \fill (\x, 2.5) circle[radius=0.05];
          }
        \filldraw[mass] (E) ++(0.2,0) rectangle ++(-0.4,-1);
        \draw (E) ++(-0.2,-0.5) node[anchor=east]{$M$};
        \node at (-2,-0.4) {(d)};
      \end{scope}
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220329-lec09.tex
modified: 2022-03-29 03:16:43.499862
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \onslide<1>{\node at  (0,0) {\includegraphics[width=5cm]{dragon}};}
    \onslide<2>{\node at  (0,0) {\includegraphics[width=3.5cm]{Emilia}};}
    \onslide<3>{\node at  (0,0) {\includegraphics[width=0.8\columnwidth]{cantilever}};}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220329-lec09.tex
modified: 2022-03-29 03:16:43.499862
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!25] (0,0) circle[radius=1.5];
    \draw[coord,->] (0,0) -- node[anchor=north west]{$R$} (45:1.5);
    \node at (135:1.15){$M$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/lec
filename: 220329-lec09.tex
modified: 2022-03-29 03:16:43.499862
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \node[opacity=0.2, anchor=south west] at (0,0)
    {\includegraphics[width=\columnwidth]{Khaleesi}};

    \fill (6,9) coordinate(A) circle[radius=0.05];

    \draw (A) ++(-140:5) node
    {\includegraphics[width=0.5cm]{Emilia.png}};


    % Draw the initial position of the diabolical arm
    \draw[line width=1.5,gray!50!black] (A) -- ++(-100:5) coordinate (B);
    \fill (B) circle[radius=0.2];
    \node[shift={(0.4,0)}] at (B) {$m$};

    \draw[coord,->] (A) ++(-95:5.5) arc(-95:-105:5.5);
    \draw[DarkGreen] (A) ++(-100:5.5) node[anchor=north]{$\omega_{0}$};

    \node[Red] at (2,9){\textsf{top view}};

    \node[text width=5cm, anchor=north west] at (9,9)
    {Unless $m$ slows to $\omega_{0}/2$ or less, Khaleesi is toast!};


    \onslide<2->{
      \foreach \q in {-130} {
          \draw[line width=1.5,opacity=0.35] (A) -- ++(\q:4.8)
          coordinate (B);
          \fill[opacity=0.35] (A) ++(\q:5) circle[radius=0.2];
        }
    }

    % Now the dragon

    \onslide<2->{
      \draw (A) ++(-130:2.5) coordinate(D) node
        {\includegraphics[width=1.25cm]{dragon}};
      \draw (D) ++(-0.1,0.4) node[anchor=south,Orange!67!black] {$4m$};
    }

    \onslide<2>{
      \node[text width=5cm, anchor=north west,color=Orange!67!black]
      at (9,6) {A dragon of mass $4m$ lands gently on the rod halfway between the pivot
        and $m$.};
    }

    \onslide<3-|handout:0>{
    \begin{scope}[shift={(9,9)}]

      \node[text width=5cm, anchor=north west] at (0,-4){
        A. Yes\\
        B. No \\
        C. Buy a vowel
      };
      }

      \onslide<3|handout:0>{
        \node[text width=5cm, anchor=north west] at (0,-2)
        {Is \textbf{momentum} conserved from the instant before the collision to
          the instant immediately after it?};

      }
      \onslide<4|handout:0>{
        \node[text width=5cm,anchor=north west] at (0,-2) {Is Khaleesi saved?};
      }
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/rec
filename: rec04-prof.tex
modified: 2022-02-12 00:17:24.589739
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!20] (0,0) -- (2,0) arc(0:90:2) -- cycle;
    \draw[coord] (0,0) -- (2.5,0) node[anchor=north]{$x$};
    \draw[coord] (0,0) -- (0,2.5) node[anchor=east]{$y$};
    \draw[coord] (0,0) -- node[anchor=south] {$R$} (30:2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/rec
filename: rec09-p18.tex
modified: 2022-03-29 21:53:29.279736
domain: p24a
source:
  \begin{tikzpicture}[scale=0.75]
    \fill (6,9) coordinate(A) circle[radius=0.05];

    \draw (A) ++(-140:5) node
    {\includegraphics[width=0.5cm]{Emilia.png}};


    % Draw the initial position of the diabolical arm
    \draw[line width=1.5,gray!50!black] (A) -- node[anchor=west]{$\ell$}
    ++(-100:5) coordinate (B);
    \fill (B) circle[radius=0.2];
    \node[shift={(0.4,0)}] at (B) {$m$};

    \draw[coord,->] (A) ++(-95:5.5) arc(-95:-105:5.5);
    \draw[DarkGreen] (A) ++(-100:5.5) node[anchor=north]{$\omega_{0}$};

    \node[Red] at (2,9){\textsf{top view}};

    \foreach \q in {-130} {
        \draw[line width=1.5,opacity=0.35] (A) -- ++(\q:4.8)
        coordinate (B);
        \fill[opacity=0.35] (A) ++(\q:5) circle[radius=0.2];
      }

    % Now the dragon

    \draw (A) ++(-130:2.5) coordinate(D) node
      {\includegraphics[width=1.25cm]{dragon}};
    \draw (D) ++(-0.1,0.4) node[anchor=south,Orange!67!black] {$4m$};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/rec
filename: rec09-p18.tex
modified: 2022-03-29 21:53:29.279736
domain: p24a
source:
  \begin{tikzpicture}[scale=1,line width=5]
    \def\tip{29.358}
    \draw[DarkRed] (0,0) -- ++(-90-\tip:4);
    \draw[DarkBlue] (180-\tip:0.088) -- ++(-\tip:3);
    \fill[gray] (0.07,-0.26) coordinate (A) circle[radius=0.1];
    \draw[dashed, gray,line width=1] (A) -- ++(-90:2);
    \draw[line width=1] (A) ++(-90:0.8) arc(-90:-90-\tip:1);
    \node[anchor=north] at (-105:1.05) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/rec
filename: rec03-prof.tex
modified: 2022-02-01 22:26:38.955684
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[NavyBlue, fill=blue!5!white] (0,0) circle[radius=2];
    \fill[white] (-2.05,-0.04) rectangle (2.05,0.04);
    \fill[DarkGreen] (0,0) circle[radius=0.02];
    \fill (1.5,0) circle[radius=0.04] coordinate (A);
    \draw[dashed,SlateGray,opacity=0.5] (0,0) circle[radius=1.5];
    \draw[coord] (0,-0.1) -- node[anchor=north]{$r$} ++(1.5,0);
    \draw[coord] (0,0) --node[anchor=south east]{$R_{e}$} (45:2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/rec
filename: rec05-p18.tex
modified: 2022-02-23 02:58:52.940651
domain: p24a
source:
  \begin{tikzpicture}[scale=1, line width=1]
    \def\rad{0.05}
    \draw[gray!25] (0,0) circle[radius=3];
    \fill (0,0) circle[radius=\rad] (0:3) coordinate (start)
    circle[radius=\rad]
    (180:3) coordinate (end)  circle[radius=\rad];
    \draw[DarkGreen,->] (start) -- node[anchor=north] {(a)} (end);
    \draw[DarkRed,->,dashed] (0:3) arc[radius=3,start angle=0, end angle=90]
    node[anchor=south] {(b)};
    \draw[DarkRed,->,dashed] (90:3) arc[radius=3,start angle=90, end angle=180];
    \draw[DarkBlue,->,dotted] (0:3) arc[radius=3,start angle=0, end angle=-90]
    node[anchor=north]{(c)};
    \draw[DarkBlue,->,dotted] (-90:3) arc[radius=3,start angle=-90, end
        angle=-180];

    \begin{scope}[SlateGray]
      \draw (60:2) arc[radius=2,start angle=60,end angle=120] --
      (120:1) arc[radius=1,start angle=120,end angle=60]
      -- cycle;
      \node at (90:1.5){(d)};
    \end{scope}
    \begin{scope}[SlateGray,->]
      \draw (90:2) -- (93:2);
      \draw (120:1.6) -- (120:1.4);
      \draw (90:1) -- (87:1);
      \draw (60:1.4) -- (60:1.7);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-v1.tex
modified: 2022-04-06 19:32:42.670018
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) -- node[anchor=west] {$l$} (-75:4) coordinate (A);
    \filldraw[fill=gray!25] (0,0) circle[radius=0.5] (A) circle[radius=0.5];
    \fill (0,0) circle[radius=0.05];
    \node[anchor=west] at (45:0.7){$M,R$};
    \node[anchor=east,shift={(180:0.5)}] at (A) {$M,R$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-v1.tex
modified: 2022-04-06 19:32:42.670018
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \fill (-0.5,2) rectangle (-0.75,-2);
    \begin{scope}[rotate=30]
      \filldraw[fill=gray!10] (0,-0.1) rectangle (5,0.1);
      \draw[coord, <->] (0,0.3) --node[anchor=south]{$l$} ++(5,0);
    \end{scope}
    \filldraw[fill=gray!25] (-0.5,0.25) -- ++(0:0.5) arc(90:-90:0.25) --
    ++(180:0.5) -- cycle;
    \filldraw[fill=white] (0,0) circle[radius=0.05];
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-v1.tex
modified: 2022-04-06 19:32:42.670018
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!5] (-0.1,0) rectangle (0.1,-2) coordinate (A);
    \fill (0,0) circle[radius=0.05];
    \filldraw[fill=gray!50] (A) rectangle (-0.1,-5);
    \draw[coord,<->] (-0.25,0) -- node[anchor=east]{$\alpha d$} ++ (-90:2);
    \draw[coord,<->] (0.25,0) -- node[anchor=west]{$d$} ++(-90:5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-v1.tex
modified: 2022-04-06 19:32:42.670018
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[spring] (0,0) --node[anchor=south,shift={(0,0.2)}]{$k$} (2,0);
    \draw[spring] (2.5,0) --node[anchor=south,shift={(0,0.2)}]{$k$} (4.5,0);
    \filldraw[black,fill=gray!33!white] (0,-0.25) rectangle (-0.5,0.25)
    (2,-0.25) rectangle (2.5,0.25)
    (4.5,-0.25) rectangle (5,0.25);
    \node at (-0.25,0.5){$m$};
    \node at (2.25,0.5){$3m$};
    \node at (4.75,0.5){$2m$};
    \begin{scope}[shift={(-0.25,-0.4)},coord, |->]
      \draw (0,0) --node[anchor=north]{$x_{1}$} ++(0.75,0);
      \draw (2.5,0) --node[anchor=north]{$x_{2}$} ++(0.75,0);
      \draw (5,0) --node[anchor=north]{$x_{3}$} ++(0.75,0);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-v2.tex
modified: 2022-04-06 21:21:29.983183
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \fill (-0.5,2) rectangle (-0.75,-2);
    \begin{scope}[rotate=30]
      \filldraw[fill=gray!10] (0,-0.1) rectangle (5,0.1);
      \draw[coord, <->] (0,-0.3) --node[anchor=north]{$l$} ++(5,0);
    \end{scope}
    \filldraw[fill=gray!25] (-0.5,0.25) -- ++(0:0.5) arc(90:-90:0.25) --
    ++(180:0.5) -- cycle;
    \filldraw[fill=white] (0,0) circle[radius=0.05];
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-final-practice.tex
modified: 2022-04-27 21:39:47.137599
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}
      \clip (1.5, 0) rectangle (-1.5,-1.6);
      \shadedraw[shading=ball] (0,0) circle[radius=1.5];
    \end{scope}
    \fill[fill=DarkBlue!50!white] (0,0) circle[x radius=1.5, y radius=0.1];

    \fill[gray!50] (-1.5,-1.5) rectangle (1.5,-1.7);
    \draw (-1.5,-1.51) -- ++(3,0);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt1-2022-practice.tex
modified: 2022-02-13 18:35:46.489635
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[SlateGray, fill=SlateGray!20] (-2,0) rectangle (2,1)
    (-0.5,1) rectangle (0.5, 2);
    \node at (0,1.5) {$m$};
    \node at (-1.5,0.5) {$2m$};

    % string
    \draw[DarkBlue, line width=1.25] (2,0.5) -- ++(3,0)
    ++(0,1) -- (0.5,1.5);

    % pulley
    \filldraw[SlateBlue, fill=SlateBlue!20] (5,1) coordinate (P)
    circle[radius=0.5];
    \fill (P) circle[radius=0.05];

    \draw[force] (P) -- ++(0:1.5) node[anchor=west] {$F = 6 mg$};

    % table
    \fill[gray!50] (-3,0) rectangle (7,-0.25);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt1-2022-practice.tex
modified: 2022-02-13 18:35:46.489635
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\h{2.5}
    \def\R{1}
    \foreach \y in {-\h, 0} {
        \begin{scope}[shift={(0,\y)}]
          \fill[
            left color=gray!50!black,
            right color=gray!50!black,
            middle color=gray!50,
            shading=axis,
            opacity=0.25
          ]
          (\R,0) -- (0,-\h) -- (-\R,0) arc[
              start angle=180,
              end angle=360,
              x radius=\R,
              y radius=\R*0.25];

          \fill[
            top color=gray!25,
            bottom color=gray!25,
            shading=axis,
            opacity=0.75
          ]
          (0,0) circle[x radius=\R, y radius=0.25*\R];

          % \draw 
          % (-2,0) arc (180:360:2cm and 0.5cm) -- (0,6) -- cycle;
          % \draw[dashed]
          % (-2,0) arc (180:0:2cm and 0.5cm);
          % \draw[dashed]
          % (2,0) -- node[below] {$r$} (0,0) -- node[left] {$h$} (0,6) ;
          % \draw 
          % (0,8pt) -- ++(8pt,0) -- (8pt,0);
        \end{scope}
      }
    \draw[<->,DarkGreen] (1.25*\R, 0) --node[anchor=west]{$h$} ++(-90:\h);
    \draw[->,DarkGreen] (0,0) -- node[anchor=south]{$R$} (0:\R);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-practice.tex
modified: 2022-04-06 19:33:58.072420
domain: p24a
source:
  \begin{tikzpicture}[
      scale=2,
      >=Stealth,
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw [fill=gray!50!white] (0,0) -- (1,0) arc(0:90:1) -- cycle;
    \node at (0.5,-0.2) {$R$};
    \draw [fill=blue!50!white] (-2,0.4) circle (0.1);
    \node at (-2, 0.2) {$m$};
    \draw[dashed] (-1.8,0.4) -- ++(0:3);
    \draw [->,line width=1.5pt,red!50!black] (-1.8,0.4) -- ++(0:0.5)
    node[anchor=north]{$\vv_{0}$};
    \draw[coord, <->] (-0.2,0) -- (-0.2, 0.4);
    \draw (-0.4,0.2) node {$b$};
    \node at (-1,-0.2) {top view};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-practice.tex
modified: 2022-04-06 19:33:58.072420
domain: p24a
source:
  \begin{tikzpicture}[
      scale=1.25,
      >=Stealth,
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      ice/.style={line width=2.5pt, color=blue!50!white},
      ground/.style={line width=1.5pt, color=brown}
    ]
    \draw[ground] (-5,-0.025) -- (5,-0.025);
    \draw[step=0.5,color=gray!25!white] (-5,0) grid (5,3);
    % draw the ice ramp
    \draw[ice] (0,2.5) arc(90:120:1) .. controls (-4,0)  ..(-5,0);
    \draw[ice] (0,2.5) arc(90:60:1) .. controls (2.5,.5) and (2.75,0.5)
    .. (3.5,0.5) .. controls(4,0.5) .. (4.5,1);
    % draw the radii of the circle
    \draw[line width=0.5pt] (0,1.5) -- ++(60:1) (0,1.5) -- ++(120:1);
    \draw[line width=0.5pt] (0,1.5) -- (0,2.5);
    \draw (0, 1.8) arc (90:120:0.3);
    \draw (0,1.8) arc (90:60:0.3);
    \node at (-0.45, 1.8) {$30^{\circ}$};
    \node at (0.45, 1.8) {$30^{\circ}$};
    \draw[dashed] (0,1.5) circle (1);
    \draw (0, 1.5) -- ++(-135:1);
    \node at (-0.55,1.2) {$R$};

    \draw[coord] (-2,0) -- ++(90:2.5);
    \node at (-2.2,2) {$h$};

    % draw the penguin
    \filldraw (-4.8,0.05) circle [x radius=0.1, y radius = 0.05];
    \draw (-4.8,0.15) node[anchor=south,fill=white]{penguin};
    \draw[red!50!black,->,line width=1.5pt] (-4.6,0.05) -- ++(0:0.5) node[anchor=north]{$\vv_{0}$};

    \draw[coord,-] (0,0) -- (0,0.75) node[anchor=west,fill=white]{$\frac{3}{2} R$};
    \draw[coord,->] (0,0.75)--(0,1.5);
    \node at (4.7,1.2) {P};


    \draw[coord] (4.8,0) -- (4.8,1) node[anchor=west]{$R$};
    %  \draw (5.6,-0.2)--(5.8,0.2) (5.7,-0.2)--(5.9,0.2);
    % ++(240:1) (0,2.5) arc(90:30:1) -- ++(-60:1) ;
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-practice.tex
modified: 2022-04-06 19:33:58.072420
domain: p24a
source:
  \begin{tikzpicture}[
      scale=1.25,
      >=Stealth,
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      ice/.style={line width=1.5pt, color=blue!50!white},
      ground/.style={line width=1.5pt, color=brown}
    ]
    \draw[ground] (-3,-0.025) -- (3.5,-0.025);
    \draw[ice] (0,2.5) arc(90:150:1) .. controls (-2,0) and (-2,0)
    ..(-3,0);
    \draw[ice] (0,2.5) arc(90:30:1) .. controls (1.5,.5) and (1.75,0.5)
    .. (2,0.5) .. controls(2.5,0.5) .. (3,1);
    \draw[line width=0.5pt] (0,1.5) -- ++(30:1) (0,1.5) -- ++(150:1);
    %  \draw[line width=0.5pt] (0,1.5) -- (0,2.5);

    % \draw (0, 1.8) arc (90:150:0.3);
    % \node at (-0.25, 2) {$60^{\circ}$};
    % \draw[dashed] (0,1.5) circle (1);
    % \node at (0.5,1.6) {$R$};
    % \draw[coord,-] (0,0) -- (0,0.75) node[anchor=west,fill=white]{$\frac{3}{2} R$};
    % \draw[coord,->] (0,0.75)--(0,1.5);

    % \node at (-2.8,1.25) {$h$};
    % \node at (2.8,1.2) {P};
    % \draw[coord,<->] (5,0) node[anchor=north]{$x$} --( 3,0) -- (3,2.5)
    % node[anchor=east]{$y$};

    % \filldraw[red] (6.9,0) rectangle (7.1,0.1)
    % node[anchor=north]{chocolates };
    % \draw[dashed] (3,1) .. controls (3.5,1.5) .. (3.85,1.65);
    % \draw[coord] (3.3,0) -- (3.3,1) node[anchor=west]{$R$};
    % \draw (5.6,-0.2)--(5.8,0.2) (5.7,-0.2)--(5.9,0.2);
    % ++(240:1) (0,2.5) arc(90:30:1) -- ++(-60:1) ;
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-practice.tex
modified: 2022-04-06 19:33:58.072420
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (0,-1) -- (0,4);
    \shadedraw[shading=radial,inner color=gray!20, outer color=gray]
    (0,0) circle[x radius=1, y radius = 0.25];
    \draw[coord,<->] (2,0) --node[anchor=west]{$h$} (2,3);
    \shade [shading=axis,left color=gray,right
      color=gray, middle color=gray!20!white] (-1,3) rectangle (1,0);
    \shadedraw [shading=radial,inner color=gray!20,outer color=gray]
    (0,3) circle[x radius=1, y radius=0.25];
    \draw[coord] (0,-0.5) --node[anchor=north]{$R$} ++(0:1);
    \draw[dashed] (0,3) -- (0,4);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-practice.tex
modified: 2022-04-06 19:33:58.072420
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    % the mass
    \filldraw[fill=gray!25!white] (-3.75,0) rectangle (-2.25, 1.5);
    \node at (-3,0.75) {$M$};

    % the string
    \draw (-2.25,1) -- (0.5,1)
    (1, 0.5) -- (1,-2.5);

    % the mass
    \filldraw[fill=gray!25!white] (1,-3) circle[radius=0.5];
    \node at (1,-3) {$M$};

    % the table
    \draw[line width=2] (-4,0) -- (0,0) -- (0,-3);

    % the barrel
    \shadedraw[shading=radial,inner color=white,outer color=gray] (0.5,0.5)
    circle[radius=0.5];
    \node at (1.2,1.2) {$M,R$};
    \draw[line width=3] (0,0) -- (0.5, 0.5); % the support
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-practice.tex
modified: 2022-04-06 19:33:58.072420
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[->] (-0.5,0) -- (6,0) node[anchor=north]{$r$};
    \draw[->] (0,-2) -- (0,2) node[anchor=east]{$U_{\rm eff}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-final-2022-sol.tex
modified: 2022-05-13 23:20:56.154539
domain: p24a
source:
  \begin{tikzpicture}[scale=1.25]
    \draw (105:1.05) node[anchor=north,rotate=15,opacity=0.33]
    {\includegraphics[scale=0.3]{racket}} ;
    \fill[color=DarkRed] (0,0) coordinate (peg) circle[radius=0.05];
    \draw[<-,DarkRed] (0.3,0) -- ++(1.5,0) node[anchor=west] {peg};
    \fill[color=DarkGreen] (-75:1.5) coordinate (CM) circle[radius=0.1];
    \draw[blue!33!black] (peg) -- (CM) (peg) -- ++(-90:2.5) (-82:1) node{$\theta$}
    (-90:0.75) arc(-90:-75:0.75);
    \draw[<-,DarkGreen] (CM) ++(0.3,0) -- ++(1.1,0) node[anchor=west] {CM};
    \draw[coord, <->] (195:1.5) -- node[anchor=east] {$d$} ++(-75:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-final-2022-sol.tex
modified: 2022-05-13 23:20:56.154539
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \draw[dashed] (0,0) -- (90:4);
    \draw[vel] (-0.5,2) --node[anchor=east]{$g$} ++(-90:1);
    \begin{scope}[rotate=60]
      \draw[line width=3,color=gray] (0,0) -- (3.5,0);
      \filldraw[fill=gray!50] (3.4,0) circle[y radius=1.25,x radius=0.35];
      \draw (3.4,1.25)--(3.5,1.25) (3.4,-1.25) --(3.5,-1.25);
      \foreach \x in {3.41, 3.42, ..., 3.49}{
          \fill[fill=gray!50] (\x,0) circle[y radius=1.25, x radius=0.35];
        }
      \filldraw[fill=gray!50] (3.5,0) circle[y radius=1.25,x radius=0.35];
      \draw (3.5,0) -- (5,0);
      \draw[->,line width=1.5] (4.5,-0.4) arc[start angle=-45, end angle=-350, x radius=0.2,
          y radius=0.6];
      \node at (4.6, -0.8) {$\omega$};
    \end{scope}
    \fill (0,0) circle[radius=0.1];
    \draw (0,1) arc (90:60:1);
    \node at (75:1.4) {$\psi$};
    \node at (52:2) {$d$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-final-2022-sol.tex
modified: 2022-05-13 23:20:56.154539
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \foreach \x in {-6,-5.5,...,-0.5} { \roller{(\x,-0.1)}}
    \foreach \x in {0.5, 1 } { \roller{(\x, -0.1)}}
    \roller{(1.5,0)}
    \roller{(2,0.1)}
    \roller{(2.5, 0.3)}
    \roller{(3, 0.6)}
    \roller{(3.5, 1)}
    \roller{(4, 1.4)}
    \roller{(4.5, 1.8)}
    \roller{(5, 2.1)}
    \roller{(5.5, 2.3)}
    \roller{(6, 2.4)}
    \foreach \x in {6.5,7,...,9} {\roller{(\x,2.4)}}


    \filldraw[fill=gray!50,rounded corners] (-5.2,0) rectangle ++ (1.2,0.6);
    \node at (-4.6,0.3) {$m$};
    \draw[vel] (-3,0.5) -- ++ (0:1) node[anchor=south] {$v_{0}$};

    \filldraw[fill=gray!25] (0,-0.3) coordinate (roller) circle[radius=0.35];
    \fill (roller) circle[radius=0.04];
    \draw[DarkGreen,->] (roller) ++(-30:0.5) arc(-30:-150:0.5)
    node[anchor=north east]{$\omega_{0}$};
    \draw (roller) ++(-60:0.5) node[anchor=north west] {$M,R$};

