Dynamical Properties of Rigid Bodies

Abstract

Fix a set of cartesian axes in space. Suppose a finite system of particles is distributed in space, the ith particle having mass m _i and position r _i . The center of mass of the system is defined to be the point $\bar{r}$, where

$$\bar{r}=\frac{\Sigma m_i r_i}{\Sigma m_i}$$

(425)

and the summation is over all of the particles. Being defined vectorially, the center of mass is independent of the orientation of the axes in space; it also is easy to see that it is independent of the choice of origin.