### Parallel Axis Theorem

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

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

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