    \draw[DarkGreen,dashed] (0.5,-0.1) --++ (8.5,0);
    \draw[coord,<->] (8.25,-0.1) --node[anchor=west] {$h$} ++(0,2.5);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-final-2022-sol.tex
modified: 2022-05-13 23:20:56.154539
domain: p24a
source:
  \begin{tikzpicture}[scale=1.25]
    \draw[color=blue!40!black,line width=3] (0,2) -- (0,-2);
    \node[text width=2.25cm, font=\scriptsize] at (0.25, -2.5){ tower continues down to the ground below };
    \draw[color=gray!75,line width=5] (-2,0) -- (6,0);
    \draw[color=brown!50!black] (-2,0.05)
    --node[rotate=45,font=\scriptsize,anchor=south]{cable 1} (-0.05,2)
    (0.05,2) --node[rotate=-36,font=\scriptsize,anchor=south]{cable 2} (2.67,0.05)
    (6,0) -- (6,-1);
    \filldraw[fill=gray] (5.75,-1) rectangle (6.25,-1.5);
    \node at (6,-1.75){$m_{l}$};
    \fill[fill=white] (0,0) circle[radius=0.05];
    \draw[color=red,line width=2] (-0.15, 0.15) -- (0.15, -0.15);
    \draw[color=red,line width=2] (0.15, 0.15) -- (-0.15, -0.15);
    \fill[color=black] (-2.05,0.3) rectangle (-1.9,-0.075);
    \node at (-2.4,0) {$\frac{5}{3}M$};
    \draw[<-] (-2,0.35) -- ++(120:0.5) node[anchor=south,font=\scriptsize]{counterweight};
    \node at (4,0.35){$M$};
    \draw[coord,<->] (0,-0.5) --node[fill=white]{$\frac{d}{3}$} +(0:2.67);
    \draw[coord,<->] (0,-0.85) --node[fill=white]{$\frac{3d}{4}$} +(0:6);
    \draw[coord,<->] (0,-0.5) --node[fill=white]{$\frac{d}{4}$} +(180:2);
    \draw (-1.5,0) arc(0:45:0.5);
    \node at (-1.2,0.35){$\dg{45}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-final-2022-sol.tex
modified: 2022-05-13 23:20:56.154539
domain: p24a
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[coord,<->] (0,-0.5) --node[fill=white]{$\frac{d}{4}$} +(180:2);
    \draw[color=blue!40!white,line width=3] (0,2) -- (0,-2);
    \draw[color=gray!75,line width=5] (-2,0) -- (6,0);
    \fill[fill=white] (0,0) circle[radius=0.05];
    \fill[color=black] (-2.05,0.3) rectangle (-1.9,-0.075);
    \node at (-2.4,0) {$\frac{5}{3}M$};
    \node at (4,0.35){$M$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt1-2022-v1.tex
modified: 2022-02-16 18:30:29.845078
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-1.1, xmax=1.1,
        ymin=-1.1, ymax=1.1,
        zmin=-1.1,
        colormap/hot2,
        point meta min=-1.1,point meta max=0.4,
        hide axis,
      ]
      \addplot3 [
        surf,
        shader=flat, %interp,
        samples=43,
        domain=0:1,
        y domain=0:2*pi,
        z buffer=sort,
      ]
      ({x*cos(deg(y))},{x*sin(deg(y))},{-sqrt(x)});
      \draw[DarkGreen,->] (0,0,0) -- (0,0,0.2) node[anchor=west]{$z$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt1-2022-v1.tex
modified: 2022-02-16 18:30:29.845078
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[Navy,fill=Goldenrod!10!white] (0,0) circle[radius=3];
    \node at (-60:2.5) {$M, R$};
    \filldraw[white,fill=white] (45:3) -- (135:3) -- (140:3) -- (40:3) --
    cycle;
    \draw[Navy,dashed] (45:3) -- (135:3) -- (140:3) -- (40:3) -- cycle;
    \draw[DarkGreen,dashed] (42.5:3) -- (0,0) -- (137.5:3);
    \draw[DarkGreen,<->] (42.5:0.5) arc(42.5:137.5:0.5);
    \draw[DarkGreen] (90:0.5) node[anchor=south]{$\theta$};
    \fill[DarkRed] (60:2.33) circle[radius=0.05] node[anchor=south] {$m$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt1-2022-v1.tex
modified: 2022-02-16 18:30:29.845078
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\len{10}
    \fill[fill=gray!15!white] (0,-0.1) coordinate (A) rectangle (\len,0.1) coordinate (B);
    \draw (A) -- ++ (\len,0) (B) -- ++(-\len,0);
    \filldraw[fill=white] (0.4,0) coordinate (C) circle[radius=0.07];
    \draw[coord] (0,-0.2) -- node[anchor=north]{$r_0$} ++(0.4,0);
    \draw[coord, <->] (0, 0.4) -- node[anchor=south]{$L$} ++(\len,0);
    \fill (0,0) circle[radius=0.03]; % axis
    \draw[DarkGreen,->] (-5:\len+.5) arc(-5:5:\len+.5);
    \node at (0:\len+0.75) {$\omega$};
    \node[anchor=west,font=\sffamily] at (0,0.7){top view};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-solution.tex
modified: 2022-04-18 15:43:15.112951
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!25!white] (0,0) circle[radius=2];
    \fill (-1.9,0) circle[radius=0.15] (0,0) circle[radius=0.05];
    \fill[DarkRed] (-1,0) circle[radius=0.025] node[anchor=north] {CM};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-solution.tex
modified: 2022-04-18 15:43:15.112951
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!10] (0,-0.1) rectangle (5,0.1);
    \begin{scope}[opacity=0.25]
      \fill (-0.5,2) rectangle (-0.75,-2);
      \filldraw[fill=gray!25] (-0.5,0.25) -- ++(0:0.5) arc(90:-90:0.25) --
      ++(180:0.5) -- cycle;
      \filldraw[fill=white] (0,0) circle[radius=0.05];
    \end{scope}

    \draw[coord] (1.5,1) coordinate(O) -- ++(0:1) node[anchor=west] {$x$};
    \draw[coord] (O) -- ++(90:1) node[anchor=south] {$y$};

    \draw[force] (0,0) -- ++(90:1) node[anchor=south]{$N_{v}$};
    \draw[force] (0,0) -- ++(180:2) node[anchor=east]{$N_{h}$};
    \draw[force] (2.5,0) -- ++(-90:2) node[anchor=north]{$Mg$};

    \begin{scope}[shift={(-1.5,-4)},scale=1.5]
      \draw[dashed] (0,0) -- node[anchor=south]{$\frac34 Mg$} ++(3,0)
      -- node[anchor=west]{$\frac14 Mg$} ++(0,-1);
      \draw[force] (0,0) -- node[anchor=north] {$\frac{\sqrt{10}}{4} Mg $}
      (3,-1);
      \node at (-8:1.4) {$\phi$};
      \draw (0:1.2) arc(0:-19.83:1.2);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-solution.tex
modified: 2022-04-18 15:43:15.112951
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!5] (-0.1,0) rectangle (0.1,-2) coordinate (A);
    \fill (0,0) circle[radius=0.05];
    \filldraw[fill=gray!50] (A) rectangle (-0.1,-5);
    \draw[coord,<->] (-0.25,0) -- node[anchor=east]{$\alpha d$} ++ (-90:2);
    \draw[coord,<->] (0.25,0) -- node[anchor=west]{$d$} ++(-90:5);

    \draw[force,DarkRed, <-] (-0.1,-4) -- node[anchor=north]{$\Delta p$} ++(180:1);
    \draw[coord] (-1,0) -- node[anchor=east]{$x$} ++(-90:4);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2022/exams22
filename: p24a-mt2-2022-solution.tex
modified: 2022-04-18 15:43:15.112951
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[->,line width=2,DarkGoldenrod]
      \draw (0,0) -- ++(1,0);
      \draw (2,0) -- ++(0.5,0);
      \draw (4,0) -- ++(-1,0);
      \draw (0,-1) -- ++(1,0);
      \draw (2,-1) -- ++(-0.5,0);
      \draw (3,-1) -- ++(1,0);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK
filename: tikz.tex
modified: 2021-01-31 17:59:19
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[color=gray] (1.5,0) -- (0,0) -- (30:5) ;
    \draw (1,0) arc(0:30:1);
    \node at (15:1.25) {$\theta$};
    \begin{scope}[rotate=30, shift={(2.5,0)}]
      \draw[fill=gray!25!white,draw=SlateGray] (-0.5,0) rectangle (0.5,0.5);
      \draw[force] (0,0) -- ++(90:1.75) node[anchor=south]{$N$};
      \draw[force] (0,0) -- ++(0:1.5) node[anchor=south]{$f$};
      \draw[force] (0,0.25) -- ++(-120:1.25) node[anchor=north]{$mg$};
    \end{scope}
    \draw[coord,<->] (4,0) node[anchor=north]{$x$} -- ++(180:0.75)
    -- ++(90:0.75) node[anchor=south]{$y$};
    \draw[accel] (1,1) -- ++(180:1) node[anchor=south] {$a$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK
filename: tikz.tex
modified: 2021-01-31 17:59:19
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    % isolation of beam
    \draw[line width=2] (-2,0) -- (3,0);
    \draw[force] (-2,0) -- ++(-90:2) node[anchor=east]{$m_{1}g$};
    \draw[force] (3,0) -- ++(-90:1.5) node[anchor=east]{$T_{1}$};
    \draw[force] (0,0) --node[anchor=east]{$N$} ++(90:3);
    \draw[line width=2, Red] (45:0.25) -- (225:0.25) (-45:0.25) -- (135:0.25);
    \draw[coord] (-1,0) node[anchor=south]{$l_{1}$ };
    \draw[DarkGreen] (1.5,0) node[anchor=south]{$l_{2}$ };
    \node at (0,-2.5){$m_{1}g l_{1} = T_{1} l_{2}$};

    \begin{scope}[shift={(5.5,0)}]
      \filldraw[fill=gray!20] (0,0) circle[radius=0.5];
      \draw[force] (0,0) -- ++(90:1.5) node[anchor=east]{$T_{1}$};
      \draw[force] (-0.5,0) -- ++(-90:1) node[anchor=east]{$T_{2}$};
      \draw[force] (0.5,0) -- ++(-90:1) node[anchor=west]{$T_{2}$};

      \node at (0,-2.5) {$T_{1} = 2 T_{2}$};
    \end{scope}

    \def\side{0.2}
    \begin{scope}[shift={(8,0)}]
      \filldraw[fill=gray] (-\side,-\side) rectangle (\side,\side);
      \node[anchor=east] at (-\side,0) {$m_{2}$};
      \draw[force] (0,0) -- (-90:0.75) node[anchor=east]{$m_{2}g$};
      \draw[force] (0,\side) -- ++(90:1) node[anchor=east]{$T_{2}$};
      \draw[coord] (2*\side,0) -- ++ (-90:1) node[anchor=west]{$x$};
      \node at (0,-2.5) {$m_{2}\xdd = m_{2}g - T_{2}$};
    \end{scope}

    \begin{scope}[shift={(11,0)}]
      \filldraw[fill=gray] (-\side,-\side) rectangle (\side,\side);
      \node[anchor=east] at (-\side,0) {$m_{3}$};
      \draw[force] (0,0) -- (-90:0.75) node[anchor=east]{$m_{3}g$};
      \draw[force] (0,\side) -- ++(90:1) node[anchor=east]{$T_{2}$};
      \draw[coord] (2*\side,0) -- ++ (90:1) node[anchor=west]{$x$};
      \node at (0,-2.5) {$m_{3}\xdd = T_{2} - m_{3}g $};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK
filename: tikz.tex
modified: 2021-01-31 17:59:19
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\dq{15} % the angular range
    \def\rad{8cm} % the radius
    \draw[line width=5pt,color=Brown!70] (0,0) arc(0:\dq:\rad)
    (0,0) arc(0:-\dq:\rad);
    \draw[force] (0,0) -- ++(0:0.75) node[anchor=west]{$\dd{N}$};
    \draw[coord,<->] (1.5,1) node[anchor=west]{$x$} -- (0.5,1) -- (0.5,2)
    node[anchor=south]{$y$};
    \draw[force] (0,0) -- ++(-90:1.75) node[anchor=west]{$dF$};
    \begin{scope}[shift={(-\rad,0)}]
      \draw[dashed] (\dq:\rad*.75) -- (\dq:\rad) (-\dq:\rad*.75) -- (-\dq:\rad);
      \draw (0:\rad*.75) -- (0:\rad);
      \draw[force] (\dq+1:\rad) -- node[anchor=west]{$T_{2} = T(\theta
          + \dd{\theta}) \approx T(\theta) + T'(\theta)\dd{\theta}$}
      ++(\dq+90:2);
      \draw[force] (-\dq-1:\rad) -- node[anchor=west]{$T_{1} = T(\theta
          - \dd\theta) \approx T(\theta) - T'(\theta)\dd\theta$} ++(-\dq-90:2);
      \draw[<->] (0:0.8*\rad) arc(0:\dq:0.8*\rad);
      \draw[<->] (0:0.8*\rad) arc(0:-\dq:0.8*\rad);
      \node at (\dq/2:0.85*\rad){$\dd{\theta}$};
      \node at (-\dq/2:0.85*\rad){$\dd{\theta}$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK
filename: tikz.tex
modified: 2021-01-31 17:59:19
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[vector] (0,0) --node[anchor=south east]{$A$} (2,3);
    \draw[vector] (2,3) --node[anchor=south west]{$B$} (4,-1);
    \draw[vector] (4,-1) --node[anchor=north]{$C$} (0,0);
    \draw[dashed] (0,0) -- (2,-4) -- (4,-1);
    % label the angles
    \node at (0.5,0.3){$\beta$};
    \node at (2,2.35){$\gamma$};
    \node at (3.5,-0.6) {$\alpha$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK
filename: tikz.tex
modified: 2021-01-31 17:59:19
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \shade[ball color=NavyBlue!70] (0,0) circle[radius=0.3];
    \node at (0.6,0){$m$};
    \draw[force] (135:0.4) -- ++(135:1.2) node[anchor=south]{$T_{\rm up}$};
    \draw[force] (-135:0.4) -- ++(-135:1.2) node[anchor=north]{$T_{\rm low}$};
    \draw[force] (0,0) -- ++(-90:1.5) node[anchor=west]{$mg$};
    \draw[accel] (180:0.6) -- ++(180:1) node[anchor=south]{$a$};
    \draw[coord, ->] (0.75,0.75) -- ++(0.5,0) node[anchor=north]{$\ur$};
    \draw[coord, ->] (0.75,0.75) -- ++(0,0.5) node[anchor=east]{$\uz$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK
filename: tikz.tex
modified: 2021-01-31 17:59:19
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \draw[line width=6,color=gray] (-1.5,-1.1) -- ++(0:3);
    \draw[line width=2] (0,0) circle[radius=0.3];
    \draw[line width=2] (0,0) circle[radius=1];
    \draw[color=red] (0,0) -- (-16.7:0.3);
    \draw[dashed] (-16.7:0.3) -- ++ (0:0.75);
    \begin{scope}[shift={(-16.7:0.3)}]
      \draw (0:0.25) arc (0:73.3:0.25);
      \node at (36:0.5){$\theta$};
    \end{scope}
    \draw[dashed] (0,-1) -- (0,.25);
    \draw[dashed, line width=1.5] (0,-1) -- ++(73.3:1);
    \draw[line width=2,->] (-16.7:0.3) -- ++(73.3:1.6);
    \draw[force] (0,-1) -- ++(180:1) node[anchor=south]{$f$};
    \draw[force] (0,0) -- (-90:0.75) node[anchor=east]{$mg$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK/prob
filename: KK0426.tex
modified: 2020-12-31 05:34:37
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!25] (0,0.707) -- ++(5,0) -- ++(-45:1)
    -- ++(-135:1) -- ++(-5,0) -- cycle;
    \draw[vel] (7.5,0.25) -- node[anchor=south]{$mv$} (5.5,0.25);
    \draw[vel] (5.5,0.25) -- ++(90:2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK/sol
filename: KK0204.tex
modified: 2019-02-01 21:58:22
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed,yellow!50!black] (0,0) circle[radius=3];
    \draw[dashed, DarkRed] (0,0) circle[radius=2];
    \shade[ball color=yellow] (30:3) circle[radius=0.5];
    \node at (30:3.75){$m$};
    \shade[ball color=red] (210:2) circle[radius=0.75];
    \node at (210:3){$M$};
    \draw[->,line width=1.5,DarkSlateBlue] (0,0) --node[anchor=north west]{$r_{1}$}
    (30:3);
    \draw[->,line width=1.5,DarkSlateBlue] (0,0) --node[anchor=north west]{$r_{2}$} (210:2);
    \draw[SlateGray,->] (-0.5,0) -- (3.5,0) node[anchor=north]{$x$};
    \draw[SlateGray,->] (0,-0.5) -- (0,3) node[anchor=east]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK/sol
filename: KK0214.tex
modified: 2020-12-29 04:24:23
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[fill=gray!15!white] (0,0) rectangle node{$M_{3}$} (1,1) ;
    \draw[force] (0.5,1) -- ++(90:1.25) node[anchor=south]{$T$};
    \draw[force] (0.5,0.25) -- ++(-90:1.25) node[anchor=north]{$M_{3}g$};
    \draw[force,opacity=0.75] (1,0.8) -- ++ (180:1.5) node[anchor=south]{$N_{3}$};
    \draw[coord] (-1,0.5) -- node[anchor=east]{$x_{2}$}++(-90:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK/sol
filename: KK0720.tex
modified: 2016-04-04 17:34:59
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (0,0) -- ++(90:1);
    \draw[force] (0,0) -- (-1.5,0.5) node[anchor=east]{$F$};
    \draw (90:0.75) arc(90:161.6:0.75);
    \node at (125:1) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK/sol
filename: KK0735.tex
modified: 2019-04-11 03:30:34
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-90, xmax=90, ymin=-0.5, ymax=0.5, enlargelimits=false,
        width=5in, height=3in,
        xlabel={$\theta (^{\circ})$},
        ylabel={$U(\theta)$},
        legend entries={$L/R = 0.5$, $L/R = 1$, $L/R = 2$, $L/R = 3$},
        legend pos={outer north east},
        % ytick={0,1}, xtick={0,1},
        % xticklabel=\empty, xticklabels{0,,$a$,,a$},
        % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \def\ratio{0.5} % L/R
      \addplot[SlateGray, domain=-90:90, samples=100, line width=2pt,]
      {(1+\ratio/2)*(cos(x)-1) + rad(x)*sin(x)};
      \def\ratio{1} % L/R
      \addplot[DarkGreen, domain=-90:90, samples=100, line width=2pt,]
      {(1+\ratio/2)*(cos(x)-1) + rad(x)*sin(x)};
      \def\ratio{2} % L/R
      \addplot[DarkRed, domain=-90:90, samples=100, line width=2pt,]
      {(1+\ratio/2)*(cos(x)-1) + rad(x)*sin(x)};
      \def\ratio{3} % L/R
      \addplot[DarkBlue, domain=-90:90, samples=100, line width=2pt,]
      {(1+\ratio/2)*(cos(x)-1) + rad(x)*sin(x)};

    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK/sol
filename: KK0119.tex
modified: 2022-01-22 23:49:00.799792
domain: p24a
source:
  \begin{tikzpicture}[scale=1, arrows = {-Stealth[scale width=0.5]}, line width=2pt]
    \draw[coord,<->,opacity=0.5] (0,2) node[anchor=east]{$y_{A}$} -- (0,0) -- (3,0)
    node[anchor=north]{$x_{A}$};
    \coordinate (B) at (-1,-3);
    \coordinate (P) at (2.5,1);
    \fill[fill=DarkRed!70!white] (P) circle[radius=0.1]
    node[anchor=west,color=DarkRed]{$P$};

    \begin{scope}[shift={(B)}]
      \draw[coord,<->,opacity=0.5] (0,2) node[anchor=east]{$y_{B}$} -- (0,0) -- (3,0)
      node[anchor=north]{$x_{B}$};
    \end{scope}

    % draw vector to point P
    \draw (0,0) -- node[anchor=south]{$r_{A}$} (P);
    \draw (0,0) -- node[anchor=south west]{$R$} (B);
    \draw (B) -- node[anchor=west]{$r_{B}$} (P);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK/sol
filename: KK0736.tex
modified: 2021-04-18 19:43:16
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \coordinate (B) at (0,0);
    \coordinate (A) at (0,3);
    \coordinate (CM) at (0,1);
    \draw (A) -- node[anchor=east]{$l$} (B);
    \filldraw[fill=gray!20] (B) circle[radius=0.2] (A) circle[radius=0.2] ;
    \node[anchor=east,shift={(-0.2, 0)}] at (B) {$m_{b}$};
    \node[anchor=east,shift={(-0.2, 0)}] at (A) {$m_{a}$};
    \draw[vel] (B) ++(0.3,0) -- ++ (0:1) node[anchor=west] {$v_{0}$};
    \draw[coord] (1.5,1.5) -- ++(1,0) node[anchor=north]{$x$};
    \draw[coord] (1.5,1.5) -- ++(0,1) node[anchor=east]{$y$};
    \draw[DarkRed, line width=2] (CM) ++(45:0.125) -- ++ (225:0.25)
    (CM) ++(-45:0.125) -- ++ (135:0.25) (CM) node[shift={(-0.125,0)},anchor=east]
    {\tiny CM};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK/sol
filename: KK0806.tex
modified: 2021-04-26 01:32:33
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[color=DarkGreen,shift={(-1.5,0)}]
      \draw[->] (0,0) -- (0.5,0) node[anchor=west]{$\rho$};
      \draw[->] (0,0) -- (0,0.5) node[anchor=south]{$z$};
      \filldraw[fill=white] (0,0) circle[radius=0.1];
      \draw (45:0.1) -- (225:0.1) (-45:0.1)--(135:0.1);
      \node at (-0.2,-0.2) {$\phi$};
    \end{scope}
    \begin{scope}[rotate=15]
      \draw[gray] (-0.05,-1) rectangle (0.05,1);
      \draw[<->,DarkGreen] (0.5,0) node[anchor=north]{$x$} -- (0,0) -- (0,0.5) node[anchor=east]{$y$};
      %      \draw (-0.5,1) arc(180:165:0.5);
      %      \node at (-0.3,1.25){$\alpha$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/KK/sol
filename: KK0208.tex
modified: 2016-01-29 22:24:24
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \node[draw] at (0,0) {\phantom{$M_{1}$}};
    \draw[force] (0,0) -- (-90:1.5) node[anchor=east]{$M_{1}g$};
    \draw[force] (0,0.25) -- (90:1.5) node[anchor=east]{$T_{1}$};
    \draw[coord] (-0.75,0) -- ++(90:1) node[anchor=east]{$x_{1}$};

    \begin{scope}[shift={(4,0)}]
      \draw (0,0) circle[radius=0.5];
      \draw[force] (-0.5,0) -- ++(-90:1.5) node[anchor=east]{$T_{2}$};
      \draw[force] (0.5,0) -- ++(-90:1.5) node[anchor=west]{$T_{2}$};
      \draw[force] (0,0) -- (90:1.5) node[anchor=east]{$T_{1}$};
      \draw[coord] (-0.75,0) -- ++(90:1) node[anchor=east]{$x_{3}$};
    \end{scope}

    \begin{scope}[shift={(8,0)}]
      \node[draw] at (0,0) {\phantom{$M_{1}$}};
      \draw[force] (0,0) -- ++(-90:1.5) node[anchor=east]{$M_{2}g$};
      \draw[force] (0,0.25) -- ++(90:1.5) node[anchor=east]{$T_{2}$};
      \draw[coord] (-0.75,0) -- ++(90:1) node[anchor=east]{$x_{2}$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/p24a_pns
filename: tikz.tex
modified: 2021-01-31 17:17:39
domain: p24a
source:
  \begin{tikzpicture}[
      decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm},
      >=Stealth
    ]
    \def\ell{2}
    \filldraw (0,0) circle(0.1);
    \draw[decorate] (0,0) -- (30:\ell);
    \shade[ball color=gray] (30:\ell) circle(0.25) ++(-90:0.25) node[anchor=north]{
        $m$ };
    \draw[decorate] (30:2.25) -- ++(30:\ell);
    \shade[ball color=gray] (30:4.5) circle(0.25) ++(-90:0.25)
    node[anchor=north]{$m$};
    \draw (30:1) ++(120:0.5) node {$k$};
    \draw (30:3) ++(120:0.5) node {$k$};
    \draw[->] (24:5) arc(24:36:5) node[anchor=south]{$\omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/p24a_pns
filename: tikz.tex
modified: 2021-01-31 17:17:39
domain: p24a
source:
  \begin{tikzpicture}[scale=0.75,
      decoration={coil,aspect=0.3,segment
          length=3mm,amplitude=3mm},
      >=Stealth,
      coord/.style={line width=1,color=green!50!black,|->},
      beef/.style={line width=1.5}]
    \draw[line width=2] (-1,0) -- (3.5,0);
    \draw[line width=2] (-1,6) -- +(0:4.5);

    % Draw the applied force
    \draw[->, beef] (0,3) -- (0,1.5)
    node[anchor=north]{$\vb{F}$};
    \draw[coord] (-0.5,2) -- +(270:1) node[anchor=north]{$x$};
    % Draw the second spring
    \draw[decorate,beef] (2,0) -- ++(90:2);
    \draw[beef] (2,2) -- (2,3);
    \node at (2.9,.8) {$k_{2}$};
    % Draw the pulley
    \filldraw[fill=blue!10!white,draw=blue] (1,3) circle(1);
    \filldraw[fill=blue!50!black] (1,3) circle(0.05);
    \draw[coord] (-0.5,4.5) -- +(270:1) node[anchor=north]{$x_{1}$};
    \draw[coord] (3,1.75) -- +(90:1) node[anchor=south]{$x_{2}$};
    % Draw the first spring
    %\usetikzlibrary{decorations.pathmorphing}
    \draw[decorate,beef] (1,6) -- ++(270:2) ;
    \node at (1.9,5.2) {$k_{1}$};
    \draw[beef] (1,3) -- (1,4);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/p24a_pns
filename: tikz.tex
modified: 2021-01-31 17:17:39
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[red, line width=2,shift={(0.05,0)}] (-0.1,-0.1) -- (0.1,0.1)
    (-0.1,0.1) -- (0.1,-0.1);
    \fill[fill=gray] (0,-2.5) rectangle (0.1,-4);
    \draw (0,0) rectangle (0.1,-4);
    \draw[coord,<->] (1,0) -- node[fill=white]{$d$} ++(-90:4);
    \draw[coord,<->] (0.5,0) -- node[fill=white]{$\alpha d$} ++(-90:2.5);
    \draw[coord] (-0.5,0) -- node[fill=white]{$x$} ++(-90:3.25);
    \draw[force] (-1.,-3.25) --node[anchor=north]{$\Delta \vb{p}$} ++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/p24a_pns/prob
filename: Tension.tex
modified: 2021-02-03 00:52:22
domain: p24a
source:
  \begin{tikzpicture}[scale=1,
      string/.style={SlateGray,line width=2pt},
      mass/.style={DarkSlateGray, fill=SlateGray!25},
      ceiling/.style={gray!50,line width=4pt},
      pulley/.style={fill=SlateBlue!50!white}
    ]
    \begin{scope}[shift={(0,0)}]
      \draw[mass] (-0.2, 0) rectangle (0.2, 1);
      \node[anchor=west] at (0.2,0.5) {$M$};
      \draw[string] (0,1) -- (0,4);
      \draw[ceiling] (-0.5,4) -- (0.5,4);
      \draw[<-,DarkGreen] (-0.1,2.5) -- ++(180:0.5);
      \node at (0,-0.4) {(a)};
    \end{scope}

    \begin{scope}[shift={(2,0)}]
      \draw[mass] (-0.2, 0) rectangle (0.2, 1);
      \node[anchor=west] at (0.2,0.5) {$M$};
      \draw[spring] (0,2) -- (0,3);
      \draw[string] (0,1) -- (0,2) (0,3) -- (0,4);
      \draw[ceiling] (-0.5,4) -- (0.5,4);
      \node[anchor=west] at (0.2,2.5) {$k$};
      \node at (0,-0.4) {(b)};
    \end{scope}

    \begin{scope}[shift={(7,0)}]
      \draw[mass] (-0.2, 0) rectangle (0.2, 1);
      \node[anchor=west] at (0.2,0.5) {$M$};

