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 $kg \cdot m / s$ ). 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} = Δ \vec{p} = {\vec{p}}_{f} - {\vec{p}}_{i}

or {\vec{p}}_{f} = {\vec{p}}_{i} + \vec{J}

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

Optional

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

According to Newton's Second Law,	${\vec{F}}_{a v g} = m {\vec{a}}_{a v g}$
The average acceleration is related to the change in velocity	$\begin{aligned} {\vec{a}}_{a v g} & = \frac{{\vec{v}}_{f} - {\vec{v}}_{i}}{Δ t} \\ ⟹ {\vec{a}}_{a v g} Δ t & = {\vec{v}}_{f} - {\vec{v}}_{i} \end{aligned}$
The Impulse is equal to	$\begin{aligned} \vec{J} & = {\vec{F}}_{a v g} Δ t \\ = (m {\vec{a}}_{a v g}) Δ t \\ = m ({\vec{a}}_{a v g} Δ t) \\ = m ({\vec{v}}_{f} - {\vec{v}}_{i}) \\ = m {\vec{v}}_{f} - m {\vec{v}}_{i} \end{aligned}$
And since momentum is $\vec{p} = m \vec{v}$ ,	$\vec{J} = {\vec{p}}_{f} - {\vec{p}}_{i}$