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Parallel Axis Theorem

Let $ I_0$ denote the moment of inertia for a rotation axis passing through the center of mass, and let $ I_d$ denote the moment of inertia for a rotation axis parallel to the first but a distance $ d$ away from it. Then the parallel axis theorem says that

$\displaystyle I_d = I_0 + Md^2
$

where $ M$ denotes the total mass. Thus, the added inertia due to displacement by $ d$ meters away from the centroidal axis is equal to that of a point mass $ M$ rotating a distance $ d$ from the center of rotation.


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-06-11 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA