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# 3.5: Linear Momentum

[ "article:topic", "authorname:tatumj", "linear momentum" ]

Theorem:

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

Thus:

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