The center of mass (or centroid) of a rigid body is found by averaging the spatial points of the body [画像:$ \underline{x}_i\in\mathbb{R}^3$] weighted by the mass $ m_i$ 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 $ M$ , we can write where the volume integral is taken over a volume $ V$ of 3D space that includes the rigid body, and $ dm(\underline{x}) = m(\underline{x})dV = m(\underline{x}),円 dx,円dy,円dz$ denotes the mass contained within the differential volume element $ dV$ located at the point [画像:$ \underline{x}\in\mathbb{R}^3$] , with $ \rho(\underline{x})$ denoting the mass density at the point $ \underline {x}$ . The total mass isA 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.
