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### Center of Mass

The center of mass (or centroid) of a rigid body is found by averaging the spatial points of the body weighted by the mass of those points:B.12

Thus, the center of mass is the mass-weighted average location of the object. For a continuous mass distribution totaling up to , we can write

where the volume integral is taken over a volume of 3D space that includes the rigid body, and denotes the mass contained within the differential volume element located at the point , with denoting the mass density at the point . The total mass is

A nice property of the center of mass is that gravity acts on a far-away object as if all its mass were concentrated at its center of mass. For this reason, the center of mass is often called the center of gravity.

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