      \draw[string] (0,1) -- (0,2.5) arc(0:90:0.5) -- ++(-1,0) coordinate (R);
      \draw[spring] (R) -- ++(-1,0) coordinate (L);
      \draw (R) ++(-0.5, -0.2) node[anchor=north] {$k$};
      \draw[string] (L) -- ++(-1,0) coordinate (W);
      \filldraw[pulley] (-0.5,2.5) coordinate (C) circle[radius=0.5];
      \fill (C) circle[radius=0.05];
      \draw[ceiling] (W) ++(0,0.5) -- ++(0,-1);
      \node at (-2,-0.4) {(c)};
    \end{scope}

    \begin{scope}[shift={(12,0)}]
      \draw[mass] (-0.2, 0) rectangle (0.2, 1);
      \node[anchor=west] at (0.2,0.5) {$M$};

      \draw[string] (0,1) -- (0,2.5) arc(0:90:0.5) -- ++(-0.75,0) coordinate (R);
      \draw[spring] (R) -- ++(-1,0) coordinate (L);
      \draw (R) ++(-0.5, -0.2) node[anchor=north] {$k$};
      \draw[string] (L) -- ++(-0.75,0) arc(90:180:0.5) -- ++(0,-1)
      coordinate (E);
      \foreach \x in {-0.5, -3}{
          \filldraw[pulley] (\x,2.5) circle[radius=0.5];
          \fill (\x, 2.5) circle[radius=0.05];
        }
      \filldraw[mass] (E) ++(0.2,0) rectangle ++(-0.4,-1);
      \draw (E) ++(-0.2,-0.5) node[anchor=east]{$M$};
      \node at (-2,-0.4) {(d)};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/p24a_pns/prob
filename: AsymmetricRotor.tex
modified: 2022-04-12 21:26:12.248330
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\aa{2} \def\bb{2}
    \draw[dashed,<-] (0,\bb+1) node[anchor=south]{$z$} -- (0,-2);
    \draw[dashed,->] (-\aa,0) -- (\aa,0) node[anchor=west]{$x$};
    \draw[->] (-0.25,\bb+0.6) arc[x radius=0.5,y radius=0.2,start angle=120,end angle=420];
    \draw[line width=2,color=gray] (\aa,\bb) --node[anchor=south]{$a$} (0,\bb)
    --node[anchor=east]{$b$} (0,0)
    -- node[anchor=west]{$b$} (0,-\bb)
    -- node[anchor=north]{$a$} (-\aa,-\bb) ;
    \shade[ball color=red] (\aa,\bb) circle[radius=0.25];
    \shade[ball color=red] (-\aa,-\bb) circle[radius=0.25];
    \node at (\aa+0.5,\bb) {$m$};
    \node at (-\aa-0.5,-\bb) {$m$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/p24a_pns/sol
filename: precession.tex
modified: 2022-04-06 19:13:10.490786
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[coord] (0,0) -- ++ (0:3) node[anchor=north]{$x$};
    \draw[coord] (0,0) -- ++ (90:3) node[anchor=east]{$y$};
    \begin{scope}[rotate=30]
      \draw[line width=2,gray] (0,0) -- ++(0:2);
      \draw[line width=4,gray!75!black] (2,-0.5)  -- (2,0.5);
      \draw[DarkRed,line width=1,->] (0,0) -- ++(0:4) node[anchor=south]{$L$};
      \draw[DarkGreen,line width=2,->] (0,0) -- ++(90:1.5)
      node[anchor=south]{$\vb*{\tau}$};
    \end{scope}
    \draw[DarkGreen,->] (0:1)  arc(0:30:1);
    \node[DarkGreen] at (12:1.2){$\phi$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/p24a_pns/sol
filename: polar-unit-vectors.tex
modified: 2019-01-23 17:36:57
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \draw[coord,->] (0,0) -- (4,0) node[anchor=north]{$x$};
    \draw[coord,->] (0,0) -- (0,3) node[anchor=east]{$y$};
    \draw[->] (0,0) -- node[anchor=south]{$r$} (30:3) coordinate(A);
    \draw[vel] (A) -- ++(30:2) node[anchor=west]{$\ur$};
    \draw[vel] (A) -- ++(120:2) node[anchor=south]{$\uth$};
    \draw (0.8,0) arc (0:30:0.8);
    \node at (15:1){$\theta$};
    \draw[dashed] (A) -- ++(90:2);
    \begin{scope}[shift={(A)}]
      \draw (0,0.8) arc(90:120:0.8);
      \node at (105:1){$\theta$};
      \draw[opacity=0.5,line width=2,->] (0,0) --
      node[anchor=west]{$\cos\theta$} (90:1.732) coordinate (B);
      \draw[opacity=0.5,line width=2,->] (B) --
      node[anchor=south] {$\sin\theta$}   ++(180:1);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2019/rec19
filename: rec11.tex
modified: 2019-04-12 04:18:34
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[coord,->] (0,0) -- ++(1,0) node[anchor=north]{$y$};
    \draw[coord,->] (0,0) -- ++(0,1) node[anchor=east]{$z$};
    \draw[coord,->] (0,0) -- ++(240:0.7) node[anchor=east]{$x$};
    \coordinate (CM) at (3,2);
    \foreach \x/\y in {2/-1, 4/-0.5, 5/3, 2/4} {
        \fill[gray] (\x,\y) circle[radius=0.1];
      }
    \draw[vel,line width=1.25] (0,0) --node[anchor=south east]{$R$} (CM);
    \fill[red] (CM) circle[radius = 0.05] node[anchor=south]{CM};
    \coordinate (A) at (4,1);
    \fill (A) circle[radius=0.1] node[anchor=west]{$m_{i}$};
    \draw[vel, line width=1.25] (0,0) --node[anchor=north]{$r_{i}$} (A);
    \draw[vel, line width=1.25] (CM) -- node[anchor=south west]{$r'_{i}$} (A);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2019/rec19
filename: rec07-p18.tex
modified: 2019-03-13 16:41:02
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{0.25}
    \draw[spring] (-3,\rad) -- (-1.5,\rad);
    \draw[spring] (1.5,\rad) -- (3,\rad);
    \draw[line width=1.25,color=SlateGray] (-3,-\rad) -- ++(0:6);
    \foreach \x in {-1, 1} {
        \filldraw[fill = gray] (\x,0) circle[radius=\rad];
      }
    \filldraw[fill=SlateBlue!25] (-1.5,0) rectangle node{$m$} (1.5, 2*\rad);
    \filldraw[fill=DarkRed!40] (-0.3,0) rectangle (0.3,-0.2); % the damper
    \foreach \x in {-3, 3} {
        \draw[line width=1.5, color=SlateGray] (\x,-\rad) -- ++(90:1);
      }
    \foreach \x in {-2.25, 2.25}{ \node at (\x, 0.75) {$k/2$}; }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2019/exams
filename: p24a-mt1-2019-v3-sol.tex
modified: 2019-02-24 19:56:20
domain: p24a
source:
  \begin{tikzpicture}[scale=1.75]
    \begin{scope}[rotate={30}]
      %\draw (0,0) --node[anchor=south,rotate=30]{$\alpha^{2} t^{2} L$} (2,0)
      %      --node[anchor=west]{$\alpha L$} (2,-1) -- cycle;
      \draw[vel] (0,0) --node[anchor=south,rotate=30]{$\alpha^{2} t^{2} L$} (2,0);
      \draw[vel] (2,0) --node[anchor=west]{$\alpha L$} (2,-1);

      \draw[vel] (0,0) --node[anchor=north]{$\mu_{s} g$} (2,-1);
      \draw (0:0.75) arc (0:-28:0.75);
      \node at (-15:1){$\phi$};
      \draw[coord,<->] (3.0,0) node[anchor=west]{$\ur$} -- (2.5,0) -- (2.5,0.5)
      node[anchor=east]{$\uth$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2019/exams
filename: p24a-mt1-2019-v3-sol.tex
modified: 2019-02-24 19:56:20
domain: p24a
source:
  \begin{tikzpicture}[
      decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm},
      >=stealth'
    ]
    \def\lv{2}
    \def\ang{30}
    \filldraw (0,0) circle(0.05);
    \draw[gray, line width=2pt] (\ang:0.05) --node[anchor=south, black]{$\ell$}
    (\ang:\lv);
    \draw[decorate] (\ang:\lv) -- ++(\ang:\lv);
    \draw[decorate] (\ang:2*\lv) -- ++(\ang:\lv);

    \foreach \r in {2, 4, 6}{
        \shade[ball color=gray] (\ang:\r) circle(0.25);
        \draw (\ang:\r) ++ (-90:0.25) node[anchor=north]{$m$};
      }
    \foreach \r in {3, 5}{
        \draw (\ang:\r) ++(120:0.5) node {$k$};
      }
    \draw[->] (24:6.5) arc(24:36:6.5) node[anchor=south]{$\omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2019/exams
filename: p24a-mt1-2019-v3-sol.tex
modified: 2019-02-24 19:56:20
domain: p24a
source:
  \begin{tikzpicture}[
      decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm},
      >=stealth'
    ]
    \def\lv{2}
    \def\ang{30}
    \shade[ball color=gray] (0,0) circle(0.25);
    \draw[force] (0,0) -- ++(210:1) node[anchor=north]{$k\Delta x_{2}$};

    \shade[ball color=gray] (0,-2) circle(0.25);
    \draw[force] (0,-2) -- ++(210:1) node[anchor=north]{$k\Delta x_{1}$};
    \draw[force] (0,-2) -- ++(30:1) node[anchor=west]{$k\Delta x_{2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt1-2021-sol.tex
modified: 2021-03-01 05:05:48
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[coord] (0,0) -- (2,0) node[anchor=north]{$x$};
    \draw[coord] (0,0) -- (0,2) node[anchor=east] {$y$};
    \def\ang{35}
    \draw[vector,line width=1] (0,0) -- node[anchor=south east]{$r$} (\ang:2) coordinate(P);
    \draw[coord, line width=1.25] (P) -- ++(\ang:0.5) node[anchor=south west] {$\ur$};
    \draw[coord,line width=1.25] (P) -- ++(\ang+90:0.5) node[anchor=east] {$\uth$};
    \draw (0.5,0) arc (0:\ang:0.5);
    \node[anchor=west] at (\ang/1.5:0.6) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt1-2021-sol.tex
modified: 2021-03-01 05:05:48
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!33] (0,0) circle[radius=0.25];
    \draw[force] (0,0) -- ++(-90:1.5) node[anchor=north]{$mg$};
    \draw[force] (0,0.1) -- ++(90:1.25) node[anchor=south] {$C v^{2}$};
    \draw[coord] (-0.5,0) -- ++(-90:1) node[anchor=north] {$z$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt1-2021-sol.tex
modified: 2021-03-01 05:05:48
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=2.5, ymin=0, ymax=1, enlargelimits=false,
        width=2.5in, height=2in,
        xlabel={$t/\tau$}, ylabel={$v$}, ytick={0,1}, xtick={0,1, 2},
        yticklabels={0, $v_{T}$},
      ]
      \addplot[DarkGreen, domain=0:2.5, samples=100, line width=2pt]   {tanh(x)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt1-2021-sol.tex
modified: 2021-03-01 05:05:48
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[SlateGray, fill=SlateGray!20] (-2,0) rectangle (2,1)
    (-0.5,1) rectangle (0.5, 2); \node at (0,1.5) {$m$}; \node at
    (-1.5,0.5) {$2m$};

    \draw[coord] (0, 2.2) -- ++ (0:1) node[anchor=west]{$x_{1}$};
    \draw[coord] (0, 0.5) -- ++ (0:1) node[anchor=west]{$x_{2}$};

    % string
    \draw[DarkBlue, line width=1.25] (2,0.5) -- ++(3,0) ++(0,1) --
    (0.5,1.5);

    % pulley
    \filldraw[SlateBlue, fill=SlateBlue!20] (5,1) coordinate (P)
    circle[radius=0.5]; \fill (P) circle[radius=0.05];

    \draw[force] (P) -- ++(0:1.5) node[anchor=west] {$F = 6 mg$};
    \draw[coord] (P) ++ (0, 0.75) -- ++ (0:1) node[anchor=west]{$x_{3}$};
    % table
    \fill[gray!50] (-3,0) rectangle (7,-0.25);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt1-2021-sol.tex
modified: 2021-03-01 05:05:48
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[SlateGray, fill=SlateGray!20] (-0.5,0) rectangle (0.5, 1);
    \draw[force] (0, 0.5) -- ++(-90:1.5) node[anchor=east] {$mg$};
    \draw[force] (0.5,0.5) -- ++(0:1.5) node[anchor=west] {$T$};
    \draw[force] (0.1,0) -- ++(90:1.5) node[anchor=south] {$N_{1}$};
    \draw[force] (0,0) -- ++(180:1) node[anchor=south] {$f_{1}$};
    \draw[coord] (-3,0.5) -- node[anchor=north]{$x_{1}$} ++(1,0);
    \begin{scope}[shift={(6,1)}]
      \node at (0,0) {$N_{1} = mg$}; \node at (0,-0.5)
      {$T - f_{1} = m \ddot{x_{1}}$}; \node at (2, 0) {(1)}; \node at (2,
      -0.5) {(2)};
    \end{scope}

    \begin{scope}[shift={(0,-3)}]
      \filldraw[SlateGray, fill=SlateGray!20] (-2,0) rectangle (2,1);
      \draw[force] (0, 0.5) -- ++(-90:2) node[anchor=east] {$2mg$};
      \draw[force] (2,0.5) -- ++(0:1.5) node[anchor=west] {$T$}; \draw[force]
      (0.2,1) -- ++(-90:1.5) node[anchor=west] {$N_{1}$}; \draw[force] (-0.2,0)
      -- ++(90:1.5) node[anchor=east] {$N_{2}$}; \draw[force] (0,1) -- ++(0:1)
      node[anchor=south] {$f_{1}$}; \draw[force] (0,0) -- ++(180:1.5)
      node[anchor=north] {$f_{2}$};

      \draw[coord] (-4,0.5) -- node[anchor=north]{$x_{2}$} ++(1,0);

      \begin{scope}[shift={(6,0.5)}]
        \node at (0,0) {$N_{2} - N_{1} - 2 m g = 0$}; \node at (2,0) {(3)};

        \node at (0,-0.5) {$T + f_{1} - f_{2} = 2m \ddot{x}_{2}$}; \node at
        (2,-0.5) {(4)};
      \end{scope}
    \end{scope}

    % Now the pulley
    \begin{scope}[shift={(0,-6)}]
      \filldraw[SlateBlue, fill=SlateBlue!20] (0,0) coordinate (P)
      circle[radius=0.5]; \fill (P) circle[radius=0.05];

      \draw[force] (P) -- ++(0:1.5) node[anchor=west] {$F = 6 mg$};
      \draw[coord] (P) ++ (0, 0.75) -- ++ (0:1) node[anchor=west]{$x_{3}$};

      \draw[force] (P) ++(0, 0.5) -- ++(180:2) node[anchor=east] {$T$};
      \draw[force] (P) ++(0, -0.5) -- ++(180:2) node[anchor=east] {$T$};

      \node at (6,0) {$F = 6 mg = 2T$}; \node at (8,0) {(5)};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt2-2021-v1.tex
modified: 2021-04-05 01:14:32
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[coord] (0,0) -- (5,0) node[anchor=north] {$x$};
    \draw[coord] (0,0) -- (0,4) node[anchor=east] {$y$};

    \draw[gray!33,dashed] (4,1.5) -- (4,-2.5);
    \draw[spring] (0,0) -- node[anchor=south,shift={(0,0.15)}]{$k$}
    (4,0) coordinate (m) ++ (0.35,0.35) node {$m$};

    \draw[coord, <->] (0,-0.5) -- node[anchor=north]{$\ell$} (4,-0.5);

    % the origin
    \fill (0,0) circle[radius=0.075];

    \filldraw[fill=gray] (m) circle[radius=0.2];
    \filldraw (m) ++ (0,-2.5) circle[radius=0.2] coordinate (M)
    node[shift={(0.5,0)}] {$M$};
    \draw[vel] (M) ++ (90:0.25) -- ++(90:1) node[anchor=west] {$V_{0}$};
    \node[red] at (4,3.5) {\small\textsf{top view}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt2-2021-v1.tex
modified: 2021-04-05 01:14:32
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\tip{2} % tip angle
    \def\len{12} % length of the rail

    \begin{scope}[rotate=\tip]
      \filldraw[fill=gray!10] (0,0) rectangle (\len,-1);
      % support legs
      \filldraw[fill=SlateGray!50] (0.19*\len,-1) -- ++(0,-1) arc(180:360:0.01*\len)
      -- ++(0,1) -- cycle;
      \filldraw[fill=SlateGray!50] (0.79*\len,-1) -- ++(0,-1) arc(180:360:0.01*\len)
      -- ++(0,1) -- cycle;

      \draw[coord,<->] (0.2*\len,-1.85) --node[anchor=south]{$L =
          \SI{1.500}{m}$}
      (0.8*\len,-1.85);

      % glider
      \fill[fill=gray!50] (0.75,0) coordinate (front) rectangle ++(1,-0.5);
      \fill[fill=gray!25] (front) rectangle ++(1,0.2);
      \fill[black] (front) ++(0,0.2) rectangle ++(0.3, 0.2)
      (0,0.2) rectangle ++(0.3,0.2);
      \draw[line width=2,gray] (0,-1) -- (0,0.4);

      \draw[coord,|->] (0.15, 0.5) -- node[anchor=south] {$x$} ++ (0.75,0);
    \end{scope}

    \draw[Brown!50,line width=2] (0,-2.08) -- ++(\len,0);
    % block
    \filldraw[fill=Brown!33] (9,-2.06) rectangle ++(1.5,0.26);
    \draw[coord,<-] (10.25,-2.08) coordinate (h) -- ++(0,-0.3);
    \draw[coord,<-] (h) ++ (0,0.28) -- ++(0,0.3) node[anchor=south] {$h$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt2-2021-v1.tex
modified: 2021-04-05 01:14:32
domain: p24a
source:
  \begin{tikzpicture}[scale=1.2]
    \begin{scope}[shift={(0,0)}]
      \filldraw[fill=gray!10] (0,-0.75) rectangle (3, 0.75);
      \filldraw[red, fill=red!20] (0.5,0)
      circle[radius=0.3] node[shift={(0,-0.05)}] {$-q$}; % (0.35,0) -- ++(0.3,0); 
      \filldraw[blue, fill=blue!15] (2.5,0)
      node[shift={(0,-0.05)}]{$+q$}
      circle[radius=0.3];% (2.35,0) -- ++(0.3,0) (2.5,-0.15) -- ++(0,0.3);
      \draw[coord,<->] (0.5,0.5) -- node[anchor=north] {$s$} (2.5,0.5);
    \end{scope}

    \begin{scope}[shift={(6,0)}]
      \filldraw[fill=gray!10] (0,-0.75) rectangle (3, 0.75);
      \filldraw[blue, fill=blue!20] (0.5,0)
      circle[radius=0.3] node[shift={(0,-0.05)}] {$+q$}; % (0.35,0) -- ++(0.3,0); 
      \filldraw[red, fill=red!15] (2.5,0)
      node[shift={(0,-0.05)}]{$-q$}
      circle[radius=0.3];% (2.35,0) -- ++(0.3,0) (2.5,-0.15) -- ++(0,0.3);
      \draw[coord,<->] (0.5,0.5) -- node[anchor=north] {$s$} (2.5,0.5);
    \end{scope}

    \draw[coord,<->] (1.5,-1) -- node[anchor=north] {$x$} (7.5,-1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt2-2021-v1.tex
modified: 2021-04-05 01:14:32
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \foreach \x in {0, 6} {
        \foreach \y in {0, -4, -8} {
            \begin{scope}[shift={(\x, \y)}]
              \ethylene
            \end{scope}
          }
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt2-2021-v2.tex
modified: 2021-04-08 18:45:51
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[coord] (0,0) -- (5,0) node[anchor=north] {$x$};
    \draw[coord] (0,0) -- (0,4) node[anchor=east] {$y$};

    \draw[gray!33,dashed] (4,1.5) -- (4,-2.5);
    \draw[spring] (0,0) -- node[anchor=south,shift={(0,0.15)}]{$k$}
    (3.8,0) ++(0.2,0) coordinate (m) ++ (0.35,0.35) node {$m$};

    \draw[coord, <->] (0,-0.5) -- node[anchor=north]{$\ell$} (4,-0.5);

    % the origin
    \fill (0,0) circle[radius=0.075];

    \filldraw[fill=gray] (m) circle[radius=0.2];
    \filldraw (m) ++ (0,-2.5) circle[radius=0.2] coordinate (M)
    node[shift={(0.5,0)}] {$M$};
    \draw[vel] (M) ++ (90:0.25) -- ++(90:1) node[anchor=west] {$V_{0}$};
    \node[red] at (4,3.5) {\small\textsf{top view}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt2-2021-v2.tex
modified: 2021-04-08 18:45:51
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{0.25}
    \def\cart{2}
    \def\xspring{2}

    % middle spring
    \draw[spring] (-0.5*\xspring,\rad) --node[shift={(0,0.5)}]{$k$} (0.5*\xspring,\rad);
    \draw[spring] (-0.5*\xspring-\cart-\xspring, \rad) coordinate (left) -- node[shift={(0,0.5)}]{$k$}
    ++(0:\xspring);
    \draw[spring] (0.5*\xspring+\cart, \rad) -- node[shift={(0,0.5)}] {$k$}
    ++(0:\xspring) coordinate (right);
    \foreach \x in {-2.5, -1.5, 1.5, 2.5} {
        \filldraw[fill = gray] (\x,0) circle[radius=\rad];
      }

    \filldraw[fill=SlateBlue!25] (-3,0) rectangle node{$m$} (-1, 2*\rad)
    (1,0) rectangle node{$m$} ++(\cart,2*\rad);

    \draw[line width=1.5,color=SlateGray] (left) ++(0,.25) -- ++(0,-0.75)
    -- ++(10,0);

    \fill (right) circle[radius=0.1];
    \draw[coord] (right) ++ (0.25,0) -- ++(0:1)
    node[anchor=west]{$D\cos\omega t$};

    % coordinates
    \draw[coord] (-2,-0.5) -- ++(0,-0.25) -- ++(1,0)
    node[anchor=west]{$x_{1}$};
    \draw[coord] (2,-0.5) -- ++(0,-0.25) -- ++(1,0) node[anchor=west]{$x_{2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt1-2021-v1.tex
modified: 2021-02-14 00:18:01
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[SlateGray, fill=SlateGray!20] (-2,0) rectangle (2,1)
    (-0.5,1) rectangle (0.5, 2);
    \node at (0,1.5) {$m$};
    \node at (-1.5,0.5) {$2m$};

    % string
    \draw[DarkBlue, line width=1.25] (2,0.5) -- ++(3,0)
    ++(0,1) -- (0.5,1.5);

    % pulley
    \filldraw[SlateBlue, fill=SlateBlue!20] (5,1) coordinate (P)
    circle[radius=0.5];
    \fill (P) circle[radius=0.05];

    \draw[force] (P) -- ++(0:1.5) node[anchor=west] {$F = 6 mg$};

    % table
    \fill[gray!30] (-3,0) rectangle (7,-0.25);

    \node at (-3,1.5) {$\mu = 1$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt1-2021-v1.tex
modified: 2021-02-14 00:18:01
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0.1) -- ++(0:6);
    \draw (0,-0.1) -- ++(0:6);
    \draw (0,-0.5) -- (0, 0.75);
    \fill[DarkGreen] (0.5,0) circle[radius = 0.1];
    \draw[->,DarkGreen] (0.,1) arc[start angle=90, end angle=315, x radius=0.75, y
        radius = 0.25];
    \draw[DarkGreen] (-0.5,0.6) node[anchor=north east]{$\omega$};
    \draw[coord] (0,-0.5) -- node[anchor=north]{$r_{0}$} ++(0:0.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt2-2021-sol.tex
modified: 2021-04-18 19:54:51
domain: p24a
source:
  \begin{tikzpicture}[scale=0.8]
    \draw[coord] (0,0) -- (5,0) node[anchor=north] {$x$};
    \draw[coord] (0,0) -- (0,4) node[anchor=east] {$y$};

    \draw[gray!33,dashed] (4,1.5) -- (4,-2.5);
    \draw[spring] (0,0) -- node[anchor=south,shift={(0,0.15)}]{$k$}
    (3.8,0) ++(0.2,0) coordinate (m) ++ (0.35,0.35) node {$m$};

    \draw[coord, <->] (0,-0.5) -- node[anchor=north]{$\ell$} (4,-0.5);

    % the origin
    \fill (0,0) circle[radius=0.075];

    \filldraw[fill=gray] (m) circle[radius=0.2];
    \filldraw (m) ++ (0,-2.5) circle[radius=0.2] coordinate (M)
    node[shift={(0.5,0)}] {$M$};
    \draw[vel] (M) ++ (90:0.25) -- ++(90:1) node[anchor=west] {$V_{0}$};
    \node[red] at (4,3.5) {\small\textsf{top view}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt2-2021-sol.tex
modified: 2021-04-18 19:54:51
domain: p24a
source:
  \begin{tikzpicture}[scale=1,vib/.style={->,DarkGreen,line width=1}]
    \begin{scope}[shift={(0,0)}]
      \normalmode{%
        \draw[vib] (h1)  -- ++(\Hang:0.6);
        \draw[vib] (h2)  -- ++ (-\Hang:0.6);
        \draw[vib] (h3) -- ++(180-\Hang:0.6);
        \draw[vib] (h4)  -- ++(-180+\Hang:0.6);
        \draw[vib] (c1) -- ++(0:0.4);
        \draw[vib] (c2) -- ++(180:0.4);
      }
    \end{scope}

    \begin{scope}[shift={(6,0)}]
      \normalmode{%
        \draw[vib] (h1)  -- ++(\Hang:0.6);
        \draw[vib] (h2)  -- ++ (-\Hang:0.6);
        \draw[vib] (h3) -- ++(180-\Hang:0.6);
        \draw[vib] (h4)  -- ++(-180+\Hang:0.6);
        \draw[vib] (c1) -- ++(180:0.4);
        \draw[vib] (c2) -- ++(0:0.4);
      }
    \end{scope}

    \begin{scope}[shift={(0,-4)}]
      \normalmode{%
        \draw[vib] (h1)  -- ++(\Hang+90:0.6);
        \draw[vib] (h2)  -- ++ (-\Hang-90:0.6);
        \draw[vib] (h3) -- ++(90-\Hang:0.6);
        \draw[vib] (h4)  -- ++(-90+\Hang:0.6);
        % \draw[vib] (c1) -- ++(180:0.4);
        %\draw[vib] (c2) -- ++(0:0.4);                  
      }
    \end{scope}

    \begin{scope}[shift={(6,-4)}]
      \normalmode{%
        \draw[vib] (h1)  -- ++(\Hang+90:0.6);
        \draw[vib] (h2)  -- ++ (-\Hang+90:0.6);
        \draw[vib] (h3) -- ++(90-\Hang:0.6);
        \draw[vib] (h4)  -- ++(90+\Hang:0.6);
        \draw[vib] (c1) -- ++(-90:0.3);
        \draw[vib] (c2) -- ++(-90:0.3);
      }
    \end{scope}

    \begin{scope}[shift={(0,-8)}]
      \normalmode{%
        \draw[vib] (h1)  -- ++(\Hang:0.6);
        \draw[vib] (h2)  -- ++ (180-\Hang:0.6);
        \draw[vib] (h3) -- ++(-\Hang:0.6);
        \draw[vib] (h4)  -- ++(-180+\Hang:0.6);
        \draw[vib] (c1) -- ++(-90:0.3);
        \draw[vib] (c2) -- ++(90:0.3);
      }
    \end{scope}

    \begin{scope}[shift={(6,-8)}]
      \normalmode{%
        \draw (h1) ++ (0.4,0) node{$\bigotimes$};
        \draw (h2)  ++ (0.4, 0) node{$\bigodot$};
        \draw (h3) ++ (-0.4, 0) node{$\bigodot$};
        \draw (h4) ++ (-0.4, 0) node{$\bigotimes$};
        % \draw[vib] (c1) -- ++(-90:0.3);
        % \draw[vib] (c2) -- ++(-90:0.3);                  
      }
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/exams21
filename: p24a-mt1-2021-practice.tex
modified: 2021-02-23 03:59:44
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \fill[fill=gray] (-3,0) rectangle (3,-0.2);
    \draw (-1, 1.82) -- (-0.24, 1.82);
    \draw (-0.1,1.675) -- ++(-90:0.5);
    \coordinate (A) at (-0.25,1.675);
    \fill[fill=gray!50!white] (A) circle[radius=0.15];

