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20.5: Rotational Kinetic Energy for a Rigid Body Undergoing Fixed Axis Rotation

  • Page ID
    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}


    This page titled 20.5: Rotational Kinetic Energy for a Rigid Body Undergoing Fixed Axis Rotation is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Peter Dourmashkin (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.