Houjun Liu

rotational energy theorem

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.