20.5: Rotational Kinetic Energy for a Rigid Body Undergoing Fixed Axis Rotation
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- 24554
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The rotational kinetic energy for the rigid body, using \(\overrightarrow{\mathbf{v}}_{\mathrm{cm}, i}=\left(r_{\mathrm{cm}, i}\right)_{\perp} \omega_{\mathrm{cm}} \hat{\boldsymbol{\theta}}\), simplifies to
\[K_{\mathrm{rot}}=\frac{1}{2} I_{\mathrm{cm}} \omega_{\mathrm{cm}}^{2} \nonumber \]
Therefore the total kinetic energy of a translating and rotating rigid body is
\begin{equation}K_{\text {total }}=K_{\text {trans }}+K_{\text {rot }}=\frac{1}{2} m V_{\text {cm }}^{2}+\frac{1}{2} I_{\text {cm }} \omega_{\text {cm }}^{2}\end{equation}