    \draw[fill=gray!20!white] (-2,0) -- ++(90:1.5)
    -- ++(0:1.5) --  ++(45:0.2914) arc(135:-45:0.05)
    -- ++(-135:0.35) -- ++(-90:1) -- ++(0:0.6)
    -- ++(90:1.1) -- ++(0:1) --++(-90:1.48) -- cycle;
    \fill (A) circle[radius=0.025];
    \draw[fill=gray!15!white] (-1.75,1.5) rectangle node{$M_{2}$} (-1,2);
    \draw[fill=gray!15!white] (-0.45,1.25) rectangle node{$M_{3}$} (0.1,0.75);
    \node at (-1.5, 0.25) {$M_{1}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/hw
filename: tmp.tex
modified: 2021-02-01 01:50:36
domain: p24a
source:
  \begin{tikzpicture}[scale=1,
      string/.style={SlateGray,line width=2pt},
      mass/.style={DarkSlateGray, fill=SlateGray!25},
      ceiling/.style={gray!50,line width=4pt},
      pulley/.style={fill=SlateBlue!50!white}
    ]
    \begin{scope}[shift={(0,0)}]
      \draw[mass] (-0.2, 0) rectangle (0.2, 1);
      \node[anchor=west] at (0.2,0.5) {$M$};
      \draw[string] (0,1) -- (0,4);
      \draw[ceiling] (-0.5,4) -- (0.5,4);
      \draw[<-,Dark Green] (-0.1,2.5) -- ++(180:0.5);
      \node at (0,-0.4) {(a)};
    \end{scope}

    \begin{scope}[shift={(2,0)}]
      \draw[mass] (-0.2, 0) rectangle (0.2, 1);
      \node[anchor=west] at (0.2,0.5) {$M$};
      \draw[spring] (0,2) -- (0,3);
      \draw[string] (0,1) -- (0,2) (0,3) -- (0,4);
      \draw[ceiling] (-0.5,4) -- (0.5,4);
      \node[anchor=west] at (0.2,2.5) {$k$};
      \node at (0,-0.4) {(b)};
    \end{scope}

    \begin{scope}[shift={(7,0)}]
      \draw[mass] (-0.2, 0) rectangle (0.2, 1);
      \node[anchor=west] at (0.2,0.5) {$M$};

      \draw[string] (0,1) -- (0,2.5) arc(0:90:0.5) -- ++(-1,0) coordinate (R);
      \draw[spring] (R) -- ++(-1,0) coordinate (L);
      \draw (R) ++(-0.5, -0.2) node[anchor=north] {$k$};
      \draw[string] (L) -- ++(-1,0) coordinate (W);
      \filldraw[pulley] (-0.5,2.5) coordinate (C) circle[radius=0.5];
      \fill (C) circle[radius=0.05];
      \draw[ceiling] (W) ++(0,0.5) -- ++(0,-1);
      \node at (-2,-0.4) {(c)};
    \end{scope}

    \begin{scope}[shift={(12,0)}]
      \draw[mass] (-0.2, 0) rectangle (0.2, 1);
      \node[anchor=west] at (0.2,0.5) {$M$};

      \draw[string] (0,1) -- (0,2.5) arc(0:90:0.5) -- ++(-0.75,0) coordinate (R);
      \draw[spring] (R) -- ++(-1,0) coordinate (L);
      \draw (R) ++(-0.5, -0.2) node[anchor=north] {$k$};
      \draw[string] (L) -- ++(-0.75,0) arc(90:180:0.5) -- ++(0,-1)
      coordinate (E);
      \foreach \x in {-0.5, -3}{
          \filldraw[pulley] (\x,2.5) circle[radius=0.5];
          \fill (\x, 2.5) circle[radius=0.05];
        }
      \filldraw[mass] (E) ++(0.2,0) rectangle ++(-0.4,-1);
      \draw (E) ++(-0.2,-0.5) node[anchor=east]{$M$};
      \node at (-2,-0.4) {(d)};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210420-lec11.tex
modified: 2021-04-20 03:48:45
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \xyzframe
    \onslide<2>{
      \foreach \ang in {0, 15, ..., 90} {
          \draw[vector,opacity=0.25] (0,0) -- (\ang:2);
        }
      \draw[vector] (0,0) -- (90:2);
    }
    \draw[vector] (0,0) -- (0:2);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210420-lec11.tex
modified: 2021-04-20 03:48:45
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[->,line width=1.5,DarkRed] (-1,1) -- ++(-90:1.5) node[anchor=north]{$g$};
    \fill (0,0) -- ++(-60:0.5) -- ++(180:0.5) -- cycle;
    \draw[gray,line width=3] (-0.2,0) -- ++(0:3) coordinate (a);
    \fill[SlateGray,opacity=0.5] (a) ++(-0.2,2) rectangle ++(.4,-4);
    \draw[vel] (a) ++(0.5,0) -- ++(0:1) node[anchor=south]{$\vb*{\omega}$};
    \onslide<2->{
      \draw[force] (a) -- ++(-90:3) node[anchor=east]{$mg$};
      \draw[force] (0,0) -- ++(90:3) node[anchor=west]{$N$};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210420-lec11.tex
modified: 2021-04-20 03:48:45
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \node[Red] at (0,3) {\textsf{top view}};
    \draw[gray,line width=3] (-0.2,0) -- ++(0:3) coordinate (a);
    \fill[SlateGray!50] (a) ++(-0.2,2) rectangle ++(.4,-4);
    \draw[vel,DarkGreen] (0,0) -- ++(0:6) node[anchor=north,shift={(0,-0.1)}]{$\vb{L} = I\vb*{\omega}$};
    \draw[force] (0,0) -- ++(90:2) node[anchor=south]{$\vb*{\tau}$};
    \draw[Red,line width=2] (45:.25) -- (225:.25) (-45:.25) -- (135:.25);

    \onslide<2->{
      \draw[force] (6,0) --node[anchor=west]{$\dd{\vb{L}} = \tau \dd{t}$} ++(90:1) coordinate (q);
      \draw[vel,DarkGreen,opacity=0.5] (0,0) -- (q) node[anchor=south]{$\vb{L}
          + \dd{\vb{L}}$};
      \draw[coord,<-] (1,0) arc(0:-30:1);
      \draw[coord,<-] (9.5:1) arc (9.5:39.5:1)
      node[anchor=west]{$\dd{\phi} = \Omega\dd{t}$};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210420-lec11.tex
modified: 2021-04-20 03:48:45
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\a{1.5}
    \def\b{2}
    \draw[dashed] (0,\b+0.5) -- (0,-\b-0.5);
    \draw[line width=2] (\a,\b) --  (0,\b)
    -- (0,-\b) -- (-\a,-\b);

    \foreach \x/\y in {\a/\b, -\a/-\b}{
        \draw[dashed, gray] (0,\y) circle[x radius=\a, y radius=0.25];
        \shade[ball color=DarkSlateBlue] (\x,\y) circle[radius=0.25];
        \node at (1.4*\x,\y) {$m$};
        \foreach \q in {0,180}{
            \fill[Red] (0,0.925*\y) ++(\q-45:0.08) rectangle ++(\q+45:0.16);
          }}
    \draw[DarkGreen,->,line width=2] (0,2.7) -- ++(0,1)
    node[anchor=east]{$\vb*{\omega}$};
    \draw[DarkRed,->,line width=2] (0,0) --
    node[anchor=east]{$\mathbf{L}$}  (-1.25*\a,1.2*\b);

    \fill[yellow] (0,0) circle[radius=0.05];

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210420-lec11.tex
modified: 2021-04-20 03:48:45
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\a{1.5}
    \def\b{2}
    \draw[dashed] (0,\b+0.5) -- (0,-\b-0.5);
    \draw[line width=2] (\a,\b) --node[anchor=south]{$b$} (0,\b)
    -- (0,-\b) -- node[anchor=north]{$b$} (-\a,-\b);

    \foreach \x/\y in {\a/\b, -\a/-\b}{
        \draw[dashed, gray] (0,\y) circle[x radius=\a, y radius=0.25];
        \shade[ball color=DarkSlateBlue] (\x,\y) circle[radius=0.25];
        \node at (1.4*\x,\y) {$m$};
        \foreach \q in {0,180}{
            \fill[Red] (0,0.925*\y) ++(\q-45:0.08) rectangle ++(\q+45:0.16);
          }}
    \draw[DarkGreen,->] (0.4,2.65) arc[start angle=45,
        end angle=300,x radius=0.5, y radius=0.15];
    \node[DarkGreen] at (-0.65,2.6){$\omega$};
    \fill[yellow] (0,0) circle[radius=0.05];
    \draw[DarkGreen,<->] (-0.5,0) -- node[anchor=east]{$c$} ++(90:\b);
    \draw[DarkGreen,<->] (-0.5,0) -- node[anchor=east]{$c$} ++(-90:\b);

    \draw[coord] (1,0) coordinate (O) -- ++ (0.75,0) node[anchor=north]{$\ux$};
    \draw[coord] (O) -- ++ (0,0.75) node[anchor=east]{$\uz$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210302-lec5.tex
modified: 2021-03-02 16:30:21
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) node{\includegraphics[width=2cm]{earth}};
    \fill (45:1.1) coordinate (p1) circle[radius=0.05];
    \fill[gray] (-45:3.5) coordinate (p2) circle[radius=0.05];
    \draw[dashed, gray, ->] (p1) .. controls (75:3) and (30:5.75) .. (0:2)
    .. controls (-20:1.2) and (35:1.1) .. (0:3)
    .. controls (-30:5.5) and (-40:2.5) .. (p2);
    \node[anchor=west] at (p1) {$A$};
    \node[anchor=west] at (p2) {$B$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210216-lec04.tex
modified: 2021-02-16 15:43:30
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \xyzframe
    \masspt[pos={(2.5,2)}]
    \masspt[pos={(1.75,2.25)},label={$m_{j}$}, rvec={j}, rotate=45]
    \masspt[pos={(1.25,0.5)}]
    \masspt[pos={(0.75,2.5)}]
    \masspt[pos={(-0.5,1.5)}]
    \masspt[pos={(1,1.5)}]
    \masspt[pos={(2.75,0.75)}]
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210216-lec04.tex
modified: 2021-02-16 15:43:30
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \foreach \x in {0, 2.598}{
        \filldraw[fill=gray!25] (\x,0) -- ++(150:3) -- ++(270:3) -- cycle;
      }
    \fill (0,0) circle[radius=0.05];
    \node[anchor=west] at (0,0) {$P$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210216-lec04.tex
modified: 2021-02-16 15:43:30
domain: p24a
source:
  \begin{tikzpicture}[scale=1,
      coord/.style={color=green!40!black,|->},
    ]
    \def\radius{3}
    \def\axislength{3.25}
    \shade[ball color=blue!50!white, opacity=0.3] (0,0) circle[radius=\radius];
    % cartesian system
    \draw[coord,->] (0,0) -- (\axislength,0) node[anchor=west]{$y$};
    \draw[coord,->] (0,0,0) -- (0,0,1.75*\axislength) node[anchor=north east]{$x$};
    \draw[coord,->] (0,0) -- (0,\axislength) node[anchor=south]{$z$};
    % cover up the z axis underneath an upcoming label
    \draw[gray!35!white] (0,1.7) -- ++(90:0.25);
    % coordinate of the point
    \coordinate (A) at (1.5,2.121, 1.5);
    \draw[line width=1, ->,color=DarkRed] (0,0,0) -- node[anchor=north west]{$r$}  (A);
    % projection to the xy plane
    \draw[dashed,color=DarkBlue] (A) -- (1.5, 0, 1.5) -- (0,0);
    % circle of latitude
    \draw[dashed] (2.2,2) arc[x radius=2.2, y radius=0.5, start angle=0, end
        angle=-180];
    \draw[dashed,opacity=0.2] (2.2,2) arc[x radius=2.2, y radius=0.5, start
        angle=0, end angle=180];
    % circle of longitude
    \draw[dashed,color=black] (0,-3) arc[x radius=1.075, y radius=3, start angle=-90,
        end angle=90];
    \draw[dashed,color=gray, opacity=0.2] (0,-3) arc[x radius=1.1, y radius=3,
        start angle=-90, end angle=-270];
    % definition of phi
    \draw[->] (0,0,0.5) arc[start angle=-135, end angle=-45,
        x radius=0.35, y radius =0.25];
    \node at (0,-0.5){$\phi$};
    % theta definition
    \draw[->] (0,0.6) arc[start angle=90, end angle=50,
        y radius=0.6, x radius = 0.4];
    \node at (0.2, 0.85) {$\theta$};
    % circle of longitude at \phi + d\phi
    \draw[dashed,color=black] (0,-3) arc[x radius=1.4, y radius=3, start angle=-90,
        end angle=90];
    \draw[dashed,color=gray, opacity=0.2] (0,-3) arc[x radius=1.4, y radius=3,
        start angle=-90, end angle=-270];
    % circle of latitude at \theta + d\theta
    \draw[dashed] (2.35,1.8) arc[x radius=2.35, y radius=0.5, start angle=0, end
        angle=-180];
    \draw[dashed,opacity=0.2] (2.35,1.8) arc[x radius=2.35, y radius=0.5, start
        angle=0, end angle=180];
    % label the arcs
    \draw[<-] (1.08,1.6) -- ++(135:0.3) node[anchor=east] {$r \sin\theta
        \dd{\phi}$};
    \draw[<-] (1.28,1.45) -- ++(-30:0.3) node[anchor=west] {$r \dd{\theta}$};
    % draw dA
    \fill[fill=black,opacity=0.2] (A) -- ++(6:0.27) -- ++(-75:0.2) -- ++(186:0.28)
    -- cycle;
    % label dA
    \draw[<-] (1.08,1.48) -- ++(-50:1) node[anchor=west]{$\dd{A} = r^{2} \sin\theta
        \dd{\phi} \dd{\theta}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210406-lec09.tex
modified: 2021-04-06 02:03:43
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \node[opacity=0.2, anchor=south west] at (0,0)
    {\includegraphics[width=\columnwidth]{Khaleesi}};

    \fill (6,9) coordinate(A) circle[radius=0.05];

    \draw (A) ++(-140:5) node
    {\includegraphics[width=0.5cm]{Emilia.png}};


    % Draw the initial position of the diabolical arm
    \draw[line width=1.5,gray!50!black] (A) -- ++(-100:5) coordinate (B);
    \fill (B) circle[radius=0.2];
    \node[shift={(0.4,0)}] at (B) {$m$};

    \draw[coord,->] (A) ++(-95:5.5) arc(-95:-105:5.5);
    \draw[DarkGreen] (A) ++(-100:5.5) node[anchor=north]{$\omega_{0}$};

    \node[Red] at (2,9){\textsf{top view}};

    \node[text width=5cm, anchor=north west] at (9,9)
    {Unless $m$ slows to $\omega_{0}/2$ or less, Khaleesi is toast!};


    \onslide<2->{
      \foreach \q in {-130} {
          \draw[line width=1.5,opacity=0.35] (A) -- ++(\q:4.8)
          coordinate (B);
          \fill[opacity=0.35] (A) ++(\q:5) circle[radius=0.2];
        }
    }

    % Now the dragon

    \onslide<2->{
      \draw (A) ++(-130:2.5) coordinate(D) node
        {\includegraphics[width=1.25cm]{dragon}};
      \draw (D) ++(-0.1,0.4) node[anchor=south,Orange!67!black] {$4m$};
    }

    \onslide<2>{
      \node[text width=5cm, anchor=north west,color=Orange!67!black]
      at (9,6) {A dragon of mass $4m$ lands gently on the rod halfway between the pivot
        and $m$.};
    }

    \onslide<3->{
    \begin{scope}[shift={(9,9)}]

      \node[text width=5cm, anchor=north west] at (0,-4){
        A. Yes\\
        B. No \\
        C. Buy a vowel
      };
      }

      \onslide<3>{
        \node[text width=5cm, anchor=north west] at (0,-2)
        {Is \textbf{momentum} conserved from the instant before the collision to
          the instant immediately after it?};

      }
      \onslide<4>{
        \node[text width=5cm,anchor=north west] at (0,-2) {Is Khaleesi saved?};
      }
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210316-lec6.tex
modified: 2021-03-15 16:27:37
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=2] (0,5) -- node[anchor=east] {$\ell$} (0,0)  (2,5) -- (2,0);
    \node at (0,-0.5){$m$};
    \node at (2,-0.5){$m$};
    \filldraw[fill=gray] (0,0) circle[radius=0.2] (2,0) circle[radius=0.2];
    \draw (-0.5,5) -- (2.5,5);
    \draw[spring] (0,2) --node[anchor=south,shift={(0,0.25)}]{$k$} (2,2);
    \draw[coord,<->] (2.25,5) -- node[anchor=west]{$\lambda \ell$} (2.25,2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210316-lec6.tex
modified: 2021-03-15 16:27:37
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\Del{0.2}
    \draw[spring] (-2+\Del,0) -- (-\Del,0);
    \draw[spring] (\Del,0) -- (2-\Del,0);
    \filldraw[fill=blue!25] (0,0) node {C} circle[radius=0.25];
    \foreach \x in {-2,2} {\filldraw[fill=red!25] (\x,0) node{O}
        circle[radius=0.2];}

    \node at (0,-5) {What are the normal modes of $\rm CO_{2}$?};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210316-lec6.tex
modified: 2021-03-15 16:27:37
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=4, black!75!white] (0,1) -- (0,-0.1) -- (6,-0.1);
    \filldraw[fill=gray] (2.5,0) rectangle (3,0.5);
    \node at (2.75,0.75) {$m$};
    \node at (1.25,0.75) {$k/2$};
    \node at (4,0.75) {$k/2$};
    \draw[spring] (0,0.25) -- (2.5,0.25);
    \draw[spring] (3.,0.25) -- ++(0:2) coordinate (drive);
    \fill (drive) circle[radius=0.05];
    \draw[line width=1, DarkGreen, <->] (drive) ++(-0.5,0.5) -- ++(1,0);
    \draw (drive) ++(0,0.75) node[anchor=south] {$D\cos(\omega t)$};
    \draw[coord,|->] (2.75,-0.5) -- node[anchor=north]{$x$} ++(1,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210202-lec02.tex
modified: 2021-02-03 03:56:57
domain: p24a
source:
  \begin{tikzpicture}[scale=0.75,
      string/.style={SlateGray,line width=2pt},
      mass/.style={DarkSlateGray, fill=SlateGray!25},
      ceiling/.style={gray!50,line width=4pt},
      pulley/.style={fill=SlateBlue!50!white}
    ]
    \begin{scope}[shift={(0,0)}]
      \draw[mass] (-0.2, 0) rectangle (0.2, 1);
      \node[anchor=west] at (0.2,0.5) {$M$};
      \draw[string] (0,1) -- (0,4);
      \draw[ceiling] (-0.5,4) -- (0.5,4);
      \draw[<-,DarkGreen] (-0.1,2.5) -- ++(180:0.5);
      \node at (0,-0.4) {(a)};
    \end{scope}

    \begin{scope}[shift={(2,0)}]
      \draw[mass] (-0.2, 0) rectangle (0.2, 1);
      \node[anchor=west] at (0.2,0.5) {$M$};
      \draw[spring] (0,2) -- (0,3);
      \draw[string] (0,1) -- (0,2) (0,3) -- (0,4);
      \draw[ceiling] (-0.5,4) -- (0.5,4);
      \node[anchor=west] at (0.2,2.5) {$k$};
      \node at (0,-0.4) {(b)};
    \end{scope}

    \begin{scope}[shift={(7,0)}]
      \draw[mass] (-0.2, 0) rectangle (0.2, 1);
      \node[anchor=west] at (0.2,0.5) {$M$};

      \draw[string] (0,1) -- (0,2.5) arc(0:90:0.5) -- ++(-1,0) coordinate (R);
      \draw[spring] (R) -- ++(-1,0) coordinate (L);
      \draw (R) ++(-0.5, -0.2) node[anchor=north] {$k$};
      \draw[string] (L) -- ++(-1,0) coordinate (W);
      \filldraw[pulley] (-0.5,2.5) coordinate (C) circle[radius=0.5];
      \fill (C) circle[radius=0.05];
      \draw[ceiling] (W) ++(0,0.5) -- ++(0,-1);
      \node at (-2,-0.4) {(c)};
    \end{scope}

    \begin{scope}[shift={(5,-4.25)}]
      \draw[mass] (-0.2, 0) rectangle (0.2, 1);
      \node[anchor=west] at (0.2,0.5) {$M$};

      \draw[string] (0,1) -- (0,2.5) arc(0:90:0.5) -- ++(-0.75,0) coordinate (R);
      \draw[spring] (R) -- ++(-1,0) coordinate (L);
      \draw (R) ++(-0.5, -0.2) node[anchor=north] {$k$};
      \draw[string] (L) -- ++(-0.75,0) arc(90:180:0.5) -- ++(0,-1)
      coordinate (E);
      \foreach \x in {-0.5, -3}{
          \filldraw[pulley] (\x,2.5) circle[radius=0.5];
          \fill (\x, 2.5) circle[radius=0.05];
        }
      \filldraw[mass] (E) ++(0.2,0) rectangle ++(-0.4,-1);
      \draw (E) ++(-0.2,-0.5) node[anchor=east]{$M$};
      \node at (-2,-0.4) {(d)};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210330-lec08.tex
modified: 2021-03-30 02:24:45
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\aa{3} \def\ee{0.6}
    \pgfmathsetmacro{\bb}{\aa*sqrt(1-\ee*\ee)}
    \draw[SlateBlue] (0,0) circle[x radius=\aa, y radius=\bb];

    \filldraw[fill=yellow] (1.8,0) coordinate (O) circle[radius=0.2];
    \draw[coord] (1.8,-3) -- (1.8,3) node[anchor=east] {$y$};
    \draw[coord] (-3.5,0) -- (3.5,0) node[anchor=north] {$x$};

    % planet
    \fill[brown] (2.5,1.33) coordinate (P) circle[radius=0.1];
    \draw[coord] (O) -- node[anchor=west] {$r$} (P);
    \begin{scope}[shift={(1.8,0)}]
      \draw (0:0.4) arc(0:63:0.4);
      \node at (25:0.55) {$\theta$};
    \end{scope}

    % ellipse properties
    \begin{scope}[DarkRed,line width=1.5]
      \draw (0,0) -- node[anchor=north] {$\varepsilon a$} (\aa*\ee,0);
      \filldraw[fill=gray,draw=black,line width=0.5pt] (-\aa*\ee,0)
      coordinate (f2) circle[radius=0.05];
      \draw (0,0) -- node[anchor=north] {$\varepsilon a$} (f2);
      \draw[dashed,line width=0.75,gray] (f2) --node[anchor=south]{$s$} (P);
    \end{scope}
    \draw[coord,DarkRed,<->] (0,-0.5) -- node[anchor=north]{$a$} (-\aa,-0.5);
    \draw[coord,DarkRed,<->] (0,-0.5) -- node[anchor=north]{$a$} (\aa,-0.5);
    \draw[coord,DarkRed,<->] (0,0) -- node[anchor=east]{$b$} (0,\bb);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210330-lec08.tex
modified: 2021-03-30 02:24:45
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \fill[gray] (210:2) coordinate(m1) circle[radius=0.1]
    node[anchor=north,shift={(0,-0.1)}] {$m_{1}$};
    \fill[gray] (30:4) coordinate(m2) circle[radius=0.05]
    node[anchor=north,shift={(0,-0.1)}] {$m_{2}$};
    \fill[DarkRed] (0,0) circle[radius=0.05] node[anchor=south east] {CM};
    \draw[coord] (0,0) -- node[anchor=north] {$r_{1}$} (m1);
    \draw[coord] (0,0) -- node[anchor=north]{$r_{2}$} (m2);

    \begin{scope}[shift={(-60:0.65)}]
      \draw[vel,line width=1.25] (210:2) -- node[anchor=north] {$r$} (30:4);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/lec
filename: 210330-lec08.tex
modified: 2021-03-30 02:24:45
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\angmom{0.004} \def\grav{0.1}
    \def\xlim{0.5}
    \begin{axis}[
        xmin=0, xmax=0.5, ymin=-1, ymax=1, enlargelimits=false,
        width=2.5in, height=2.5in,
        xlabel={$r$}, ylabel={}, ytick={0}, xtick=\empty,
        % xticklabel=\empty, xticklabels{0,,$a$,,a$},
        axis x line=middle, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0.01:0.45, samples=100, line width=1pt,]
      {\angmom / (x*x)};
      \addplot[DarkRed,domain=0.01:\xlim,samples=100,line width=1pt]
      {-\grav/x};
      \addplot[DarkBlue,domain=0.01:\xlim,samples=100,line width=1.5pt]
      {\angmom/(x*x) - \grav/x};
      \draw (0,0) -- (\xlim,0);
      \node[DarkGreen,anchor=south] at (0.2,0.15) {$\frac{L^2}{2\mu r^2}$};
      \node[DarkRed,anchor=west] at (0.15,-0.7) {$- \frac{G m_1 m_2}{r}$};
      \node[DarkBlue] at (0.05,-0.7) {$U_{\rm eff}$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2021/rec
filename: 210201-M2.tex
modified: 2021-02-01 03:37:14
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[SlateGray,fill=SlateGray!25] (0,0) circle[radius=3];
    \fill (0,0) circle[radius=0.05];
    \node at (2.5,0) {\includegraphics[width=0.2in]{penny}};
    \draw[coord] (0,0) -- node[anchor=south]{$r$} (2.5,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020
filename: tikz.tex
modified: 2021-01-31 22:08:38
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{3}
    \node[anchor=south east,DarkRed] at (-5,2.5) {\textsf{top view}};
    \filldraw[fill=gray!25] (0,0) circle[radius=\rad];
    \foreach \q in {30, 150}{
        \fill[black] (\q:0.9*\rad) circle[radius=0.2];
        \node at (\q:0.75*\rad) {$m$};
      }
    % The run mat
    \fill[DarkGreen!35] (-100:3.1) arc(-100:-135:3.1) --
    ++(180:5) -- ++(-90:1) -- ++(0:6.65) -- cycle;
    \node at (-6.5,-3) {\textsf{\small{runway}}};

