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:
 * $$\gamma = \frac c {\sqrt{c^2 - v^2}} = \frac 1 {\sqrt{1 - v^2 / c^2}}$$

where:
 * $$c$$ is the speed of light;
 * $$v$$ 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 $$c$$.