---
title: "rotational energy theorem"
source: https://www.jemoka.com/posts/kbhrotational_energy/
---

total kinetic energy \begin{equation} KE_{rigid} = \frac{1}{2} M{V_{cm}}^2 + \frac{1}{2} I_{CM}{\omega_{CM}}^2 \end{equation}
torque from gravity For even non rigid bodies, the following follows:
\begin{equation} \vec{\tau}_g = \vec{R}_{CM} \times M\vec{g} \end{equation}
Actually, this follows for any \(f\) (like \(g\)) evenly applied across point masses.
potential energy \begin{equation} \Delta PE_g = mg\Delta h \end{equation}
where, \(\Delta h\) is the travel of center of mass. Regardless of whether or not its point.
