Momentum

$\vec p$

Units:Ns

The momentum of an object is the product of its mass and its velocity, and is represented by the letter $\vec p$:

$$\vec p=m\vec v$$

It has the same SI units as impulse does (Ns, which can also be written as $\u{kg\cdot m/s}$). The momentum is a vector which points in the direction that the object is moving, and there is a relationship between the momentum and the impulse: when an impulse acts on an object, it changes its momentum according to

$\vec J=\Delta\vec p=\vec p_f-\vec p_i$
$\text{or }\vec p_f = \vec p_i + \vec J$

This is incredibly useful, as we will see in the following pages.

We can actually prove this relationship, if you're interested:

According to Newton's Second Law,	$$\RED{\vec F_{avg}} = \RED{m\vec a_{avg}}$$
The average acceleration is related to the change in velocity	$$\begin{align} \vec a_{avg}&=\frac{\vec{v}_f-\vec v_i}{\Delta t}\\ \implies \BLUE{\vec a_{avg}\Delta t} &=\BLUE{\vec v_f-\vec v_i}\\ \end{align}$$
The Impulse is equal to	$$\begin{align} \vec J&=\RED{\vec F_{avg}}\Delta t\\ &=(\RED{m\vec a_{avg}})\Delta t\\ &=m(\BLUE{\vec a_{avg}\Delta t})\\ &=m(\BLUE{\vec v_f-\vec v_i})\\ &=m\vec v_f-m\vec v_i\\ \end{align}$$
And since momentum is $\vec p=m\vec v$,	$$\vec J=\vec p_f-\vec p_i$$