    \draw[dashed] (-90:0.9*\rad) circle[radius=0.2];
    \fill[DarkRed] (-4,-0.9*\rad) coordinate (A) circle[radius=0.2]
    node[anchor=east,shift={(-0.15,0)}] {$m$};

    \draw[vel, DarkRed] (A) ++ (0:0.25) -- ++(0:1.5) node[anchor=north]{$v_{0}$};
    \draw[coord,->] (0,0) -- node[anchor=north]{$R$} (\rad,0);
    \node at (90:0.9*\rad) {$M$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020
filename: tikz.tex
modified: 2021-01-31 22:08:38
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    % draw the table
    \filldraw[fill=gray!15] (1,-1.5) -- (5,1) -- (-1,1.5) -- (-5,-1) -- cycle;

    % draw the circular path
    \draw[dashed] (0,0) circle[x radius=2.5, y radius=1];
    % the mass that goes in a circle
    \draw (0,0) --node[anchor=south]{$r$} (2.25,0.5);
    \filldraw[fill=gray!33,gray] (2.25,0.5) circle[x radius=0.25, y radius=0.1];
    \foreach \z in {0.5,0.51,...,0.55} {
        \fill[gray!50] (2.25,\z) circle[x radius=0.25, y radius=0.1];
      }
    \draw[->,DarkGreen] (3.5,0.5) arc[x radius=3.5, y radius=1.,
        start angle=10, end angle=45];

    % Now the hanging weight
    \begin{scope}[shift={(0,-3)},shading=cylinder]
      \shade[shading angle=90] (-0.25,0) arc[x radius=0.25, y radius=0.05,
          start angle=180, end angle=360] --
      ++(0,-0.25) arc[x radius=0.25, y radius=0.05, start angle=0, end angle=-180]
      -- ++(0,0.25) -- cycle;
      \fill[gray!33] (0,0) circle[x radius=0.25, y radius = 0.05];
      %        \draw[line width=1.5,gray] (0,0) circle[x radius=0.1, y radius=0.1];
      %\fillnode[anchor=west]{$m$};
    \end{scope}

    \filldraw[fill=gray!33,draw=gray] (2.25,0.55) circle[x radius=0.25, y radius=0.1];
    \filldraw[fill=white] (0,0) circle[x radius=0.075,y radius=0.03];
    \draw[dashed] (0,0) -- (0,-1.5);
    \draw (0,-1.5) -- ++(-90:1.5) coordinate (B);

    % mass labels
    \node[anchor=west,shift={(0.2,-0.05)}] at (B) {$M$};
    \node at (2.75,0.5) {$m$};

    \draw[->,DarkRed,line width=1.5] (3,-1) --node[anchor=west]{$g$} ++(-90:1);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/exams20
filename: p24a-mt1-2020-v2-sol.tex
modified: 2020-02-24 04:32:49
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \fill[fill=gray] (-3,0) rectangle (3,-0.2);
    \draw (-1, 1.82) -- (-0.24, 1.82);
    \draw (-0.1,1.675) -- ++(-90:0.5);
    \coordinate (A) at (-0.25,1.675);
    \fill[fill=gray!50!white] (A) circle[radius=0.15];

    \draw[fill=gray!20!white] (-2,0) -- ++(90:1.5)
    -- ++(0:1.5) --  ++(45:0.2914) arc(135:-45:0.05)
    -- ++(-135:0.35) -- ++(-90:1) -- ++(0:0.6)
    -- ++(90:1.1) -- ++(0:1) --++(-90:1.48) -- cycle;
    \fill (A) circle[radius=0.025];
    \draw[fill=gray!15!white] (-1.75,1.5) rectangle node{$M_{2}$} (-1,2);
    \draw[fill=gray!15!white] (-0.45,1.25) rectangle node{$M_{3}$} (0.1,0.75);
    \node at (-1.5, 0.25) {$M_{1}$};

    \draw[coord] (-3,0.25) -- node[anchor=south]{$x_{1}$} ++(0:1);
    \draw[coord] (-2,2) --node[anchor=south]{$x_{2}$} (-1.75,2);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/exams20
filename: p24a-mt1-2020-v2-sol.tex
modified: 2020-02-24 04:32:49
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[rotate=30]
      \draw[gray,dashed] (-1,-0.2) -- ++(2,0);
      \draw[gray,dashed] (-1,0.2) -- ++(2,0);
    \end{scope}
    \filldraw[fill=DarkGreen!60!white] (0,0) circle[radius=0.2];
    \draw[force] (-60:0.2) -- ++(120:1) node[anchor=east]{$N$};
    \draw[coord,<->] (30:1.5) node[anchor=north]{$\ur$} -- ++(210:0.75)
    -- ++(120:0.75) node[anchor=east]{$\uth$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/exams20
filename: p24a-mt2-2020-sol.tex
modified: 2020-04-25 01:18:29
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray] (-.3,-.1) rectangle (.3, .1) ;
    \draw[force] (0,0) -- ++(-90:1) node[anchor=west]{$Mg$};
    \draw[force] (0,0.1) -- ++(90:1) node[anchor=west]{$T$};
    \draw[coord] (-0.5,0) -- ++(90:1) node[anchor=east]{$r$};

    \begin{scope}[shift={(2.25,0)}]
      \filldraw[fill=gray] (0,0) circle[radius=0.25];
      \draw[force] (210:0.25) -- ++(210:1) node[anchor=north]{$T$};
      \draw[coord, <->] (30:1.) node[anchor=north]{$\ur$} -- ++(210:0.5)
      -- ++(120:0.5) node[anchor=east]{$\uth$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/rec20
filename: rec02-p18.tex
modified: 2021-01-31 21:45:09
domain: p24a
source:
  \begin{tikzpicture}[decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm}]
    \filldraw (0,0) circle(0.1);
    \draw[decorate] (0,0) -- (30:2);
    \shade[ball color=gray] (30:2) circle(0.25) ++(-90:0.25) node[anchor=north]{
        $m$ };
    \draw[decorate] (30:2.25) -- ++(30:2);
    \shade[ball color=gray] (30:4.5) circle(0.25) ++(-90:0.25)
    node[anchor=north]{$m$};
    \draw (30:1) ++(120:0.5) node {$k$};
    \draw (30:3) ++(120:0.5) node {$k$};
    \draw[->] (24:5) arc(24:36:5) node[anchor=south]{$\omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/lec20
filename: p24a-200330.tex
modified: 2020-03-29 20:09:05
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \filldraw (0,0) circle[radius=0.025];
    \draw[gray] (-0.5,0) -- (3.5,0);
    \draw[gray,dashed] (3,-0.5) -- (3,5);
    \fill (3,1.5) coordinate (A) circle[radius=0.05] node[anchor=west]{$m$};
    \draw[gray] (0,0) --node[anchor=south]{$r$} (A);
    \draw[vel] (A) ++(90:0.2) -- ++(90:1.25) node[anchor=east]{$v$};
    \node[anchor=north] at (1.5,0) {$x$};

    % now show the angle
    \draw (0:1)  arc(0:26.6:1);
    \node at (13.3:1.2) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/lec20
filename: p24a-200330.tex
modified: 2020-03-29 20:09:05
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \node[opacity=0.2, anchor=south west] at (0,0)
    {\includegraphics[width=\columnwidth]{Khaleesi}};
    \node[anchor=south west] at (1,4)
    {\includegraphics[width=0.5cm]{Emilia.png}};
    \fill (6,7) coordinate(A) circle[radius=0.05];

    % Draw the initial position of the diabolical arm
    \draw[line width=1.5,gray!50!black] (A) -- ++(-100:5) coordinate (B);
    \fill (B) circle[radius=0.2];
    \node[shift={(0.4,0)}] at (B) {$m$};

    \draw[coord,->] (A) ++(-95:5.5) arc(-95:-105:5.5);
    \draw[DarkGreen] (A) ++(-100:5.5) node[anchor=north]{$\omega_{0}$};

    \node[Red] at (2,7){\textsf{top view}};

    \node[text width=5cm, anchor=north west] at (7,7)
    {Unless $m$ slows to $\omega_{0}/2$ or less, Khaleesi is toast!};


    \onslide<2->{
      \foreach \q in {-130} {
          \draw[line width=1.5,opacity=0.35] (A) -- ++(\q:4.8)
          coordinate (B);
          \fill[opacity=0.35] (A) ++(\q:5) circle[radius=0.2];
        }
    }

    % Now the dragon

    \onslide<2->{
      \begin{scope}[shift={(6,7)}]
        \node at (-130:2.5) {\includegraphics[width=1.25cm]{dragon}};
        \node[Orange!67!black] at (-145:2.1) {$4m$};
      \end{scope}
    }

    \onslide<2>{
      \node[text width=5cm, anchor=north west,color=DarkOrange] at (7,6) {A dragon of mass $4m$ lands gently on the rod halfway between the pivot
        and $m$.}
    }

    \onslide<3->{
    \begin{scope}[shift={(7,7)}]

      \node[text width=5cm, anchor=north west] at (0,-4){
        A. Yes\\
        B. No \\
        C. Buy a vowel
      };
      }

      \onslide<3>{
        \node[text width=5cm, anchor=north west] at (0,-2)
        {Is \textbf{momentum} conserved from the instant before the collision to
          the instant immediately after it?};

      }
      \onslide<4>{
        \node[text width=5cm,anchor=north west] at (0,-2) {Is Khaleesi saved?};
      }
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/lec20
filename: lec200414.tex
modified: 2020-04-14 02:34:24
domain: p24a
source:
  \begin{tikzpicture}[scale=1.25]
    \def\fat{0.25}
    \fill[gray!50] (0,0) -- (2,0) -- (2,-\fat) -- (-\fat,-\fat)
    -- (-\fat,3) -- (0,3) -- cycle;
    \draw[line width=1] (0,3) -- (0,0) -- (2, 0);
    \draw[line width=2,DarkRed] (0.05,2.5) -- (1.5,0.03);
    \draw (1.2,0) arc(180:125:0.3);
    \node at (1.1,0.25) {$\theta$};
    \node[anchor=south west] at (1.5, 0){$\mu$};
    \node[anchor=south west] at (0, 2.5){$\mu$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/lec20
filename: lec200414.tex
modified: 2020-04-14 02:34:24
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \def\fat{0.25}
    \fill[gray!50] (-2,0) -- (1,0) -- ++(0,-\fat) -- (-2,-\fat) -- cycle;
    \draw (-2,0) -- (1,0);


    \fill (-2,1) circle[radius=0.1] node[anchor=north,shift={(0,-0.15)}] {$m$};

    \draw[vel,line width=1] (-1.8,1) -- node[anchor=south]{$v$} ++(0:0.5);

    \filldraw[fill=gray!15] (0,0) -- (-1, 0) -- (-1, 1) -- (0,1) -- cycle;

    \node at (-0.5,0.5) {$m$};
    \node[anchor=south] at (-0.5,1) {$\ell$};
    \filldraw[fill=white] (0,0) circle[radius=0.05];
    \draw[line width=0.75,<-] (0.1,0.1) -- (45:0.5) node[anchor=west]{hinge};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/lec20
filename: 200331.tex
modified: 2020-03-31 00:10:53
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \node[opacity=0.2, anchor=south west] at (0,0)
    {\includegraphics[width=\columnwidth]{Khaleesi}};
    \node[anchor=south west] at (1,4)
    {\includegraphics[width=0.5cm]{Emilia.png}};
    \fill (6,7) coordinate(A) circle[radius=0.05];

    % Draw the initial position of the diabolical arm
    \draw[line width=1.5,gray!50!black] (A) -- ++(-100:5) coordinate (B);
    \fill (B) circle[radius=0.2];
    \node[shift={(0.4,0)}] at (B) {$m$};

    \draw[coord,->] (A) ++(-95:5.5) arc(-95:-105:5.5);
    \draw[DarkGreen] (A) ++(-100:5.5) node[anchor=north]{$\omega_{0}$};

    \node[Red] at (2,7){\textsf{top view}};

    \node[text width=5cm, anchor=north west] at (7,7)
    {Unless $m$ slows to $\omega_{0}/2$ or less, Khaleesi is toast!};


    \onslide<2->{
      \foreach \q in {-130} {
          \draw[line width=1.5,opacity=0.35] (A) -- ++(\q:4.8)
          coordinate (B);
          \fill[opacity=0.35] (A) ++(\q:5) circle[radius=0.2];
        }
    }

    % Now the dragon

    \onslide<2->{
      \begin{scope}[shift={(6,7)}]
        \node at (-130:2.5) {\includegraphics[width=1.25cm]{dragon}};
        \node[Orange!67!black] at (-145:2.1) {$4m$};
      \end{scope}
    }

    \onslide<2>{
      \node[text width=5cm, anchor=north west,color=DarkOrange] at (7,6) {A dragon of mass $4m$ lands gently on the rod halfway between the pivot
        and $m$.};
    }

    \onslide<3->{
    \begin{scope}[shift={(7,7)}]

      \node[text width=5cm, anchor=north west] at (0,-4){
        A. Yes\\
        B. No \\
        C. Buy a vowel
      };
      }

      \onslide<3>{
        \node[text width=5cm, anchor=north west] at (0,-2)
        {Is \textbf{momentum} conserved from the instant before the collision to
          the instant immediately after it?};

      }
      \onslide<4>{
        \node[text width=5cm,anchor=north west] at (0,-2) {Is Khaleesi saved?};
      }
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/lec20
filename: lec200421.tex
modified: 2021-04-21 03:16:30
domain: p24a
source:
  \begin{tikzpicture}[scale=1.25]
    \def\a{1.5}
    \def\b{2}
    \begin{scope}[opacity=0.25]
      \draw[dashed] (0,\b+0.5) -- (0,-\b-0.5);
      \draw[line width=2] (\a,\b) coordinate (m) --node[anchor=south]{$b$} (0,\b)
      -- (0,-\b) -- node[anchor=north]{$b$} (-\a,-\b) coordinate (M);

      \foreach \x/\y in {\a/\b, -\a/-\b}{
          \draw[dashed, gray] (0,\y) circle[x radius=\a, y radius=0.25];
          \shade[ball color=SlateGray,opacity=0.25] (\x,\y) circle[radius=0.25];
          \node at (1.4*\x,\y) {$m$};
          \foreach \q in {0,180}{
              \fill[Red] (0,0.925*\y) ++(\q-45:0.08) rectangle ++(\q+45:0.16);
            }}
      \draw[DarkGreen,->] (0.4,2.65) arc[start angle=45,
          end angle=300,x radius=0.5, y radius=0.15];
      \node[DarkGreen] at (-0.65,2.6){$\omega$};
      \fill[yellow] (0,0) circle[radius=0.05];
      \draw[DarkGreen,<->] (-0.5,0) -- node[anchor=east]{$c$} ++(90:\b);
      \draw[DarkGreen,<->] (-0.5,0) -- node[anchor=east]{$c$} ++(-90:\b);
    \end{scope}

    % the coordinate system
    \begin{scope}[DarkSlateGray,->,shift={(1.2*\a,-\b)}]
      \draw (0,0) -- ++(0:.8) node[anchor=north]{$x$};
      \draw (0,0) -- ++(90:1) node[anchor=east]{$z$};
      \draw (0,0) -- ++(45:0.5) node[anchor=south west]{$y$};
    \end{scope}

    \begin{scope}[->,line width=2]
      \draw[Red] (0,0) --node[anchor=west]{$\vb{r}$} (m);
      \draw[DarkGreen] (m) --node[anchor=south west]{$\vb*{\ell}$} ++(-0.5*\b,0.5*\a);
      \draw[DarkGreen] (M) --node[anchor=south west]{$\vb*{\ell}$}
      ++(-0.5*\b,0.5*\a);

      \onslide<2->{ \draw[DarkGreen] (0,0) -- ++(-\b,\a) node[anchor=east]{$\vb{L}$};}
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/lec20
filename: lec200421.tex
modified: 2021-04-21 03:16:30
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \fill (0,0) -- ++(-60:0.5) -- ++(180:0.5) -- cycle;
    \draw[gray,line width=3] (-0.2,0) -- ++(0:3) coordinate (a);
    \fill[SlateGray,opacity=0.5] (a) ++(-0.2,2) rectangle ++(.4,-4);
    \draw[vel] (a) ++(0.5,0) -- ++(0:1) node[anchor=south]{$\vb*{\omega}$};
    \onslide<2->{
      \draw[force] (a) -- ++(-90:3) node[anchor=east]{$mg$};
      \draw[force] (0,0) -- ++(90:3) node[anchor=west]{$N$};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/lec20
filename: lec200421.tex
modified: 2021-04-21 03:16:30
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \node[Red] at (0,3) {\textsf{top view}};
    \draw[gray,line width=3] (-0.2,0) -- ++(0:3) coordinate (a);
    \fill[SlateGray!50] (a) ++(-0.2,2) rectangle ++(.4,-4);
    \draw[vel,DarkGreen] (0,0) -- ++(0:6) node[anchor=north,shift={(0,-0.1)}]{$\vb{L} = I\vb*{\omega}$};
    \draw[force] (0,0) -- ++(90:2) node[anchor=south]{$\vb*{\tau}$};
    \draw[Red,line width=2] (45:.25) -- (225:.25) (-45:.25) -- (135:.25);

    \onslide<2->{
      \draw[force] (6,0) --node[anchor=west]{$\dd{\vb{L}} = \tau \dd{t}$} ++(90:1) coordinate (q);
      \draw[vel,DarkGreen,opacity=0.5] (0,0) -- (q) node[anchor=south]{$\vb{L}
          + \dd{\vb{L}}$};
      \draw[coord,<-] (1,0) arc(0:-30:1);
      \draw[coord,<-] (9.5:1) arc (9.5:39.5:1)
      node[anchor=west]{$\dd{\theta} = \Omega\dd{t}$};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2020/lec20
filename: rec200415.tex
modified: 2020-04-15 04:03:41
domain: p24a
source:
  \begin{tikzpicture}[scale=0.5,font=\tiny]
    \def\peg{0.15} % the radius of the dowel

    % the ramp; corner is at (0,0), but the line width screws that up
    \draw[line width=2] (-6,3) .. controls (-3,0) and (-3,0) .. (0,0)
    -- (0, -3) -- ++(6,0);
    \coordinate (yo-yo) at (-5.25,2.5); % center of yo-yo on ramp

    \draw[coord] (0, -3.3) --node[anchor=north]{$x$} ++(0:2.5);

    %\filldraw [fill=gray] (yo-yo) circle[radius=0.15];
    % \fill[gray,opacity=0.95] (yo-yo) circle[radius=1];

    \filldraw[fill=gray!15!white] (yo-yo) circle[radius=1];
    \draw[dashed, black] (yo-yo) circle[radius=\peg];
    \draw[gray,dashed,line width=2] (-6,3) -- (-4.5,1.5);

    % Edge of the ramp
    \begin{scope}[dashed]
      \draw[line width=0.75] (0,\peg+0.05) circle[radius=\peg];
      \draw (0,\peg+0.05) circle[radius=1];
    \end{scope}

    % illustrate the radius of the dowel
    \begin{scope}[shift={(yo-yo)}]
      \draw[dashed] (-2*\peg,\peg) -- (-2, \peg)
      (-2*\peg,-\peg) -- (-2,-\peg);
      \node at (-2.3,0) {$2a$};
      \draw[coord,<-] (-2,\peg) -- +(90:0.5);
      \draw[coord,<-] (-2,-\peg) -- +(-90:0.5);
      \draw (45:0.75) -- (45:1.25) -- ++(0:0.5) node[anchor=west]{$m, R$};
    \end{scope}

    % illustrate the yo-yo ready to fly off
    \begin{scope}[shift={(5,-2+\peg/2)}]
      \draw[dashed, line width=0.75] (0,0) circle[radius=\peg];
      \draw[dashed] (0,0) circle[radius=1];
      \draw[-> ] (135:1.25)
      arc(135:45:1.25) node[anchor=south,shift={(-.4,.3)}]{$\omega$};
      \draw[vel,line width=1] (0.75,0) --node[anchor=south]{$V_{\rm f}$} ++(0:1.5);
    \end{scope}

    % Dashed level lines
    \draw[dashed,SlateBlue] (yo-yo) -- ++(0:8)
    (0,\peg+0.05) -- ++(0:4)
    (5,-2+\peg/2) -- ++(180:3);

    \draw[coord,<->] (2,\peg+0.05) --node[anchor=west]{$h$} (2,2.5);
    \draw[coord,<->] (2.25,\peg+0.05) --node[anchor=east]{$H$} (2.25,-2+\peg/2);


    % Inset showing the ramp from the right

    \begin{scope}[shift={(-8,-3.5)}]
      \filldraw[color=SlateGray,fill=gray!15,line width=2] (0,0) rectangle
      (4.5,3.25);
      % the ramp
      \shadedraw[color=black,bottom color=SlateGray!10!white,
        top color=SlateGray!50!white]
      (1.25,2.6) rectangle (1.55,0.25);

      %draw the floor
      \fill[gray!50] (0.5,0.25) rectangle (2.5,0.1);
      \draw (0.5,0.25) -- (2.5,0.25); % floor

      \node[anchor=south west] at (0,3.25) {\textsf{\small view from right}};

      % yo-yo
      \fill[gray] (1,1) rectangle (1.2,3)
      (1.6,1) rectangle (1.8,3);
      \fill[gray] (1.2,1.875) rectangle (1.6,2.125);
      \draw[dotted] (1.25,0.875) -- (1.55,0.875);

      \draw[DarkGreen,<-] (2,0.25) -- ++(45:0.4) -- ++(0:0.4)
      node[anchor=west]{floor};
      \draw[DarkGreen,<-] (1.4,1.4) -- ++(45:0.4) -- ++(0:0.4)
      node[anchor=west]{ramp};
      \draw[DarkGreen,<-] (1.6,0.875) -- ++(0:0.6) node[anchor=west]
      {end of ramp};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2016/lab
filename: lab03.tex
modified: 2016-02-04 00:07:53
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[rounded corners, line width=2pt, color=SlateGray] (210:1) -- (0,0) --
    (-30:4);
    \draw[dashed] (0,0) -- (2,0);
    \draw (0:1) arc(0:-30:1);
    \node at (-15:1.3){$\phi$};
    \draw[dashed] (0,0) parabola bend (1.5,3) (2,2.5);
    \fill[fill=SlateBlue] (2,2.5) circle[radius=0.1];
    \draw (0.75,0) arc(0:72:0.75);
    \node at (36:1){$\theta$};
    \draw[vel] (0,0) -- (75:1.25) node[anchor=east]{$v_{0}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2016/exams
filename: p24a-mt1-2016-key.tex
modified: 2016-02-20 16:22:22
domain: p24a
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      photon/.style={line width=1.5pt,color=DarkRed,decorate,decoration={snake,post length=0.1in}},
      spring/.style={decorate,decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm}},
      traj/.style={dashed, color=gray, line width=1pt}
    ]
    \draw[step=0.5,color=gray!25!white] (-2.5,-2) grid (2.5,2);
    \draw[color = gray!50!white,line width=0.5pt] (-2.5,0) -- (2.5,0);
    \draw (0,0) -- (2,1.2) -- (2,-1.2) --
    cycle ;
    \draw (-2,0) -- (0,1.2) -- (0,-1.2) --
    cycle ;
    \draw[dashed,color=blue] (0.03,-2) -- (0.03,2);
    \draw[coord,<->] (4,0) node[anchor=north]{$x$} -- (3,0) -- (3,1)
    node [anchor=east]{$y$};

    \foreach \x in {-1,1} {
        \begin{scope}[shift={(\x,0)}]
          \draw[color=DarkRed,line width=2pt] (-0.1,0.1) -- (0.1,-0.1)
          (-0.1,-0.1) -- (0.1,0.1);
        \end{scope}
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2016/exams
filename: p24a-mt1-2016-key.tex
modified: 2016-02-20 16:22:22
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \fill[fill=gray] (-3,0) rectangle (3,-0.2);
    \draw (-1, 1.82) -- (-0.24, 1.82);
    \draw (-0.1,1.675) -- ++(-90:0.5);
    \coordinate (A) at (-0.25,1.675);
    \fill[fill=gray!50!white] (A) circle[radius=0.15];

    \draw[fill=white] (-2,0) -- ++(90:1.5)
    -- ++(0:1.5) --  ++(45:0.2914) arc(135:-45:0.05)
    -- ++(-135:0.35) -- ++(-90:1) -- ++(0:0.6)
    -- ++(90:1.1) -- ++(0:1) --++(-90:1.48) -- cycle;
    \fill (A) circle[radius=0.025];
    \draw[fill=gray!15!white] (-1.75,1.5) rectangle node{$M_{2}$} (-1,2);
    \draw[fill=gray!15!white] (-0.45,1.25) rectangle node{$M_{3}$} (0.1,0.75);
    \node at (-1.5, 0.25) {$M_{1}$};

