Momentum

Describes a characteristic of the motion of an object, or the ”mass in motion”

$p$ - momentum (kg m s^-1) $m$ - mass (kg) $v$ - velocity (m s^-1) $p$ = $mv$

Change in Momentum §

To change the momentum of an object ($\Delta p$), a net force needs to be applied over time. A change in momentum would in most cases require a change in velocity, so $\Delta p=m\Delta v$ and $\therefore \Delta p=m(v-u)$. This means that if $\sum p=0$ then $p_i=p_f$ meaning that if the sum of all momentum in a system is zero then the initial momentum will equal the final momentum.

Because a net force is required, $\Delta p=F_{net}\Delta t$ or $\Delta p=Ft$, which is a change in momentum over time. Changes in momentum don’t happen instantaneously, there is always some period (no matter how small) over which this occurs.

Impulse §

An impulse is the net force experienced by an object over time. It results in a change in momentum.

$$F_{net}=\frac{m\Delta v}{\Delta t}$$

Derivation §

From Newton’s Second Law, we know that $F_{net}=ma$. We also know that $a=\frac{\Delta v}{\Delta t}=\frac{v-u}{\Delta t}$. Subbing this into Newton’s Second Law, we get $F_{net}=\frac{m(v-u)}{\Delta t}=\frac{m\Delta v}{\Delta t}=\frac{\Delta p}{\Delta t}$.