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Translational Kinetic Energy

The translational kinetic energy of a collection of masses $ m_i$ is given by

$\displaystyle E_K \eqsp \frac{1}{2} M v_c^2
$

where $ M=\sum_i m_i$ is the total mass, and $ v_c$ denotes the speed of the center-of-mass. We have $ v_c\isdeftext \left\Vert\,\underline{v}_c\,\right\Vert$ , where $ \underline{v}_c$ is the velocity of the center of mass.

More generally, the total energy of a collection of masses (including distributed and/or rigidly interconnected point-masses) can be expressed as the sum of the translational and rotational kinetic energies [272, p. 98].


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2015-05-22 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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