    \draw[coord] (-3,0.25) -- node[anchor=south]{$x_{1}$} ++(0:1);
    \draw[coord] (-2,2) --node[anchor=south]{$x_{2}$} (-1.75,2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2016/exams
filename: p24a-mt1-2016-key.tex
modified: 2016-02-20 16:22:22
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[fill=gray!15!white] (0,0) rectangle node{$M_{2}$} (1.5,1) ;
    \draw[force] (1.5,0.5) -- ++(0:1.25) node[anchor=west]{$T$};
    \draw[force] (0.75,0.25) -- ++(-90:1.25) node[anchor=north]{$M_{2}g$};
    \draw[force] (1,0) -- ++(90:1.25) node[anchor=south]{$N_{2}$};
    \draw[coord] (-1.5,0.5) -- node[anchor=south]{$x_{1} + x_{2}$}++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2016/exams
filename: p24a-mt1-2016-key.tex
modified: 2016-02-20 16:22:22
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \draw[fill=gray!15!white] (0,0) rectangle node{$M_{3}$} (1,1) ;
    \draw[force] (0.5,1) -- ++(90:1.25) node[anchor=south]{$T$};
    \draw[force] (0.5,0.25) -- ++(-90:1.25) node[anchor=north]{$M_{3}g$};
    \draw[coord] (-1,0.5) -- node[anchor=east]{$x_{2}$}++(-90:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2016/exams
filename: p24a-mt2-2016-v3.tex
modified: 2016-03-29 22:55:59
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \foreach \ang in {0,15,30,...,345} {
        \draw[color=SlateGray] (0,0) -- (\ang:1.5);
      }
    \fill[fill=gray,opacity=0.75] (0,0) circle[radius=0.2];
    \draw[line width=4] (0,0) circle[radius=1.5];
    \draw[line width=2,color=gray!50] (0,0) circle[radius=1.48];
    \fill[fill=black!80!white] (0,0) circle[radius=0.05];

    \foreach \y in {1, -0.75} {
        \draw[spring] (0,\y) -- ++(0:2);
        \fill (0,\y) circle[radius=0.04];
        \draw[<->,color=DarkGreen] (2.25,0) --
        node[anchor=west]{$r_{\ifthenelse{\equal{\y}{1}}{1}{2}}$} (2.25,\y);
      }
    \draw[line width=3] (2,-1.5) -- (2,1.5);
    \node at (1.7,-1.1) {$k_{2}$};
    \node at (1.7,1.35) {$k_{1}$};
    \node at (135:1.75) {$m$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2016/exams
filename: p24a-mt2-2016-v3.tex
modified: 2016-03-29 22:55:59
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \fill[fill=gray] (0,0) -- (4,0) -- (4,-0.25) -- (-0.25,-0.25)
    -- (-0.25, 4.5) -- (0, 4.5) -- cycle;

    \draw[line width=2.5,color=DarkRed] (2.25,0) --node[anchor=west]{$\;2L$} (0,4);
    \draw (1.75,0) arc(180:125:0.5);
    \node at (1.55,0.35){$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2016/exams
filename: p24a-mt1-2016-v2.tex
modified: 2016-02-18 16:10:49
domain: p24a
source:
  \begin{tikzpicture}[scale=1.5]
    \fill[fill=gray] (-3,0) rectangle (3,-0.2);
    \draw (-1, 1.82) -- (-0.24, 1.82);
    \draw (-0.1,1.675) -- ++(-90:0.5);
    \coordinate (A) at (-0.25,1.675);
    \fill[fill=gray!50!white] (A) circle[radius=0.15];

    \draw[fill=white] (-2,0) -- ++(90:1.5)
    -- ++(0:1.5) --  ++(45:0.2914) arc(135:-45:0.05)
    -- ++(-135:0.35) -- ++(-90:1) -- ++(0:0.6)
    -- ++(90:1.1) -- ++(0:1) --++(-90:1.48) -- cycle;
    \fill (A) circle[radius=0.025];
    \draw[fill=gray!15!white] (-1.75,1.5) rectangle node{$M_{2}$} (-1,2);
    \draw[fill=gray!15!white] (-0.45,1.25) rectangle node{$M_{3}$} (0.1,0.75);
    \node at (-1.5, 0.25) {$M_{1}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2016/exams
filename: p24a-mt2-2016-key.tex
modified: 2016-04-18 00:07:17
domain: p24a
source:
  \begin{tikzpicture}[scale=0.5]
    \fill[fill=gray] (0,0) -- (4,0) -- (4,-0.25) -- (-0.25,-0.25)
    -- (-0.25, 4.5) -- (0, 4.5) -- cycle;

    \draw[line width=2.5,color=DarkRed] (2.25,0) --node[anchor=west]{$\;2L$} (0,4);
    \draw (1.75,0) arc(180:125:0.5);
    \node at (1.55,0.35){$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2016/exams
filename: p24a-mt2-2016-key.tex
modified: 2016-04-18 00:07:17
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \fill[fill=gray] (0,0) -- (4,0) -- (4,-0.25) -- (-0.25,-0.25)
    -- (-0.25, 4.5) -- (0, 4.5) -- cycle;

    \draw[line width=2.5,color=DarkRed] (2.25,0) --node[anchor=west]{$\;2L$} (0,4);
    \draw (1.75,0) arc(180:125:0.5);
    \node at (1.55,0.35){$\theta$};
    \draw[line width=2] (0,0) --node[anchor=south east]{$r$} (1.125,2);
    \draw (0.5,0) arc(0:55:0.5);
    \node at (0.65,0.4) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24a/2016/hw16
filename: hw03-sol.tex
modified: 2016-02-06 06:37:36
domain: p24a
source:
  \begin{tikzpicture}[scale=1]
    \def\dq{15} % the angular range
    \def\rad{8cm} % the radius
    \draw[line width=5pt,color=Brown!70] (0,0) arc(0:\dq:\rad)
    (0,0) arc(0:-\dq:\rad);
    \draw[force] (0,0) -- ++(0:0.75) node[anchor=west]{$\DD N$};
    \draw[coord,<->] (1.5,1) node[anchor=west]{$x$} -- (0.5,1) -- (0.5,2)
    node[anchor=south]{$y$};
    \draw[force] (0,0) -- ++(-90:1.75) node[anchor=west]{$dF$};
    \begin{scope}[shift={(-\rad,0)}]
      \draw[dashed] (\dq:\rad*.75) -- (\dq:\rad) (-\dq:\rad*.75) -- (-\dq:\rad);
      \draw (0:\rad*.75) -- (0:\rad);
      \draw[force] (\dq+1:\rad) -- node[anchor=west]{$T_{2} = T(\theta
          + \dd\theta) \approx T(\theta) + T'(\theta)\dd\theta$}
      ++(\dq+90:2);
      \draw[force] (-\dq-1:\rad) -- node[anchor=west]{$T_{1} = T(\theta
          - \dd\theta) \approx T(\theta) - T'(\theta)\dd\theta$} ++(-\dq-90:2);
      \draw[<->] (0:0.8*\rad) arc(0:\dq:0.8*\rad);
      \draw[<->] (0:0.8*\rad) arc(0:-\dq:0.8*\rad);
      \node at (\dq/2:0.85*\rad){$\DD\theta$};
      \node at (-\dq/2:0.85*\rad){$\DD\theta$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Personal/Family/Philip Max Saeta
filename: tzlabel.tex
modified: 2020-01-26 21:35:48.082369
domain: Family
source:
  \begin{tikzpicture}[
      outline/.style={
          rectangle,
          rounded corners=12pt,
          minimum height=\Lheight,
          minimum width=\Lwidth,
          thick,
          draw=gray!5!white
        }]
    \node[outline]{};
    {\fontspec{Avenir Heavy}%
    \ifthenelse{\equal{#1}{}}{\fontsize{24}{24}}
    {% Now deal with small or really small
      \ifthenelse{\equal{#1}{s}}%
      {\fontsize{20}{20}}
      {\fontsize{18}{18}}
    }
    \selectfont
    \node[anchor=north] at (0,0.45\Lheight){#2};
    }
    % headshot
    \node[anchor=south east] at (0.375\Lwidth,-0.45\Lheight) {
      \headshot};
    % who am i?
    {
    \fontsize{16}{16}\selectfont
    \node at (0,1.25) {\textit{#3}};
    }

    \ifthenelse{\equal{#3}{}}{
      \draw[gray] (-0.45\Lwidth,0.1) -- (0.35\Lwidth,0.1);
      \node at (-.85,-0.2) {\color{gray}\textit{How I knew Phil}};
    }{}
    % 
    \begin{scope}
      \fontsize{9}{9}\selectfont\itshape
      \path[decoration={text along path,
            text = {|\color{gray}|Philip M.\ Saeta, 21 February 1931 – 27 December 2019},
            text align=fit to path,
            raise=2pt,
            pre length=0.5em,
            post length=0em},
        decorate] (-0.45\Lwidth,0) --
      (-0.45\Lwidth,-0.24\Lheight) arc(180:270:0.2\Lheight) --
      ++(0:0.425*\Lwidth);
      \node[rotate=-90,anchor=north east] at (0.42\Lwidth,-0.425\Lheight) {
        Celebrating a life well lived};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Personal/House/patio
filename: draw.tex
modified: 2022-05-29 16:49:05.135387
domain: House
source:
  \begin{tikzpicture}[scale=0.6]
    \draw[line width=2]
    (0.00, 5.12)
    -- (3.00, 5.12)
    -- (3.00, 2.12)
    -- (4.42, 2.12)
    -- (4.42, 0.00)
    -- (11.58, 0.00)
    -- (11.58, 2.12)
    -- (12.88, 2.12)
    -- (12.88, 4.31)
    -- (16.04, 4.31)
    -- (16.04, 2.12)
    -- (27.54, 2.12)
    -- (27.54, 5.15)
    -- (30.54, 5.15)
    -- (30.54, 17.29)
    -- (20.46, 17.29)
    -- (20.46, 26.88)
    -- (11.75, 26.88)
    -- (8.25, 26.88) coordinate(G)
    -- (0.00, 26.88) coordinate(TL)
    -- (0.00, 5.12);

    % Should probably install the path

    \filldraw[gray, fill=gray!5!white] (G) -- ++(-90:53/12)
    -- ++(180:27/12) -- (72/12,0)
    -- ++(0:42/12) -- ++(90:19) -- ++(0:27/12) -- ++(90:7.88) --cycle;


    % grid
    \foreach \y in {0, 1,..., 27} {
        \draw[gray!25] (0, \y) -- ++(31,0);
      }
    \foreach \x in {1, 2, ..., 31} {
        \draw[gray!25] (\x, 0) -- ++(0,27);
      }


  \end{tikzpicture}


folder: /Users/saeta/Documents/References/c15/Berger
filename: 141231-Caltech.tex
modified: 2014-12-31 17:30:16
domain: References
source:
  \begin{tikzpicture}[scale=0.75,>=stealth']
    \draw [red] (0,0) circle [radius=2];;
    \draw [fill=red] (1.732,1) circle [radius=0.3];;
    \draw [red] (0,0)-- (1.732,1);
    \draw [red, dashed] (0,-0.67) arc [radius=0.67, start angle = -90, end angle=30];;
    \draw [green!50!black] (0,0) circle [radius=3];;
    \draw [fill=green!50!black] (-1.5,-2.598) circle [radius=0.3];;
    \draw [green!50!black] (0,0)-- (-1.5,-2.598);
    \draw [green!50!black, dashed] (0,-1.33) arc [radius=1.33, start angle = -90, end angle=-120];;
    \draw [black, dashed] (0,0) -- (0,-3);
    \draw [thick,->] (4,1.5) -- (4,-1.5) node[anchor=west]{$g$};
    \node at (0.9,-0.5) {$\theta_1$};
    \node at (-0.5,-1.6) {$-\theta_2$};
    \node at (0.5,0.7) {$\ell_1$};
    \node at (-0.9,-0.9) {$\ell_2$};
    \node at (2.28,1) {$q_1$};
    \node at (-2.1,-2.598) {$q_2$};
    \node[text width=2.2in] at (0,-4.5) {\small Two particles of equal mass constrained to
      move on concentric vertical rings interact via a Coulomb force. };
  \end{tikzpicture}


folder: /Users/saeta/Documents/References/c15/Berger
filename: 141027-NSF-Berger.tex
modified: 2014-10-30 06:06:57
domain: References
source:
  \begin{tikzpicture}[scale=0.75,>=stealth']
    \draw [red] (0,0) circle [radius=2];;
    \draw [fill=red] (1.732,1) circle [radius=0.3];;
    \draw [red] (0,0)-- (1.732,1);
    \draw [red, dashed] (0,-0.67) arc [radius=0.67, start angle = -90, end angle=30];;
    \draw [green!50!black] (0,0) circle [radius=3];;
    \draw [fill=green!50!black] (-1.5,-2.598) circle [radius=0.3];;
    \draw [green!50!black] (0,0)-- (-1.5,-2.598);
    \draw [green!50!black, dashed] (0,-1.33) arc [radius=1.33, start angle = -90, end angle=-120];;
    \draw [black, dashed] (0,0) -- (0,-3);
    \draw [thick,->] (4,1.5) -- (4,-1.5) node[anchor=west]{$g$};
    \node at (0.9,-0.5) {$\theta_1$};
    \node at (-0.5,-1.6) {$-\theta_2$};
    \node at (0.5,0.7) {$\ell_1$};
    \node at (-0.9,-0.9) {$\ell_2$};
    \node at (2.28,1) {$q_1$};
    \node at (-2.1,-2.598) {$q_2$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch09.tex
modified: 2022-05-30 19:59:56.065215
domain: Book
source:
  \begin{tikzpicture}[scale=0.8]
    \def\hght{5}
    \def\wdth{1}
    \def\dz{-2}
    \begin{scope}[shift={(0,0.3)}]
      \fill[fill=red!40!white] (0,0) rectangle (1*\wdth,\hght);
      \fill[fill=blue!40!white] (2*\wdth,0) rectangle (3*\wdth,\hght);

      % Let's get some faux 3 D
      \fill[fill=red!20!white] (0,\hght,0) -- (0,\hght,\dz) -- (\wdth,\hght,\dz)
      -- (\wdth,\hght,0) -- cycle;
      \shade[left color=red!15!white, right color=blue!15!white]
      (\wdth,\hght,0) -- (\wdth,\hght,\dz) -- (2*\wdth,\hght,\dz)
      -- (2*\wdth,\hght,0) -- cycle;
      \fill[fill=blue!20!white] (2*\wdth,\hght,0) -- (3*\wdth,\hght, 0)
      -- ++(0,0,\dz) -- ++(-\wdth,0,0) -- cycle;
      \fill[fill=blue!25!white] (3*\wdth,0,0) -- ++(0,0,\dz) --
      ++(0,\hght,0) -- ++(0,0,-1*\dz) -- cycle;
      \node at (0.5,0.3) {$T_{A}$};
      \node at (2.5,0.3) {$T_{B}$};
      \shade [left color=red!30!white, right color=blue!30!white] (1,0)
      rectangle (2,5);
      \draw[line width=0.5] (1,0) -- ++(90:5) (2,0) -- ++(90:5);
      \foreach \y in {0.5,1,1.5,...,4} {
          \draw[line width=2,color=DarkSlateGray,->] (1.2,\y) -- ++(0:0.6);
        }
      \node at (1.5,4.5) [color=DarkSlateGray]{$Q$};
      \foreach \z in {0.25, 0.5, 0.75} {
          \draw[line width=1.5,color=SlateGray,->] (1.2,\hght, \z*\dz) -- ++(0:0.6);
        }
    \end{scope}
    \draw[<->] (1,0) --node[anchor=north]{$d$} ++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch08.tex
modified: 2022-05-31 03:21:29.413386
domain: Book
source:
  \begin{tikzpicture}[
      scale=1.25,
      font=\Large
    ]
    \def\dy{0.5}
    \node[notdone] at (0,0) {$\zeta$};
    \node[notdone,rotate=-90] at (0,-\dy){$\rightarrow$};
    \node[notdone] at (0,-2*\dy) {$Z$};
    \node[notdone,rotate=-90] at (0,-3*\dy){$\rightarrow$};
    \node[notdone] at (0,-4*\dy) {$S$};
    \node[notdone,rotate=-90] at (0,-5*\dy){$\rightarrow$};
    \node[notdone] at (0,-6*\dy) {$p$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch08.tex
modified: 2022-05-31 03:21:29.413386
domain: Book
source:
  \begin{tikzpicture}[
      scale=1.25,
      font=\Large
    ]
    \def\dy{0.5}
    \node[now] at (0,0) {$\zeta$};
    \node[notdone,rotate=-90] at (0,-\dy){$\rightarrow$};
    \node[notdone] at (0,-2*\dy) {$Z$};
    \node[notdone,rotate=-90] at (0,-3*\dy){$\rightarrow$};
    \node[notdone] at (0,-4*\dy) {$S$};
    \node[notdone,rotate=-90] at (0,-5*\dy){$\rightarrow$};
    \node[notdone] at (0,-6*\dy) {$p$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch08.tex
modified: 2022-05-31 03:21:29.413386
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \def\x{4}
    \def\dy{1.0}
    \def\amp{0.4}
    \def\y{4}
    \node[anchor=north] at (\x/2,0){$L$};
    \begin{scope}[shift={(0,\dy)},color=trace01]
      \draw[dashed,color=gray] (0,0) -- (\x,0);
      \draw[line width=2] (0,0) sin (0.5*\x,\amp) cos (\x,0);
      \node[anchor=east] at (-0.2,0) {$n=1$};
      \node[anchor=west] at (\x+0.2,0) {$\lambda = 2L$};
    \end{scope}
    \begin{scope}[shift={(0,2*\dy)},color=trace02]
      \draw[dashed,color=gray] (0,0) -- (\x,0);
      \draw[line width=2] (0,0) sin (0.25*\x,0.4*\dy) cos (0.5*\x,0)
      sin(0.75*\x,-0.4*\dy) cos (\x,0);
      \node[anchor=east] at (-0.2,0) {$n=2$};
      \node[anchor=west] at (\x+0.2,0) {$\lambda = L$};
    \end{scope}
    \begin{scope}[shift={(0,3*\dy)},color=trace03]
      \draw[dashed,color=gray] (0,0) -- (\x,0);
      \draw[line width=2] (0,0) sin (\x/6,\amp) cos (\x/3,0)
      sin(\x/2,-\amp) cos (2*\x/3,0)
      sin(5*\x/6, \amp) cos(\x,0);
      \node[anchor=east] at (-0.2,0) {$n=3$};
      \node[anchor=west] at (\x+0.2,0) {$\lambda = \frac{2}{3} L$};
    \end{scope}
    \draw[color=SlateGray, line width=2] (0,0) rectangle (\x, \y);
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch08.tex
modified: 2022-05-31 03:21:29.413386
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \def\dx{0.4}
    \foreach \x in {0,1,2,...,25} {
        \draw[line width=1.25] (\x*\dx,-0.15) -- ++(90:0.4);
      }
    \draw[color=SlateGray](0,0.05) -- (25*\dx,0.05);
    \draw[line width=2] (0,-0.2) -- ++(90:0.6)
    (25*\dx,-0.2) -- ++(90:0.6);
    \node at (0,-0.4) {$0$};
    \node at (25*\dx,-0.4){$L$};
    \draw[<-] (8*\dx,-0.4) -- ++(180:2*\dx);
    \draw[<-] (9*\dx,-0.4) -- ++(0:2*\dx);
    \node at (8.5*\dx,-0.8){$\quad\Ldb$};
    \filldraw[fill=DarkRed] (16.5*\dx,0.05) circle[radius=0.4*\dx];
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch08.tex
modified: 2022-05-31 03:21:29.413386
domain: Book
source:
  \begin{tikzpicture}[
      scale=1.25,
      font=\Large
    ]
    \def\dy{0.5}
    \node[done] at (0,0) {$\zeta$};
    \node[done,rotate=-90] at (0,-\dy){$\rightarrow$};
    \node[now] at (0,-2*\dy) {$Z$};
    \node[notdone,rotate=-90] at (0,-3*\dy){$\rightarrow$};
    \node[now] at (0,-4*\dy) {$S$};
    \node[notdone,rotate=-90] at (0,-5*\dy){$\rightarrow$};
    \node[notdone] at (0,-6*\dy) {$p$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch08.tex
modified: 2022-05-31 03:21:29.413386
domain: Book
source:
  \begin{tikzpicture}[
      scale=1.25,
      font=\Large
    ]
    \def\dy{0.5}
    \node[done] at (0,0) {$\zeta$};
    \node[done,rotate=-90] at (0,-\dy){$\rightarrow$};
    \node[done] at (0,-2*\dy) {$Z$};
    \node[done,rotate=-90] at (0,-3*\dy){$\rightarrow$};
    \node[done] at (0,-4*\dy) {$S$};
    \node[done,rotate=-90] at (0,-5*\dy){$\rightarrow$};
    \node[now] at (0,-6*\dy) {$p$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch08.tex
modified: 2022-05-31 03:21:29.413386
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \def\x{2.5}
    \def\y{1.5}
    \draw[dashed] (0,-\y) -- (0,\y);
    \draw[line width=4pt,color=SlateGray] (-\x,-\y) rectangle (\x,\y);
    \node[anchor=west] at (0.15-\x, \y-0.5){$S_{1}(\nrg_{1}, V_{1})$};
    \node[anchor=east] at (\x-0.15, \y-0.5){$S_{2}(\nrg_{2}, V_{2})$};
    \draw[<->,color=DarkRed,line width=1.5] (-0.5,0) node[anchor=east]{$\Delta V$}
    -- (0.5,0) node[anchor=west]{$\Delta \nrg$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch08.tex
modified: 2022-05-31 03:21:29.413386
domain: Book
source:
  \begin{tikzpicture}[scale=1.3]
    \def\s{2}
    \draw (0,0,0) -- ++(\s,0,0) -- ++(0,\s,0)
    -- ++(-\s,0,0) -- ++(0,-\s,0)
    -- ++(0,0,-\s) --++(\s,0,0) -- ++(0,\s,0)
    -- ++(-\s,0,0) -- ++(0,-\s,0)
    (0,\s,0) -- (0,\s,-\s)
    (\s,\s,0) -- (\s,\s,-\s)
    (\s,0,0) -- (\s,0,-\s);
    \node[anchor=north] at (\s/2,0,0){$L$};
    \node[anchor=east] at (0,\s/2,0){$L$};
    \node[anchor=west] at (0,0,-\s/2){$L$};
    \draw (0,0,-1.05*\s) -- ++(135:0.2) node[anchor=south east] {$\scriptstyle \dd{L}$};
    \fill[opacity=0.5,color=gray!20!white] (0,0,0) -- (0,\s,0) -- (\s,\s,0) --
    (\s,0,0) -- cycle;
    \fill[opacity=0.5,color=gray!30!white] (\s,0,0) -- (\s,\s,0) -- (\s,\s,-\s) --
    (\s,0,-\s) -- cycle;
    \fill[opacity=0.5,color=gray!10!white] (0,\s,0) -- (0,\s,-\s) -- (\s,\s,-\s) --
    (\s,0,-\s) -- cycle;
    \def\s{2.2}
    \draw[color=SlateGray,dashed, line width=1] (0,0,0) -- ++(\s,0,0) -- ++(0,\s,0)
    -- ++(-\s,0,0) -- ++(0,-\s,0)
    -- ++(0,0,-\s) --++(\s,0,0) -- ++(0,\s,0)
    -- ++(-\s,0,0) -- ++(0,-\s,0)
    (0,\s,0) -- (0,\s,-\s)
    (\s,\s,0) -- (\s,\s,-\s)
    (\s,0,0) -- (\s,0,-\s);
    \node[anchor=north] at (\s-0.1,0,0){$\scriptstyle \dd{L}$};
    \node[anchor=east] at (0,\s-0.1,0){$\scriptstyle \dd{L}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch08.tex
modified: 2022-05-31 03:21:29.413386
domain: Book
source:
  \begin{tikzpicture}[
      scale=1.25,
      font=\Large
    ]
    \def\dy{0.5}
    \node[done] at (0,0) {$\zeta$};
    \node[done,rotate=-90] at (0,-\dy){$\rightarrow$};
    \node[done] at (0,-2*\dy) {$Z$};
    \node[done,rotate=-90] at (0,-3*\dy){$\rightarrow$};
    \node[done] at (0,-4*\dy) {$S$};
    \node[done,rotate=-90] at (0,-5*\dy){$\rightarrow$};
    \node[done,font=\huge,fill=yellow!50!white] at (0,-6*\dy) {$p$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch05.tex
modified: 2022-05-30 19:59:56.065149
domain: Book
source:
  \begin{tikzpicture}[scale=1,>=Stealth]
    \filldraw[fill=yellow!25!white,draw=gray!25!white,line width=3pt] (0,0)
    rectangle (4,3);
    \node at (0.35,0.35) {$R$};
    \filldraw[fill=red!25!white,draw=gray!25!white,line width=2pt] (4.5,1.5)
    circle[radius=0.5];
    \node at (4.5,0.7) {$S$};
    \draw[line width=1.25,<->,color=DarkRed] (3.4,1.5) --node[anchor=south]{$\Delta E$} +(0:1.2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch05.tex
modified: 2022-05-30 19:59:56
domain: Book
source:
  \begin{tikzpicture}
    \begin{axis}[
        ymin=0,
        ymax=1,
        enlargelimits=false,
        height=1.5in,
        ylabel={$\probab$},
        ytick={0,1},
        xtick={0,0.5,1,1.5,2},
        xticklabel=\empty,
      ]
      \addplot[
        trace01,
        domain=0.001:2,
        samples=201,
        line width=2pt,
      ]
      {1 / (1 + exp(-1/x))};
      \addplot[
        trace02,
        domain=0.001:2,
        samples=201,
        line width=2pt,
      ]
      {1 / (1 + exp(1/x))};
    \end{axis}

    \node[color=trace01] at (4.5,1.75) {$\probab(0)$};
    \node[color=trace02] at (4.5,0.45) {$\probab(\epsilon)$};
    \node at (5.5,0.3){(a)};

    \begin{scope}[shift={(0,-2.75)}]
      \begin{axis}[
          ymin=0,
          ymax=0.5,
          enlargelimits=false,
          height=1.5in,
          ylabel={Energy},
          minor tick num=0,
          ytick={0},
          xtick={0,0.5,1,1.5,2},
          xticklabel=\empty,
          extra y ticks={0.5},
          extra y tick labels={$\frac{\epsilon}{2}$},
        ]
        \addplot[
          trace03,
          domain=0.001:2,
          samples=201,
          line width=2pt,
        ]
        {1 / (1 + exp(1/x))};
      \end{axis}

      \node at (5.5,0.3) {(b)};
    \end{scope}

    \begin{scope}[shift={(0,-5.5)}]
      \begin{axis}[
          ymin=0,
          ymax=0.5,
          enlargelimits=false,
          height=1.5in,
          ylabel={$C$},
          xlabel={$\kT/\epsilon$},
          minor tick num=0,
          ytick={0},
          xtick={0,0.5,1,1.5,2},
          extra y ticks={0.5},
          extra y tick labels={$\frac{\kb}{2}$},
        ]
        \addplot[
          trace04,
          domain=0.001:2,
          samples=201,
          line width=2pt,
        ]
        {1 / (2*x * cosh(0.5/x))^2};
      \end{axis}

