Ce document regroupe les codes TIKZ des figures utilisées pour le cours "Théorème du moment cinétique" situé à la page http://www.femto-physique.fr/mecanique/meca_C6.php
% !TEX encoding = UTF-8 Unicode
% J.Roussel
% MAJ : 2014-06-03
% Ce document regroupe les codes TIKZ des figures utilisées pour le cours "Théorème du moment cinétique" situé à la page http://femto-physique.fr/mecanique/meca_C6.php
%-------------------------------------------
\documentclass[11pt]{article}
\input{styles_meca}
\title{Figures TikZ du cours "THÉORÈME DU MOMENT CINÉTIQUE"}
\begin{document}
%------ TIKZ bras de levier------
\begin{center}
\begin{tikzpicture}[scale=1,x={(-0.353cm,-0.353cm)}, y={(1cm,0cm)}, z={(0cm,1cm)}]
\coordinate (O) at (0, 0, 0);
\coordinate (A) at (2,2,0);
\coordinate (M) at (4,4,0);
\coordinate (N) at (2,6,0);
\coordinate (B) at (2,2,-1);
\draw (O) -- ++(5, 0, 0) ;
\draw (O) -- +(0, 6.5, 0) ;
\draw (O) -- +(0, 0, 1) ;
\shade(O) --++(5,0,0)--++(0,6.5,0)--++(-5,0,0)--cycle;
\draw[thin] (A) node{$\bullet$} -- ++(0, 0, 2) ;
\draw[tiret] (A)--(B);
\draw (M)--(A)node[pos=0.5,above]{$d$};
\draw (B)--++(0,0,-1);
\draw[vecteur] (A)node[left=2pt]{A}--++(0,0,1) node[pos=0.5, right]{$\overrightarrow{u}$};
\draw[tiret] (N)--(M);
\draw (3.8,3.8,0)--++(-0.2,0.2,0)--++(0.2,0.2);
\draw[force] (N)node{$\bullet$}node[above=2pt]{M}--++(-1,1,0) node[right]{$\overrightarrow{f}$};
\draw[->,draw=white,double=black] (2,1.5,1.5) arc(-90:180:0.5) node[above] {\tiny+};
\end{tikzpicture}
\end{center}
%--- FIN TIKZ ---
%======================================================
% Forces concourantes
%======================================================
\begin{tikzpicture}[scale=1]
\coordinate (A) at (1, -1);
\patate[scale=2,ball color=lightgray];
\foreach \x/\y/\compteur in {0.5/0/1}{
\draw[force] (\x,\y) node{$\bullet$} --++({\x-1},{(\y+1)}) node[right=5pt]{$\overrightarrow{f_{\compteur}}$};
\draw[dashed] (\x,\y)--(A) node[right]{A};}
\foreach \x/\y/\compteur in {1.5/0/2,1/-2/3}{
\draw[force] (\x,\y) node{$\bullet$} --++({\x-1},{(\y+1)}) node[right]{$\overrightarrow{f_{\compteur}}$};
\draw[dashed] (\x,\y)--(A) node[right]{A};}
\end{tikzpicture}
%======================================================
% Notion de couple
%======================================================
\begin{tikzpicture}[scale=1]
\patate[scale=2,ball color=lightgray];
\draw[dashed] (1.5,0)--++(-2,-2);
\draw[force] (1.5,0) node{$\bullet$}node[below=3pt]{A} --++(1,1) node[right]{$\overrightarrow{f_{1}}$};
\draw[dashed] (1,-2)--++(2,2);
\draw[force] (1,-2) node{$\bullet$}node[above=3pt]{B} --++(-1,-1) node[left]{$-\overrightarrow{f_{1}}$};
\end{tikzpicture}
%======================================================
% Loi des aires.
%======================================================
\begin{tikzpicture}[scale=1.2,decoration={markings,mark=at position 5mm with {\arrow[black]{stealth};}}]
\def \parametre {1.5};%parametre
\def \alphaM {160};%angle correspondant au point M
\def \alphaP {20};%angle correspondant au périgée
\def \excentric {0.7};%excentricité
\draw[dashed,variable=\t , domain=0:201,samples=50] plot ({\parametre*cos(\t)/(1+\excentric*cos(\t-\alphaP))},{\parametre*sin(\t)/(1+\excentric*cos(\t-\alphaP))});
\shade[variable=\t ,domain=-10:50,samples=20] plot ({\parametre*cos(\t)/(1+\excentric*cos(\t-\alphaP))},{\parametre*sin(\t)/(1+\excentric*cos(\t-\alphaP))})--(0,0)--cycle;
\draw[postaction={decorate},thick,variable=\t , domain=-10:50,samples=20] plot ({\parametre*cos(\t)/(1+\excentric*cos(\t-\alphaP))},{\parametre*sin(\t)/(1+\excentric*cos(\t-\alphaP))});
\shade[variable=\t ,domain=199:202,samples=5] plot ({\parametre*cos(\t)/(1+\excentric*cos(\t-\alphaP))},{\parametre*sin(\t)/(1+\excentric*cos(\t-\alphaP))})--(0,0)--cycle;
\draw[->,thick,variable=\t , domain=199:203,samples=5] plot ({\parametre*cos(\t)/(1+\excentric*cos(\t-\alphaP))},{\parametre*sin(\t)/(1+\excentric*cos(\t-\alphaP))});
\coordinate (M) at ({\parametre*cos(\alphaM)/(1+\excentric*cos(\alphaM-\alphaP))},{\parametre*sin(\alphaM)/(1+\excentric*cos(\alphaM-\alphaP))});
