Center of Mass

$\vec{R}=\frac{1}{M}\sum _{\alpha }{m}_{\alpha }{\vec{r}}_{\alpha }$

• $\vec{R}$ is the position of center of mass of the system
• $M$ is the total mass of the system
• $m_{\alpha }$ is the mass of the $\alpha$th particle
• ${\vec{r}}_{\alpha }$ is the position of the $\alpha$th particle

$\vec{R}=\frac{1}{M}\int \vec{r}\mathrm{d}m$