# Definition:Linear Momentum

## Definition

The linear momentum of a body is its mass multiplied by its velocity.

$\mathbf p = m \mathbf v$

As mass is a scalar quantity and velocity is a vector quantity, it follows that linear momentum is a vector quantity.

### Dimension

The dimension of measurement of linear momentum is: $M L T^{-1}$.

### Relativistic Model

A more accurate model for the linear momentum of a body is given by:

$\mathbf p = \gamma m \mathbf v$

where $\gamma$ is the Lorentz Factor:

$\gamma = \dfrac c {\sqrt {c^2 - v^2} } = \dfrac 1 {\sqrt {1 - v^2 / c^2} }$

where:

$c$ is the speed of light in vacuum
$v$ is the magnitude of $\mathbf v$: $v = \size {\mathbf v}$

It is clear $\gamma \approx 1$ (and thus that $\mathbf p \approx m \mathbf v$) for values of $v$ much less than $c$.

## Also known as

Linear momentum is frequently referred to as just momentum.