% miko:type: atomic
% miko:title: Rigid Body Rotation
% miko:summary: Rotation of an extended body described by angular velocity and moment of inertia.
% miko:tags: mechanics
% miko:difficulty: undergrad
% miko:related: canonical-momentum, noether-theorem, hamiltonian-mechanics
% miko:keywords: angular velocity, inertia tensor, torque

\documentclass{article}
\usepackage{amsmath}
\title{Rigid Body Rotation}
\begin{document}
\maketitle

\section{Rotational Kinetic Energy}

For rotation about a principal axis,

$$
T=\frac{1}{2}I\omega^2.
$$

In three dimensions, the inertia tensor relates angular momentum to angular
velocity:

$$
\mathbf L = I\boldsymbol\omega.
$$

\section{Torque Equation}

The rotational equation of motion is

$$
\boldsymbol\tau = \frac{d\mathbf L}{dt}.
$$

This is the rotational analogue of Newton's second law.

\end{document}