      \node at (5.5,1.85) {(c)};
    \end{scope}


  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch05.tex
modified: 2022-05-30 19:59:56.065149
domain: Book
source:
  \begin{tikzpicture}[scale=0.8]
    \draw[color=DarkRed,line width=1] (0,0) parabola (2,4) (0,0) parabola (-2,4);
    \foreach \y in {1, 3, 5, 7} {
        \pgfmathsetmacro{\x}{sqrt(\y/2)}%
        \pgfmathtruncatemacro{\n}{(\y-1)/2}%
        \draw(-\x, \y/2) -- (\x, \y/2);
        \node at (-\x-0.75,\y/2) {$\frac{\y}{2}\hw$ };
        \node at (\x+0.75,\y/2) {$n=\n$};
      }
    \draw[line width=0pt,color=white] (0,-1) -- (0.001,-1);
    %     \draw (-0.707, 0.5) -- (0.707, 0.5);
    %     \draw (-1.225, 1.5) -- (1.225,1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch05.tex
modified: 2022-05-30 19:59:56.065149
domain: Book
source:
  \begin{tikzpicture}
    \begin{axis}[
        ymin=0,
        ymax=1,
        enlargelimits=false,
        height=1.5in,
        ylabel={$\probab$},
        ytick={0,1},
        xtick={0,0.5,1,1.5,2},
        xticklabel=\empty,
      ]
      \addplot[
        trace01,
        domain=0.001:2,
        samples=201,
        line width=2pt,
      ]
      {1-exp(-1/x)};
      \addplot[
        trace02,
        domain=0.001:2,
        samples=201,
        line width=2pt,
      ]
      {exp(-1/x)*(1-exp(-1/x))};
      \addplot[
        trace05,
        domain=0.001:2,
        samples=201,
        line width=2pt,
        %draw=brown!40!black,
      ]
      {exp(-2/x)*(1-exp(-1/x))};
    \end{axis}

    \node[color=trace01] at (4.5,1.5) {$\probab(0)$};
    \node[color=trace02] at (1,0.45) {$\probab(1)$};
    \draw[color=trace05] (3.5,0.25) -- ++(135:0.6) node[anchor=south east]{$\probab(2)$};
    \node at (5.5,1.9){(a)};

    \begin{scope}[shift={(0,-2.75)}]
      \begin{axis}[
          ymin=0,
          ymax=2,
          enlargelimits=false,
          height=1.5in,
          ylabel={Energy},
          minor tick num=0,
          ytick={0}, % 0, 0.5, 1, 1.5, 2},
          xtick={0,0.5,1,1.5,2},
          xticklabel=\empty,
          extra y ticks={1, 2},
          extra y tick labels={$\hw$, $2\hw$},
        ]
        \addplot[
          trace03,
          domain=0.001:2,
          samples=201,
          line width=2pt,
        ]
        {1 / (exp(1/x)-1)};
      \end{axis}

      \node at (5.5,0.3) {(b)};
    \end{scope}

    \begin{scope}[shift={(0,-5.5)}]
      \begin{axis}[
          ymin=0,
          ymax=1,
          enlargelimits=false,
          height=1.5in,
          ylabel={$C$},
          xlabel={$\kT/\epsilon$},
          minor tick num=0,
          ytick={0},
          xtick={0,0.5,1,1.5,2},
          extra y ticks={0.5,1},
          extra y tick labels={$\frac{\kb}{2}$,$\kb$},
        ]
        \addplot[
          trace04,
          domain=0.001:2,
          samples=201,
          line width=2pt,
        ]
        {1 / (2*x * sinh(0.5/x))^2};
      \end{axis}

      \node at (5.5,0.3) {(c)};
    \end{scope}


  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch05.tex
modified: 2022-05-30 19:59:56.065149
domain: Book
source:
  \begin{tikzpicture}[scale=0.8]
    \begin{axis}[
        ymin = 0,
        ymax = 9,
        xmin = 0,
        xmax = 2.2,
        enlargelimits = false,
        height=3in,
        ylabel=\empty,
        ytick=\empty,
        xlabel={\nrg},
        xtick=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.5},
      ]
      \addplot[
        trace01,
        domain=0:2,
        samples=201,
        line width=2pt,
      ] { 8*exp(-x*8) };
      \addplot[
        trace02,
        domain=0:2,
        samples=201,
        line width=2pt,
      ] { x^8/32 };
      \addplot[
        trace03,
        domain=0:2,
        samples=201,
        line width=2pt,
      ] { 8*exp(-64*(x-1)^2)};
    \end{axis}
    \node[color=trace01] at (1.35,2.5){$e^{-\nrg/\kT}$};
    \node[color=trace02] at (4.5,2.5){$\nos$};
    \node[color=trace03] at (4,5.5){$\nos e^{-\nrg/\kT}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch10.tex
modified: 2022-05-30 19:53:20.723973
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \def\x{2.5}
    \def\y{1.5}
    \draw[dashed] (0,-\y) -- (0,\y);
    \draw[line width=4pt,color=SlateGray] (-\x,-\y) rectangle (\x,\y);
    \node[anchor=west] at (0.05-\x, \y-0.5){$S_{1}(\nrg_{1}, V_{1}, N_{1})$};
    \node[anchor=east] at (\x-0.05, \y-0.5){$S_{2}(\nrg_{2}, V_{2}, N_{2})$};
    \draw[<->,color=DarkRed,line width=1.5] (-0.5,0)
    -- (0.5,0) node[anchor=north]{$\qquad\quad\Delta \nrg, \Delta V, \Delta N$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch10.tex
modified: 2022-05-30 19:53:20.723973
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{semilogyaxis}[
        enlargelimits=false,
        ylabel={Pressure (Pa)},
        xlabel={Elevation (km)},
        width=3.5in,
        height=3in
      ]
      \addplot [only marks,trace04] coordinates {
          (0, 101327)
          (1, 89876.7)
          (2, 79497.2)
          (5, 54021.5)
          (7.5, 38252.7)
          (10, 26437.3)
          (15, 12045.1)
          (20, 5475.21)
          (25, 2511)
          (30, 1171.95)
          (35, 558.969)
          (40, 277.546)
          (45, 143.15)
          (50, 75.9541)
          (55, 39.97)
          (60, 20.3165)
          (65, 9.92326)
          (70, 4.63487)
        };
      \addplot[
        trace01,
        domain=0:70,
      ]{ 101000*exp(-x/8.49) };
      \addplot[
        trace05,
        domain=0:70,
      ]{ 101000*exp(-x/7) };
      \draw[trace01] (25,5300) -- (30,10000) node[anchor=west] {Isothermal
        atmosphere};
      \draw[trace05] (42,250) -- (37,100) node[anchor=east]{$z_{0}=\SI{7}{km}$};
    \end{semilogyaxis}

  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch07.tex
modified: 2022-05-30 16:13:05.683626
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin = 0,
        ymax = 1.2,
        xmin = 0,
        xmax = 3.3,
        enlargelimits = false,
        height=2.5in,
        width=3.5in,
        ylabel={$f(v)$},
        ytick=\empty,
        xlabel={$v / \tilde{v}$},
        xtick={0,1,2,3},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25},
        xtick align=inside,
      ]
      \addplot[
        trace01,
        domain=0:3,
        samples=201,
        line width=2pt,
      ] { x^2 * exp(1-x^2) };
      \draw[color=DarkGreen] (1.128,0) -- ++(90:0.969);
      \draw[color=DarkGreen,<-] (1.128,0.969) ++(30:0.02) -- ++(30:0.2)
      node[anchor=west] {$\overline{v}$};
      \draw[DarkBlue] (1.225,0) -- (1.225,0.91);
      \draw[DarkBlue,<-] (1.28,0.91) --++(0:0.2) node[anchor=west]{$v_{\rm rms}$};
    \end{axis}
    %\draw[color=DarkGreen] (2.504,0) -- ++(90:3.88);
    %\draw[color=DarkGreen,<-] (2.51,3.9) -- ++(45:0.6) node[anchor=south west]
    %{$\overline{v}$};
    %
    %\draw[DarkBlue] (2.720,0) -- ++(90:3.55);
    %\draw[DarkBlue,<-] (2.8, 3.55) -- ++(0:0.6) node[anchor=west]{$v_{\rm rms}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch03.tex
modified: 2022-05-31 14:46:16.192381
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \def\x{2}
    \def\y{1.5}
    \draw[dashed] (0,-\y) -- (0,\y);
    \draw[line width=4pt,color=SlateGray] (-\x,-\y) rectangle (\x,\y);
    \node[anchor=west] at (0.25-\x, \y-0.5){$\nos_{1}(\nrg_{1})$};
    \node[anchor=east] at (\x-0.25, \y-0.5){$\nos_{2}(\nrg_{2})$};
    \draw[<->,color=DarkRed,line width=1.5] (-0.5,0) -- (0.5,0)
    node[anchor=west]{$\Delta \nrg$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch01.tex
modified: 2022-06-02 19:39:12.477650
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \def\x{3}
    \def\y{3}
    \draw[dashed] (0,0) -- (0,\y);
    \draw[line width=4pt,color=SlateGray] (-\x,0) rectangle (\x,\y);
    \foreach \x/\y/\n in {-2/2.5/1, 1/2.3/2, -0.7/1.3/3, -2.5/0.4/4, 1/1.4/5, 2.6/0.8/6, -2.2/2/7} {
        \node[draw,circle,inner sep=2pt,fill=yellow!20] at (\x,\y) {\n};
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch01.tex
modified: 2022-06-02 19:39:12.477650
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \def\x{3}
    \def\y{3}
    \draw[dashed] (0,0) -- (0,\y);
    \draw[line width=4pt,color=SlateGray] (-\x,0) rectangle (\x,\y);
    \foreach \x/\y/\n in {-2/2.5/1, 1/2.3/2, -0.7/1.3/3, -2.5/0.4/4, 1/1.4/5, 2.6/0.8/6, -2.2/2/7} {
        \node[draw,circle,inner sep=2pt,fill=yellow!20] at (\x,\y) {\phantom{\n}};
      }
    \node[anchor=south] at (-\x/3,0.1) {$N-r$};
    \node[anchor=south] at (\x/3,0.1) {$\vphantom{N}r$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch01.tex
modified: 2022-06-02 19:39:12.477650
domain: Book
source:
  \begin{tikzpicture}
    \begin{axis}[
        ymin=0, ymax=3, enlargelimits=false,
        xlabel={$x$}, ylabel={$\ln x$},
        width=3in, height=2in,
      ]
      \def\x{0} \def\y{0}
      \pgfplotsforeachungrouped \x/\y in {1/0.0000, 2/0.6931, 3/1.0986,
          4/1.3863,
          5/1.6094,
          6/1.7918,
          7/1.9459,
          8/2.0794,
          9/2.1972,
          10/2.3026,
          11/2.3979,
          12/2.4849,
          13/2.5649,
          14/2.6391,
          15/2.7081,
          16/2.7726,
          17/2.8332,
          18/2.8904,
          19/2.9444,
          20/2.996} {
          \edef\temp{\noexpand\filldraw[SlateBlue, fill=SlateBlue!33!white] (axis cs:\x,0) rectangle (axis cs:\x+1,\y);}
          \temp
          %\filldraw[SlateBlue, fill=SlateBlue!33!white] (axis cs:\x,0) rectangle (axis cs:\x+1,\y);
        };
      \addplot[DarkBlue, domain=1:20, samples=25,line width=1.5pt]
      {ln(x)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch99/sol
filename: Dewar.tex
modified: 2022-05-30 01:51:35.554138
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=3pt,color=DarkBlue] (0,0) -- (0,4);
    \draw[line width=3pt, color=DarkRed!50!white] (2,0) -- (2,4);
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/pre2015
filename: Ch08.tex
modified: 2022-05-27 23:08:34.255992
domain: Book
source:
  \begin{tikzpicture}[scale=1.3]
    \def\s{2}
    \draw (0,0,0) -- ++(\s,0,0) -- ++(0,\s,0)
    -- ++(-\s,0,0) -- ++(0,-\s,0)
    -- ++(0,0,-\s) --++(\s,0,0) -- ++(0,\s,0)
    -- ++(-\s,0,0) -- ++(0,-\s,0)
    (0,\s,0) -- (0,\s,-\s)
    (\s,\s,0) -- (\s,\s,-\s)
    (\s,0,0) -- (\s,0,-\s);
    \node[anchor=north] at (\s/2,0,0){$L$};
    \node[anchor=east] at (0,\s/2,0){$L$};
    \node[anchor=west] at (0,0,-\s/2){$L$};
    \draw (0,0,-1.05*\s) -- ++(135:0.2) node[anchor=south east] {$\scriptstyle \DD L$};
    \fill[opacity=0.5,color=gray!20!white] (0,0,0) -- (0,\s,0) -- (\s,\s,0) --
    (\s,0,0) -- cycle;
    \fill[opacity=0.5,color=gray!30!white] (\s,0,0) -- (\s,\s,0) -- (\s,\s,-\s) --
    (\s,0,-\s) -- cycle;
    \fill[opacity=0.5,color=gray!10!white] (0,\s,0) -- (0,\s,-\s) -- (\s,\s,-\s) --
    (\s,0,-\s) -- cycle;
    \def\s{2.2}
    \draw[color=SlateGray,dashed, line width=1] (0,0,0) -- ++(\s,0,0) -- ++(0,\s,0)
    -- ++(-\s,0,0) -- ++(0,-\s,0)
    -- ++(0,0,-\s) --++(\s,0,0) -- ++(0,\s,0)
    -- ++(-\s,0,0) -- ++(0,-\s,0)
    (0,\s,0) -- (0,\s,-\s)
    (\s,\s,0) -- (\s,\s,-\s)
    (\s,0,0) -- (\s,0,-\s);
    \node[anchor=north] at (\s-0.1,0,0){$\scriptstyle \DD L$};
    \node[anchor=east] at (0,\s-0.1,0){$\scriptstyle \DD L$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/pre2015/tikzfigs
filename: cube.tex
modified: 2015-08-16 19:46:19
domain: Book
source:
  \begin{tikzpicture}[scale=1.2]
    \def\s{2}
    \draw (0,0,0) -- ++(\s,0,0) -- ++(0,\s,0)
    -- ++(-\s,0,0) -- ++(0,-\s,0)
    -- ++(0,0,-\s) --++(\s,0,0) -- ++(0,\s,0)
    -- ++(-\s,0,0) -- ++(0,-\s,0)
    (0,\s,0) -- (0,\s,-\s)
    (\s,\s,0) -- (\s,\s,-\s)
    (\s,0,0) -- (\s,0,-\s);
    \node[anchor=north] at (\s/2,0,0){$L$};
    \node[anchor=east] at (0,\s/2,0){$L$};
    \node[anchor=west] at (0,0,-\s/2){$L$};
    \draw (0,0,-1.05*\s) -- ++(135:0.2) node[anchor=south east] {$\scriptstyle \DD L$};
    \fill[opacity=0.5,color=gray!20!white] (0,0,0) -- (0,\s,0) -- (\s,\s,0) --
    (\s,0,0) -- cycle;
    \fill[opacity=0.5,color=gray!30!white] (\s,0,0) -- (\s,\s,0) -- (\s,\s,-\s) --
    (\s,0,-\s) -- cycle;
    \fill[opacity=0.5,color=gray!10!white] (0,\s,0) -- (0,\s,-\s) -- (\s,\s,-\s) --
    (\s,0,-\s) -- cycle;
    \def\s{2.2}
    \draw[color=SlateGray,dashed, line width=1] (0,0,0) -- ++(\s,0,0) -- ++(0,\s,0)
    -- ++(-\s,0,0) -- ++(0,-\s,0)
    -- ++(0,0,-\s) --++(\s,0,0) -- ++(0,\s,0)
    -- ++(-\s,0,0) -- ++(0,-\s,0)
    (0,\s,0) -- (0,\s,-\s)
    (\s,\s,0) -- (\s,\s,-\s)
    (\s,0,0) -- (\s,0,-\s);
    \node[anchor=north] at (\s-0.1,0,0){$\scriptstyle \DD L$};
    \node[anchor=east] at (0,\s-0.1,0){$\scriptstyle \DD L$};

  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/pre2015/tikzfigs
filename: thermalconduction.tex
modified: 2015-08-22 05:01:47
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \def\hght{5}
    \newcommand\wdth{1}
    \newcommand\dz{-2}
    \begin{scope}[shift={(0,0.3)}]
      \fill[fill=red!40!white] (0,0) rectangle (1*\wdth,\hght);
      \fill[fill=blue!40!white] (2*\wdth,0) rectangle (3*\wdth,\hght);

      % Let's get some faux 3 D
      \fill[fill=red!20!white] (0,\hght,0) -- (0,\hght,\dz) -- (\wdth,\hght,\dz)
      -- (\wdth,\hght,0) -- cycle;
      \shade[left color=red!15!white, right color=blue!15!white]
      (\wdth,\hght,0) -- (\wdth,\hght,\dz) -- (2*\wdth,\hght,\dz)
      -- (2*\wdth,\hght,0) -- cycle;
      \fill[fill=blue!20!white] (2*\wdth,\hght,0) -- (3*\wdth,\hght, 0)
      -- ++(0,0,\dz) -- ++(-\wdth,0,0) -- cycle;
      \fill[fill=blue!25!white] (3*\wdth,0,0) -- ++(0,0,\dz) --
      ++(0,\hght,0) -- ++(0,0,-1*\dz) -- cycle;
      \node at (0.5,0.3) {$T_{A}$};
      \node at (2.5,0.3) {$T_{B}$};
      \shade [left color=red!30!white, right color=blue!30!white] (1,0)
      rectangle (2,5);
      \draw[line width=0.5] (1,0) -- ++(90:5) (2,0) -- ++(90:5);

      \foreach \y in {0.5,1,1.5,...,4.5} {
          \draw[line width=2,color=DarkSlateGray,->] (1.2,\y) -- ++(0:0.6);
        }
      \foreach \z in {0.25, 0.5, 0.75} {
          \draw[line width=1.5,color=SlateGray,->] (1.2,\hght, \z*\dz) -- ++(0:0.6);
        }
    \end{scope}
    \draw[<->] (1,0) --node[anchor=north]{$d$} ++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/pre2015/tikzfigs
filename: Callen932.tex
modified: 2015-11-13 04:35:13
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \fill[color=gray!50!white] (0,0) rectangle (1.5,5);
    \fill[color=gray] (0,0) rectangle(1.5,2);
    \draw (0,6) -- (0,0) -- (1.5,0) -- (1.5,6);
    \node at (0.75,-1){$T = \degC{-5.0}$};

    \draw (1.75,2) -- (3.75,2);
    \draw (1.75,3.5) -- (3.75,3.5);
    \draw[<->] (2.75,2) --node[anchor=east]{$x$} (2.75,3.5);
    \node at (2.75,0.5) {solid};
    \node at (2.75,4) {liquid};

    \begin{scope}[shift={(4,0)}]
      \fill[color=gray!50!white] (0,0) rectangle (1.5,4.5);
      \fill[color=gray] (0,0) rectangle(1.5,3.5);
      \draw (0,6) -- (0,0) -- (1.5,0) -- (1.5,6);
      \node at (0.75,-0.5){$T = \degC{-5.2}$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/tmp
filename: image.tex
modified: 2017-06-26 23:05:47
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \shade [ball color=Blue!60!white] (0,0) circle (0.15cm);
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch20.tex
modified: 2022-06-09 22:52:30.317376
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=10,
        ymin=0,
        ymax=1.5,
        enlargelimits=false,
        width=3in,
        height=2.25in,
        xlabel={$\hb\omega/\kT$},
        ylabel={spectral density},
      ]
      \addplot[
        trace01,
        domain=0.001:10,
        samples=201,
        line width=2pt,
      ]
      {x^3/(exp(x)-1)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch90.tex
modified: 2022-06-09 22:55:27.085065
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=4,
        ymin=0,
        ymax=1.05,
        enlargelimits=false,
        height=2.75in,
        width=3.5in,
        xlabel={$\eta$},
        ylabel={$B_{S}(\eta)$}
      ]
      \addplot+[smooth,no marks,trace01,line width=1.5pt] table[x=x,
          y=B05]{\filebase Brillouin.dat};
      \addplot+[smooth,no marks,trace02,line width=1.5pt] table[x=x,
          y=B1]{\filebase Brillouin.dat};
      \addplot+[smooth,no marks,trace03,line width=1.5pt] table[x=x,
          y=B15]{\filebase Brillouin.dat};
      \addplot+[smooth,no marks,trace04,line width=1.5pt] table[x=x,
          y=B25]{\filebase Brillouin.dat};
      \addplot+[smooth,no marks,trace05,line width=1.5pt] table[x=x,
          y=B35]{\filebase Brillouin.dat};
      %      \addplot[trace01, domain=0.02:4, samples=101, line width=2pt]
      %      {2*(1/tanh(x)-0.5/tanh(x/2))};
      % \addplot[trace02, domain=0.02:4, samples=101, line width=2pt]
      % {1*(1.5/tanh(1.5*x)-0.5/tanh(x/2))};
      % \addplot[trace03, domain=0.02:4, samples=101, line width=2pt]
      % {2/3*(2/tanh(2*x)-0.5/tanh(x/2))};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch05.tex
modified: 2022-06-09 22:42:40.968708
domain: Book
source:
  \begin{tikzpicture}
    \begin{axis}[
        ymin=0,
        ymax=1,
        enlargelimits=false,
        height=1.5in,
        ylabel={$\probab$},
        ytick={0,1},
        xtick={0,0.5,1,1.5,2},
        xticklabel=\empty,
      ]
      \addplot[
        trace01,
        domain=0.001:2,
        samples=201,
        line width=2pt,
      ]
      {1 / (1 + exp(-1/x))};
      \addplot[
        trace02,
        domain=0.001:2,
        samples=201,
        line width=2pt,
      ]
      {1 / (1 + exp(1/x))};
    \end{axis}

    \node[color=trace01] at (4.5,1.75) {$\probab(0)$};
    \node[color=trace02] at (4.5,0.45) {$\probab(\epsilon)$};
    \node at (5.5,0.3){(a)};

    \begin{scope}[shift={(0,-2.75)}]
      \begin{axis}[
          ymin=0,
          ymax=0.5,
          enlargelimits=false,
          height=1.5in,
          ylabel={Energy},
          minor tick num=0,
          ytick={0},
          xtick={0,0.5,1,1.5,2},
          xticklabel=\empty,
          extra y ticks={0.5},
          extra y tick labels={$\frac{\epsilon}{2}$},
        ]
        \addplot[
          trace03,
          domain=0.001:2,
          samples=201,
          line width=2pt,
        ]
        {1 / (1 + exp(1/x))};
      \end{axis}

      \node at (5.5,0.3) {(b)};
    \end{scope}

    \begin{scope}[shift={(0,-5.5)}]
      \begin{axis}[
          ymin=0,
          ymax=0.5,
          enlargelimits=false,
          height=1.5in,
          ylabel={$C$},
          xlabel={$\kT/\epsilon$},
          minor tick num=0,
          ytick={0},
          xtick={0,0.5,1,1.5,2},
          extra y ticks={0.5},
          extra y tick labels={$\frac{\kb}{2}$},
        ]
        \addplot[
          trace04,
          domain=0.001:2,
          samples=201,
          line width=2pt,
        ]
        {1 / (2*x * cosh(0.5/x))^2};
      \end{axis}

