Regid Body

Center of mass \(\vec R\) is defined as

\[\int \rho(\vec r) \vec r d^3 \vec r = \int \rho(\vec r) \vec R d^3 \vec r .\]

Equivalently,

\[\int \rho(\vec r) \left( \vec r - \vec R \right) d^3 \vec r = 0.\]