\draw (0,0) node{$\bullet$} node[below]{\small O}--(M) node[above,fill=white]{M$(r,\theta)$}node[pos=0.5,fill=white]{$r$};
\draw[fill=white] (M) circle(0.1);
\draw (20:1.5) node{$\Delta t$};
\draw (200:5.5) node{$\Delta t$};
\end{tikzpicture}
%======================================================
% solide en rotation
%======================================================
\begin{tikzpicture}[scale=2]
\coordinate (M) at (0.5,-0.29);
\draw[thin] (0,0)--++(0,-2);
% \foreach \i in {0,2,...,30}
% \fill [black, fill opacity = 1/60] (0,-1.1) ellipse [x radius = 2+\i/40, y radius = 2/3+\i/60];
\fill [white] ellipse [x radius = 2, y radius = 2/3];
\path [left color = black!50, right color = black!50,middle color = black!25]
(-2+.05,-1.1) arc (180:360:2-.05 and 2/3-.05*2/3) -- cycle;
\path [top color = black!25, bottom color = white]
(0,.05*2/3) ellipse [x radius = 2-.05, y radius = 2/3-.05*2/3];
\path [left color = black!25, right color = black!25,middle color = white]
(-2,0) -- (-2,-1) arc (180:360:2 and 2/3) -- (2,0) arc (360:180:2 and 2/3);
\foreach \r in {225,315}
\foreach \i [evaluate = {\s=30}] in {0,2,...,30}
\fill [black, fill opacity = 1/50]
(0,0) -- (\r+\s-\i:2 and 2/3) -- ++(0,-1) arc (\r+\s-\i:\r-\s+\i:2 and 2/3) -- ++(0,1) -- cycle;
\foreach \r in {45,135}
\foreach \i [evaluate = {\s=30}] in {0,2,...,30}
\fill [black, fill opacity = 1/50]
(0,0) -- (\r+\s-\i:2 and 2/3) arc (\r+\s-\i:\r-\s+\i:2 and 2/3) -- cycle;
\draw[thin] (0,0) node{$\bullet$} --++(0,2)node[above]{$(\Delta)$};
\draw[|->,thick] (0,1)--++(0,0.5) node[pos=0.5, right]{$\overrightarrow{u}$};
\draw[->,draw=white,double=black] (-0.2,1.75) ..controls +(-1,-0.25) and +(1,-0.25).. (0.2,1.75)node[above] {\tiny+};
\draw[dashed] ellipse(1 and 1/3);
\draw (M)node[below]{M$_{i}$}--(0,0)node[left]{H$_{i}$};
\draw[vecteur] (M)--++({sqrt(3)},{1/3}) node[right]{$\overrightarrow{v_{i}}$};
\end{tikzpicture}
% ==============================================
% échelle contre un mur
% ==============================================
\begin{tikzpicture}[scale=1]
\draw[vecteur] (60:4)++(1,0)--++(0,-1) node[pos=0.5,right]{$\overrightarrow{g}$};
\draw[line width=2mm,line cap=round] (0,0)--(60:4);
\draw[shift={(60:4)}] (3pt,-1) arc (-90:-120:1);
\draw[shift={(60:4)}] (-105:1.3) node{$\alpha$};
\fill [shift={(3pt,-3pt)},pattern=north east lines,] (-0.5,0)--(2,0)--++(0,4)--++(0.3,0)--++(0,-4.3)--++(-2.8,0)-- cycle;
\draw [shift={(3pt,-3pt)}] (-0.5,0)--(2,0)--++(0,4);
\draw[dashed,shift={(3pt,0)}](60:2)--++(0,2);
\draw[shift={(3pt,-3pt)}](1,0)node{|}node[below,fill=white]{\small D};
\draw[dashed,shift={(3pt,0)}](60:4)--++(-2,0);
\draw[dashed](60:4)++(-1,0)++(3pt,0)node{•}node[above left]{C}--(0,0);
\draw (60:4)++(-1,0)++(3pt,-1) arc(-90:-106.1:1);
\draw[shift={(60:4)}](-1,0)++(-95:1.2) node{$\theta$};
\draw[force,shift={(0,-3pt)}](0,0)node{•}node[below,color=black,fill=white,]{A}--++(0.5,+1.7) node[above=2pt]{$\overrightarrow{F_{12}}$};
\draw[force,shift={(0,-3pt)}](0,0)--++(0,+1.7) node[left]{$\overrightarrow{F_1}$};
\draw[force,shift={(0,-3pt)}](0,0)--++(0.5,0) node[above]{$\overrightarrow{F_2}$};
\draw[force,shift={(3pt,0)}](60:4)node{•}node[color=black,fill=white,right]{B}--++(-0.5,0) node[above=2pt]{$\overrightarrow{F_3}$};
\draw[force,shift={(3pt,3pt)}](60:2)node{•}--++(0,-1.7) node[right]{$\overrightarrow{P}$};
\end{tikzpicture}
%======================================================
% pendule pesant
%======================================================
\begin{tikzpicture}[scale=1.3]
\coordinate (O) at (1.2,1);
\coordinate (A) at (1.7, -0.5);
\draw[vecteur] (-1,0) --++(0,-1)node[pos=0.5,right]{$\overrightarrow{g}$};
\patate[scale=2,ball color=lightgray,rotate=40];
\draw[dashed] (O) node{$\odot$} node[left]{$(\Delta)\;$}--(A)--++(0.5,-1.5);
\draw[vecteur] (1.2,0.8) arc(-90:120:0.2) node[above]{\tiny+};
\draw (A)node[right]{\,G};
\draw[force] (A) node{$\bullet$} --++(0,-1.5) node[below]{$\overrightarrow{P}$};
\draw[dashed] (O)--++(0,-3.5);
\draw[->] (1.2,0) arc(-90:-72:1);
\draw (O)++(-81:1.2) node{$\theta$};
\end{tikzpicture}
\end{document}