Moment of inertia

Some basic shapes that rotate to compute the moment of inertia: single mass point, two connected masses, a ring, a solid disk and a hollow cylinder.
Alternative diagrams are in this post. For more related figures, please see the “angular momentum” or “torque” tags.

dynamics_moment_of_inertia-001.pngdynamics_moment_of_inertia-002.pngdynamics_moment_of_inertia-003.pngdynamics_moment_of_inertia-004.pngdynamics_moment_of_inertia-005.pngdynamics_moment_of_inertia-006.pngdynamics_moment_of_inertia-007.pngdynamics_moment_of_inertia-008.pngdynamics_moment_of_inertia-009.png

Edit and compile if you like:

% Author: Izaak Neutelings (October 2020)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{physics}
\usepackage{tikz}
\usepackage[outline]{contour} % glow around text
\usetikzlibrary{calc}
\usetikzlibrary{angles,quotes} % for pic
\usetikzlibrary{arrows.meta}
\usetikzlibrary{patterns}
\tikzset{>=latex} % for LaTeX arrow head
\contourlength{1.35pt}
\colorlet{xcol}{blue!70!black}
\colorlet{vcol}{green!60!black}
\colorlet{myred}{red!65!black}
\colorlet{mydarkred}{red!40!black}
\colorlet{mypurple}{blue!60!red!80}
\colorlet{mydarkgreen}{green!20!black}
\colorlet{acol}{red!50!blue!80!black!80}
\tikzstyle{rvec}=[->,xcol,very thick,line cap=round]
\tikzstyle{vvec}=[->,vcol,very thick,line cap=round]
\tikzstyle{myarr}=[{Latex[length=3,width=3]}-,xcol]
\tikzstyle{myarr2}=[{Latex[length=2,width=2.5]}-{Latex[length=2,width=2.5]}]
\tikzstyle{force}=[->,myred,very thick,line cap=round]
\tikzstyle{Fproj}=[force,myred!40]
\tikzstyle{CM}=[mydarkred,fill=red!80!black!80]
\tikzstyle{mass}=[line width=0.6,draw=red!30!black, %rounded corners=1,
top color=mydarkred!30,bottom color=mydarkred!10,shading angle=30]
\tikzstyle{dark mass}=[line width=0.3,red!30!black, %rounded corners=1,
top color=mydarkred!40,bottom color=mydarkred!60,shading angle=30]
\tikzstyle{ground}=[preaction={fill,top color=black!10,bottom color=black!5,shading angle=20},
fill,pattern=north east lines,draw=none,minimum width=0.3,minimum height=0.6]
\tikzstyle{metal}=[fill,top color=black!40,bottom color=black!20,shading angle=10]
\tikzstyle{pulcol}=[draw=blue!30!black,%fill=blue!40!black!10
top color=blue!40!black!20,bottom color=blue!40!black!10,shading angle=20]
\tikzstyle{rope}=[brown!70!black,very thick,line cap=round]
\def\rope#1{ \draw[black,line width=1.5] #1; \draw[rope] #1; }
\tikzstyle{mount}=[blue!20!black,fill,top color=blue!20!black!70,bottom color=blue!20!black!40,shading angle=10]
\def\r{0.05} % pulley small radius
\tikzset{
 
 
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Click to download: dynamics_moment_of_inertia.texdynamics_moment_of_inertia.pdf
Open in Overleaf: dynamics_moment_of_inertia.tex

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