      \node at (5.5,1.85) {(c)};
    \end{scope}


  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch16.tex
modified: 2022-06-09 22:49:15.076326
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \def\temp{0.85}
    \begin{axis}[
        %no markers,
        xmin=0,
        xmax=1,
        ymin=-1,
        ymax=-0.5,
        enlargelimits=false,
        width=2.5in,
        height=2.5in,
        xlabel={$\redp$},
        ylabel={$g$},
        %ytick={0,1},
        %xtick={0,0.5,1,1.5,2},
        %xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
      ]
      % \addplot[
      % trace01,
      % domain=0.5:4,
      % samples=51,
      % line width=2pt,
      % ]
      % ( 2.6667 * \temp / (x-0.3333) - 3/x^2, -2.25/x - \temp * ln( x - 0.3333)
      % + \temp * x /(x - 0.3333) );
      \addplot+[mark indices={1,6,19,38,61,77,88}] table[x=p,y=g] {\filebase gibbs2.dat};
      %      \node[pin=0:0.1] at (0.5,-0.64) {2,6};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch16.tex
modified: 2022-06-09 22:49:15.076326
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin = 0,
        %      xmax = 6,
        ymin = 0,
        ymax = 0.9,
        enlargelimits=false,
        width=3in,
        height=2.5in,
        xlabel={$\redv$},
        ylabel={$\redp$}
      ]
      \addplot+[mark indices={1,6,19,38,61,77,88}] table[x=v,y=p] {\filebase gibbs2.dat}; %1,6,19,39,62,78,89
      %      \addplot table[x=v,y=p] {gibbs.dat};
      \draw[dashed] (0.5525,0.5046) -- (3.126,0.5046);
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch16.tex
modified: 2022-06-09 22:49:15.076326
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \def\temp{0.85}
    \begin{axis}[
        no markers,
        xmin=0,
        xmax=6,
        ymin=0,
        ymax=1.3,
        enlargelimits=false,
        width=3.75in,
        height=3in,
        xlabel={$\redv$},
        ylabel={$\redp$},
      ]
      \addplot+[dashed,color=black] table[x=vliq,y=p] {\filebase gibbs3.dat};
      \addplot+[dashed,color=black] table[x=vvap,y=p] {\filebase gibbs3.dat};
      \addplot+[color=DarkGreen!80!gray,line width=1.5] table[x=v,y=p075] {\filebase gibbs4.dat};
      \addplot+[color=DarkGreen!70!gray,line width=1.5] table[x=v,y=p080] {\filebase gibbs4.dat};
      \addplot+[solid,color=DarkGreen!60!gray,line width=1.5] table[x=v,y=p085] {\filebase gibbs4.dat};
      \addplot+[solid,color=DarkGreen!50!gray,line width=1.5] table[x=v,y=p090] {\filebase gibbs4.dat};
      \addplot+[solid,color=DarkGreen!40!gray,line width=1.5] table[x=v,y=p095] {\filebase gibbs4.dat};
      \addplot+[solid,color=DarkGreen!30!gray,line width=1.5] table[x=v,y=p100] {\filebase gibbs4.dat};
      \addplot+[solid,color=DarkGreen!20!gray,line width=1.5] table[x=v,y=p105] {\filebase gibbs4.dat};
      \addplot+[solid,color=DarkGreen!10!gray,line width=1.5] table[x=v,y=p110] {\filebase gibbs4.dat};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch01.tex
modified: 2022-06-10 19:06:41.264128
domain: Book
source:
  \begin{tikzpicture}
    \begin{axis}[
        ymin=0, ymax=3, enlargelimits=false,
        xlabel={$x$}, ylabel={$\ln x$},
        width=3in, height=2in,
      ]
      \def\x{0} \def\y{0}
      \pgfplotsforeachungrouped \x/\y in {1/0.0000, 2/0.6931, 3/1.0986,
          4/1.3863,
          5/1.6094,
          6/1.7918,
          7/1.9459,
          8/2.0794,
          9/2.1972,
          10/2.3026,
          11/2.3979,
          12/2.4849,
          13/2.5649,
          14/2.6391,
          15/2.7081,
          16/2.7726,
          17/2.8332,
          18/2.8904,
          19/2.9444,
          20/2.996} {
          \edef\temp{\noexpand\filldraw[SlateBlue, fill=SlateBlue!33!white] (axis cs:\x,0) rectangle (axis cs:\x+1,\y);}
          \temp
          % \filldraw[SlateBlue, fill
          =SlateBlue!33!white] (axis cs:\x,0) rectangle (axis cs:\x+1,\y);
        };
      \addplot[DarkBlue, domain=1:20, samples=25,line width=1.5pt]
      {ln(x)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch01.tex
modified: 2022-06-10 19:06:41.264128
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[black,fill=yellow,opacity=0.125] (0,0) rectangle (1.5,4) (0,0) rectangle
    (4,1.5);
    \filldraw[black,fill=blue,opacity=0.125] (0,1.5) rectangle (4,4) (1.5,0) rectangle (4,4);
    \node at (0.75,2.75) {$pq$};
    \node at (2.75, 0.75) {$qp$};
    \node at (2.75, 2.75) {$q^2$};
    \node at (0.75, 0.75) {$p^2$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch01.tex
modified: 2022-06-10 19:06:41.264128
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=1, ymin=0, ymax=1, enlargelimits=false,
        width=2.5in, height=2in,
        xlabel={$r$}, ylabel={Probability}, ytick={0.45, 0.9}, xtick=\empty,
        xticklabel=\empty,
        yticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1},
        % xticklabel=\empty, xticklabels{0,,$a$,,a$},
        % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[trace01, domain=0:1, samples=100, line width=1pt,]
      {0.9 * exp(-0.5*((x-0.5)/0.1)^2)};
      \draw[<->] (0.5-0.1177,0.45) coordinate(L) -- node[anchor=north]{FWHM}
      (0.5+0.1177,0.45) coordinate (R);
      \draw[gray,dashed] (L) -- ++(-90:0.45) (R) -- ++(-90:0.45);
    \end{axis}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: temp.tex
modified: 2022-06-08 20:38:50.964189
domain: p117
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      pathstyle/.style={line width=0.75pt,color=gray},
      dim/.style={color=green!40!black,<->},
      accel/.style={->,line width=3pt,color=gray},
      vel/.style={->,line width=2pt,color=red!50!black},
      dotted/.style={line width=0.75pt, color=gray, dashed}
    ]


    \shade[ball color=blue!30!white] (0,0) circle(0.1);
    \node at (-45:0.4){2};
    \begin{scope}[rotate=30]
      \filldraw[fill=DarkGreen!20!white,line width=0.5] (0,0) -- (4:4.5) -- (-4:4.5) --
      cycle;
      \filldraw[fill=DarkGreen!30!white, line width=0.5] (4.5,0)
      ellipse[x radius=0.1,y radius = 0.313];
      \draw[dashed] (0,0) -- (5,0);
      \node at (4.95,-0.4) {$d\Omega$};
      \draw[vel] (0:5) -- ++(0:1) node[anchor=west] {$\vb{V}$};
    \end{scope}
    \shade[left color=blue!20!white, right color=white] (-8,-2) rectangle (-3,2);
    \draw[dotted] (-8,0) -- (3,0);
    \foreach \y in {-1.75,-1.25,...,1.75} {
        \draw[vel] (-8,\y) -- ++(0:1);
      }
    \draw[line width=2] (-6.5,0.5) .. controls (-0.134,0.5) and (-0.134,0.5)
    .. (4,2.85);
    \shade[ball color=blue!30!white] (-5,0.5) circle(0.1);
    \node at (-5,0.85){1};
    \draw (1.5,0) arc (0:30:1.5);
    \node at (15:1.75) {$\theta$};
    %(-1.5,0.75) and (60:1.5) .. (60:6);

    % \shade[ball color=red!30!white] (-5,0.5) circle(0.25);
    % \shade[ball color=red!15!white] (150:1) circle(0.25);
    % \draw[pathstyle] (-5,0) -- (2,0);
    % \draw[line width=1.5] (0,0) -- (150:1);
    % \node at (-0.2,0.42) {$R + a$};
    % \draw[pathstyle] (180:0.3) arc(180:150:0.3);
    % \node at (165:0.5) {$\psi$};
    % \draw[dotted] (-5,0.5) -- +(0:4.15);
    % \draw[dotted] (150:1) -- +(120:1.5);
    % \draw[vel] (-4.75,0.5) -- +(0:0.6);
    % \draw[vel] (150:1)  +(120:1) -- +(120:1.5);
    % \draw[color=blue!70!black] (0:1.25) arc (0:120:1.825);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: Kinetics.tex
modified: 2022-06-08 21:11:16.711782
domain: p117
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      pathstyle/.style={line width=0.75pt,color=gray},
      dim/.style={color=green!40!black,<->},
      accel/.style={->,line width=3pt,color=gray},
      vel/.style={->,line width=2pt,color=red!50!black},
      dotted/.style={line width=0.75pt, color=gray, dashed}
    ]

    % particle at origin
    \shade[ball color=blue!30!white] (0,0) circle(0.1);
    \node at (-45:0.4){2};
    % outgoing scattering cone
    \begin{scope}[rotate=30]
      \filldraw[fill=DarkGreen!20!white,line width=0.5] (0,0) -- (4:4.5) -- (-4:4.5) --
      cycle;
      \filldraw[fill=DarkGreen!30!white, line width=0.5] (4.5,0)
      ellipse[x radius=0.1,y radius = 0.313];
      \draw[dashed] (0,0) -- (5,0);
      \node[vel] at (4.95,-0.4) {$d\Omega$};
      \draw[vel] (0:5) -- ++(0:1) node[anchor=west] {$\vb{V}_{\rm out}$};
    \end{scope}
    % input flux
    \shade[left color=blue!20!white, right color=white] (-8,-2) rectangle (-3,2);
    \draw[dotted] (-8,0) -- (3,0);
    \foreach \y in {-1.75,-1.25,...,1.75} {
        \draw[vel] (-8,\y) -- ++(0:1);
      }
    \node[vel] at (-6.5,1.75){$\vb{J}_{1}$};
    \node[vel] at (-7.5,2.25){$\vb{V}$};
    \draw[line width=1.75,->] (-4.5,0.5) -- +(0:0.5);
    \draw[line width=2] (-6.5,0.5) .. controls (-0.134,0.5) and (-0.134,0.5)
    .. (4,2.85);

    \shade[ball color=blue!30!white] (-5,0.5) circle(0.1);
    \node at (-5,0.85){1};
    \draw[<-,color=DarkSlateGray] (-5.75,0.5) -- +(90:0.5) node[anchor=east]{$b$};
    \draw[<-,color=DarkSlateGray] (-5.75,0) -- +(-90:0.5);
    \draw (1.5,0) arc (0:30:1.5);
    \node at (15:1.75) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: Kinetics.tex
modified: 2022-06-08 21:11:16.711782
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[rotate=90]
      \draw[line width=2pt] (0,0.5) -- (0,2) (0,-0.5) -- (0,-2) ;
      % draw the slant cylinder
      \filldraw[color=gray,fill=yellow!60!white,dashed] (0,0.5) -- ++(150:2.5) -- ++(-90:1)
      -- ++(-30:2.5) -- cycle;
      \draw[dashed] (-2,0) -- (2,0);
      \draw[gray] (150:2.5) -- ++(-30:5);
      \draw (0:1) arc (0:-30:1);
      \node at (-15:1.25){$\theta$};
      \draw[<->,DarkGreen] (0,0.75) -- node[anchor=south,rotate=60]{$v\dd{t}$}
      ++(150:2.5);
      \draw[<-,DarkGreen] (0,0.2) -- ++(30:0.75) node[anchor=south]{$\dd{A}$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: Kinetics.tex
modified: 2022-06-13 04:16:43.821163
domain: p117
source:
  \begin{tikzpicture}[
      scale=1,
      >=Stealth,
      pathstyle/.style={line width=0.75pt,color=gray},
      dim/.style={color=green!40!black,<->},
      accel/.style={->,line width=3pt,color=gray},
      vel/.style={->,line width=2pt,color=red!50!black},
      dotted/.style={line width=0.75pt, color=gray, dashed}
    ]

    % particle at origin
    \shade[ball color=blue!30!white] (0,0) circle(0.1);
    \node at (-45:0.4){2};
    % outgoing scattering cone
    \begin{scope}[rotate=30]
      \filldraw[fill=DarkGreen!20!white,line width=0.5] (0,0) -- (4:4.5) -- (-4:4.5) --
      cycle;
      \filldraw[fill=DarkGreen!30!white, line width=0.5] (4.5,0)
      ellipse[x radius=0.1,y radius = 0.313];
      \draw[dashed] (0,0) -- (5,0);
      \node[vel] at (4.95,-0.4) {$d\Omega$};
      \draw[vel] (0:5) -- ++(0:1) node[anchor=west] {$\vb{V}_{\rm out}$};
    \end{scope}
    % input flux
    \shade[left color=blue!20!white, right color=white] (-8,-2) rectangle (-3,2);
    \draw[dotted] (-8,0) -- (3,0);
    \foreach \y in {-1.75,-1.25,...,1.75} {
        \draw[vel] (-8,\y) -- ++(0:1);
      }
    \node[vel] at (-6.5,1.75){$\vb{J}_{1}$};
    \node[vel] at (-7.5,2.25){$\vb{V}$};
    \draw[line width=1.75,->] (-4.5,0.5) -- +(0:0.5);
    \draw[line width=2] (-6.5,0.5) .. controls (-0.134,0.5) and (-0.134,0.5)
    .. (4,2.85);

    \shade[ball color=blue!30!white] (-5,0.5) circle(0.1);
    \node at (-5,0.85){1};
    \draw[<-,color=DarkSlateGray] (-5.75,0.5) -- +(90:0.5) node[anchor=east]{$b$};
    \draw[<-,color=DarkSlateGray] (-5.75,0) -- +(-90:0.5);
    \draw (1.5,0) arc (0:30:1.5);
    \node at (15:1.75) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/hw
filename: hw09-sol.tex
modified: 2015-09-03 13:41:36
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray] (0,0) circle[radius = 0.4] node{$M_0$};
    \filldraw[fill=gray] (2,0) circle[radius = 0.4] node{$M_{0}$};
    \draw[vel] (1.5,0) -- ++(180:0.75) node[anchor=south]{$v_{0}$};
    \node at (1,1){Before};
    \draw[dashed] (3.5,1) -- (3.5,-0.5);
    \begin{scope}[shift={(6,0)}]
      \filldraw[fill=gray] (0,0) circle[radius = 0.4] node{$M$};
      \draw[vel] (-0.5,0) -- ++(180:0.75) node[anchor=south]{$v$};
      \draw[photon,->] (1,0) -- ++(0:1.25) node[anchor=south]{$E$};
      \node at (1,1){After};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/hw
filename: hw10-sol.tex
modified: 2015-10-13 21:42:18
domain: p23
source:
  \begin{tikzpicture}[scale=.6]
    \draw[vel] (0,0) --node[anchor=north]{$v$} (3,0);
    \draw[vel] (0,0) -- node[anchor=south east]{$c$} (3,4);
    \draw[dashed] (3,0) -- (3,4);
    \draw (1,0) arc(0:53:1);
    \node at (26.6:1.4) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/hw
filename: hw10-sol.tex
modified: 2015-10-13 21:42:18
domain: p23
source:
  \begin{tikzpicture}[scale=0.6]
    \draw (0,0) -- (3,0) -- (3.5,0.5) -- (3,1) -- (0,1) -- cycle;
    \node at (0.5,0.5){$M_{0}$};
    \node at (1.5,-1){$E = M_{0}c^{2}$};
    \node at (1.5,-2){$p_{x} = 0$};
    \node at (1.5,2){before};
    \draw[dashed] (4,-1) -- (4,2.5);
    \begin{scope}[shift={(8,0)}]
      \draw (0,0) -- (2,0) -- (2.5,0.5) -- (2,1) -- (0,1) -- cycle;
      \draw[vel] (2.75,0.5) -- ++(0:1) node[anchor=south]{$v$};
      \node at (0.5,0.5){$M$};
      \node at (1.5,-1){$E = \gamma M c^{2}$};
      \node at (1.5,-2){$p_{x} = \gamma M v$};
      \draw[photon,->] (-2,0.5) -- ++(180:1.5) node[anchor=south]{$p$};
      \node at (-2.5,-1) {$E = pc$};
      \node at (-2.5,-2) {$p_{x} = -p$};
      \node at (0.5,2){after};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/hw
filename: hw11-sol.tex
modified: 2015-08-28 16:00:30
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \shade[ball color=blue] (0,0) circle(0.4);
    \node at (0,0.75){$M$};
    \draw[vel] (0.5,0) -- node[anchor=south]{$\frac{3}{5} c$} ++(0:1.);
    \draw[dashed] (1.75,0) -- (2.25,0);
    \begin{scope}[shift={(2.4,0)}]
      \draw[dashed] (0,0) -- (0:2) (0,0) -- (30:1.5) (0,0) -- (-30:1.5);
      \draw (30:0.6) arc(30:-30:0.6);
      \draw[vel](30:2.2) -- +(30:1);
      \shade[ball color=green] (30:2) circle(0.3);
      \node at (45:2.3){$m$};
      \draw[vel](-30:2.2) -- +(-30:1);
      \shade[ball color=green] (-30:2) circle(0.3);
      \node at (-45:2.3){$m$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/hw
filename: hw03-sol.tex
modified: 2015-08-31 20:13:03
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \def\rocketlength{0.5}
    \def\earth{0.3}
    \begin{scope} % this is the Sun Frame
      \node at (2,2){\large Sun Frame};
      % Earth
      \filldraw[fill=blue!30!white,draw=brown,line width=1]
      (0,0.5) circle[radius=\earth] node{E};
      % draw the rocket leaving
      \rocket[\frac{4}{5}c]{(0,0)};
      \node at (-1.5,0){$t = 0$};
    \end{scope}

    \begin{scope}[shift={(0,-1.5)}] % this is the Sun Frame
      % Earth
      \shade[shading=radial] (0,0) circle[radius=0.6];
      \rocket[ ]{(1.5,0)};
      \draw[photon,->] (0,0) -- ++(0:0.75);
      \node at (-1.5,0){$t = t_{\rm E}$};
    \end{scope}

    \begin{scope}[shift={(0,-3)}] % this is the Sun Frame
      % Earth
      \shade[shading=radial] (0,0) circle[radius=0.3,opacity=0.5];
      \rocket[ ]{(4.5,0)};
      \node at (-1.5,0){$t = t_{\rm A}$};
      \draw[photon,->] (4,0) -- ++(0:0.75);
    \end{scope}

    \draw[dashed,color=gray] (6,2) -- ++(0,-5);

    % Now handle the ship frame
    \begin{scope}[shift={(7,0)}]
      \node at (2,2){\large Ship Frame};
      % Earth
      \filldraw[fill=blue!30!white,draw=brown,line width=1]
      (5,0.5) circle[radius=\earth] node{E};
      \draw[color=DarkGreen,line width=1.5,->] (4.5,0.5) -- ++(180:0.4)
      node[anchor=south] {$\frac{4}{5} c$};
      % draw the rocket leaving
      \rocket{(5,0)};
      \node at (6,0){$t' = 0$};

      \begin{scope}[shift={(0,-1.5)}] % this is the Sun Frame
        % Earth
        \shade[shading=radial] (2.5,0) circle[radius=0.6];
        \rocket{(5,0)};
        \draw[photon,->] (2.5,0) -- ++(0:0.75);
        \draw[color=DarkGreen,line width=1.5,->] (2.,0) -- ++(180:0.4);
        \node at (6,0){$t'_{\rm E}$};
      \end{scope}

      \begin{scope}[shift={(0,-3)}] % final event
        % Earth
        \shade[shading=radial] (0,0) circle[radius=0.3,opacity=0.5];
        \draw[color=DarkGreen,line width=1.5,->] (-0.3,0) -- ++(180:0.4);
        \rocket{(5,0)};
        \node at (6,0){$t'_{\rm A}$};
        \draw[photon,->] (4.5,0) -- ++(0:0.75);
      \end{scope}
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/rec
filename: rec04-prof.tex
modified: 2015-11-05 02:58:18
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \draw[<->] (-3,1) --node[fill=white]{$d = D\srF$} (3,1);
    \draw[color=gray] (-3,0) circle[radius=0.5] (3,0) circle[radius=0.5];
    \draw[vel] (-2.4,0) -- ++(0:0.5) node[anchor=south]{$V$};
    \draw[vel] (3.6,0) -- ++(0:0.5) node[anchor=south]{$V$};
    \draw[color=red,line width=2pt] (0,0) circle[radius=0.05];
    \foreach \x in {0,15,...,345} {
        \draw[color=red!50!white] (\x:0.1) -- ++(\x:0.1);
      }
    \node at (-4.5,0){$t=0$};

    \begin{scope}[shift={(0,-2)}]
      \node at (-4.5,0){$t=t_{C}$};
      \draw[color=gray] (-2,0) circle[radius=0.5] (4,0) circle[radius=0.5];
      \draw[vel] (-1.4,0) -- ++(0:0.5);
      \draw[vel] (4.6,0) -- ++(0:0.5);
      \draw[color=red,line width=2] (-2,0) arc(180:160:2) (-2,0) arc(180:200:2)
      (2,0) arc(0:20:2) (2,0) arc(0:-20:2);
      \draw[line width=1.5] (-2,0) -- ++(90:0.7);
    \end{scope}

    \begin{scope}[shift={(0,-4)}]
      \node at (-4.5,0){$t=t_{L}$};
      \draw[color=gray] (-0.5,0) circle[radius=0.5] (5.5,0) circle[radius=0.5];
      \draw[color=red,line width=2] %(-5.5,0) arc(180:160:5.5) (-5.5,0) arc(180:200:5.5)
      (5.5,0) arc(0:9:5.5) (5.5,0) arc(0:-9:5.5);
      \draw[line width=1.5] (5.5,0) -- ++(90:0.7);
      \draw[line width=1.5] (-0.5,0) -- ++(30:0.7);
      \draw[vel] (0.1,0) -- ++(0:0.5);
      \draw[vel] (6.1,0) -- ++(0:0.5);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/rec
filename: vectors.tex
modified: 2015-09-22 21:21:07
domain: p23
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[force,gray] (0,0) --node[anchor=north]{$a$} ++(2.5,2);
    \draw[force,red] (0.25,1) --node[anchor=west]{$b$} ++(-1, 1.5);
    \begin{scope}[shift={(3,-2)}]
      \draw[force,gray] (0,0) --node[anchor=north]{$a$} ++(2.5,2);
      \draw[force,red] (2.5,2) --node[anchor=west]{$b$} ++(-1, 1.5);
      \draw[force,line width=1pt] (0,0) --node[anchor=east]{$c$} (1.5,3.5);
      \node at (-2,1) {$\vector{c} = \vector{a} + \vector{b}$};
    \end{scope}

    \begin{scope}[shift={(0,-9)}]
      \draw[->] (0,0) -- ++(1,0) node[anchor=north]{$x$};
      \draw[->] (0,0) -- ++(0,1) node[anchor=east]{$y$};
      \draw[force] (2,0) --node[anchor=north]{$a_{x}$} ++(3,0);
      \draw[force] (5,0) --node[anchor=west]{$a_{y}$} ++(0,4);
      \draw[force] (2,0) --node[anchor=south east]{$a$} ++(3,4);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/rec
filename: vectors.tex
modified: 2015-09-22 21:21:07
domain: p23
source:
  \begin{tikzpicture}[scale=1]

    \draw[->] (0,0) -- ++(0:8) node[anchor=north]{$x$};
    \draw[->] (0,0) -- ++(90:8) node[anchor=east]{$y$};


    \draw[->] (0,0) -- ++(15:8) node[anchor=north]{$x'$};
    \draw[->] (0,0) -- ++(105:8) node[anchor=east]{$y'$};

    \draw (2,0) arc(0:15:2);
    \node at (7.5:2.2){$\theta$};
    \draw (0,2) arc(90:105:2);
    \node at (97.5:2.25){$\theta$};

    % Draw the component vectors in the xy coordinates
    \coordinate (y) at (0,6.9282);

    \draw[->,line width=4pt,opacity=0.5] (0,0) -- node[anchor=north]{$a_{x}$} (4,0);
    \draw[->,line width=4pt,opacity=0.5,DarkRed] (0,0) -- node[anchor=east]{$a_{y}$} (y);

    \coordinate (A) at (60:8);
    \coordinate (B) at (4,0);
    \coordinate (C) at (3.73205,1); % this is the point on the x' axis for the base

    \draw[->,line width=4pt,color=DarkBlue] (0,0) --node[anchor=south east]{$a$}
    (A);
    \draw[annot] (3.7,6) -- (\rmarg,6) node[anchor=west]{Vector $\vector{a}$ has
      components};
    \draw[annot] (0, 5.5) -- (\rmarg,5.5) node[anchor=west]{$\vector{a}_{y}$ and
      $\vector{a}_{x}$};
    \draw[annot] (3,0.2) -- (\rmarg + 1.2,5.3);
    \def\xht{2.5}
    \node[anchor=west,text width=2in,annot] at (\rmarg, \xht) {Resolve $\vector{a}_{x}$ into components
      along the $x'$ and $y'$ axes};
    \draw[annot] (3,1) -- (3,\xht) -- (\rmarg,\xht);
    \draw[annot] (4.15,0.3) -- (8,0.3) -- (8,\xht);

    \def\xht{4}
    \node[anchor=west,text width=2in,annot] at (\rmarg, \xht) {Resolve $\vector{a}_{y}$ into components
      along the $x'$ and $y'$ axes};
    \draw[annot] (-1.25,6.5) -- (1,\xht) -- (\rmarg,\xht);
    \draw[annot] (-1,\xht) -- (1,\xht);


    \draw[dashed] (A) -- (B);
    \draw[->, line width=2pt] (C) -- (B);
    \draw[<-] (4,0.6) -- ++(7.5:1) node[anchor=west]{$-a_{x} \sin\theta$};
    \draw[->, line width=2pt] (0,0) --node[rotate=15,anchor=south]{$a_{x}
        \cos\theta$} (C);

    % Now show the components of a_y
    \coordinate (D) at (-1.73205, 6.4641);

    \draw[->,DarkRed,line width=2pt] (0,0) --node[rotate=105,anchor=south]{$a_y \cos\theta$} (D);
    \draw[->,DarkRed,line width=2pt] (D) --node[rotate=15,anchor=south]{$a_{y}
        \sin\theta$} (y);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/rec
filename: vectors.tex
modified: 2015-09-22 21:21:07
domain: p23
source:
  \begin{tikzpicture}[scale=1]

    \draw[->] (0,0) -- ++(0:8) node[anchor=north]{$x$};
    \draw[->] (0,0) -- ++(90:8) node[anchor=east]{$y$};


    \draw[->] (0,0) -- ++(15:8) node[anchor=north]{$x'$};
    \draw[->] (0,0) -- ++(105:8) node[anchor=east]{$y'$};

    \draw (2,0) arc(0:15:2);
    \node at (7.5:2.2){$\theta$};

    % Draw the component vectors in the xy coordinates
    \coordinate (y) at (0,6.9282);

    \draw[->,line width=3pt,opacity=0.5] (0,0) -- node[anchor=north]{$a_{x}$} (4,0);
    \draw[->,line width=3pt,opacity=0.5,DarkRed] (0,0) -- node[anchor=east]{$a_{y}$} (y);

    \coordinate (A) at (60:8);
    \coordinate (B) at (4,0);
    \coordinate (C) at (3.73205,1); % this is the point on the x' axis for the base

    \draw[->,line width=4pt,color=DarkBlue] (0,0) -- %node[anchor=south east]{$a$}
    (A);

    \begin{scope}[rotate=15]
      \draw[annot,line width=1.5pt,dotted] (5.7,5) -- (0,5);
      \draw[annot,line width=1.5pt,dotted] (5.8,6.3) -- (7,6.3) -- (7,-0.3) -- (4,-0.3);
    \end{scope}

    \draw[dashed] (A) -- (B);
    \draw[->, line width=2pt,dashed] (C) -- (B);
    \draw[<-] (4,0.6) -- ++(7.5:1) node[anchor=west]{$-a_{x} \sin\theta$};
    \draw[->, line width=2pt] (0,0) --node[rotate=15,anchor=south]{$a_{x}
        \cos\theta$} (C);

    % Now show the components of a_y
    \coordinate (D) at (-1.73205, 6.4641);

    \draw[->,DarkRed,line width=2pt,dashed] (0,0) --node[rotate=105,anchor=south]{$a_y \cos\theta$} (D);
    \draw[->,DarkRed,line width=2pt,dashed] (D) --node[rotate=15,anchor=south]{$a_{y}
        \sin\theta$} (y);
    \draw[annot,line width=1.5pt,dotted] (4.,1.2) -- (-1.25, 6.5);

    \begin{scope}[rotate=15]
      \draw[->,DarkRed,line width=2pt] (5.75685,0) --node[anchor=south,rotate=-75]{$a_{y}\cos\theta$} ++(90:6.69213); % 5.65685,
      % but I'll shift slightly so the black arrow
      % brings us home
      \draw[->,line width=2pt] (5.65685,6.69213) -- ++(-90:1);
      \draw[<-] (5.6,6.2) -- ++(165:1)node[anchor=east] {$-a_{x}\sin\theta$};
    \end{scope}
    \draw[->,line width=2pt,DarkRed] (C)
    --node[anchor=south,rotate=15]{$a_{y}\sin\theta$} ++(15:1.832); % cheating by
    % 0.1
    \draw[annot,line width=1.5pt,dotted] (6,7) -- (9,7);
  \end{tikzpicture}


