# 3.5: Linear Momentum

- Page ID
- 6943

Theorem:

*The total momentum of a system of particles equals the total mass times the velocity of the centre of mass.*

Thus:

\[ \textbf{P} = \sum m_{i}\textbf{v}_{i} = \sum m_{i} (\overline{\textbf{v}} + \textbf{v}_{i}^{'}) = M \overline{\textbf{v}} + 0. \tag{3.5.1}\label{eq:3.5.1} \]