Center-of-mass velocity
= Center-of-mass velocity
{title2=$\mathbf V_{\rm CM}=\sum_i m_i\mathbf v_i/\sum_i m_i$}
= Centre-of-mass velocity
{synonym}
For fixed classical particle <masses>, differentiating the <center of mass> position gives the displayed mass-weighted <velocity>. The total <momentum> is $M\mathbf V_{\rm CM}$. The relativistic zero-momentum frame instead has velocity $c^2\mathbf P/E$; treating rest mass as the only weight there generally fails.