Velocity of Centre of Mass

Just as the centre of mass position is the mass-weighted average of the individual particles' positions, the VELOCITY of the centre of mass of a system of particles (with velocities $\vec{v_1}, \vec{v_2}, \ldots, \vec{v_n}$) is the mass-weighted average of the individual velocities: $\vec{v}_{cm}=\frac{\sum_{i=1}^n m_i\vec{v_i}}{M}$, with the x, y and z components obtained the same way component-wise. For a continuous mass distr …