Center of Mass

up:: 031 MOC Classical Mechanics

Given an ensemble of particles $\{m_i,\overrightarrow{r_i}{\}}_{i=1}^n$, one defines their center of mass as

$$\vec{R}=\frac{\sum _i{m}_i\overrightarrow{r_i}}{\sum _i{m}_i}=\frac{\sum _i{m}_i\overrightarrow{r_i}}{M}=\sum _i\frac{m_i}{M}\overrightarrow{r_i}$$

where $M=\sum _i{m}_i$ is the total system’s mass.

The center of mass is essentially a weighted average of the position of the particles.