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@jemoka / Jemoka Knowledge Base / raw/concept/kbhrotational_energy.md
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--- 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.