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
Linear momentum has dimension $M L T^{-1}$.

Relativistic Model
A more accurate model for this quantity 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 $\mathbf v$: $v = \left|{\mathbf v}\right|$

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