4.2 Change in Momentum and Impulse

Forces play a key role in changing or transferring momentum, and they do this through a concept called impulse. Impulse connects force and momentum directly, helping us understand how applying a force over time changes an object’s motion. Impulses cause an object’s momentum to change. Impulse is a vector, measured in kilograms - meters per second, and represented with either the variable ${J}$ or ${p}$. The direction of the impulse vector on an object is in the same direction as the net force exerted on the object.

p represents the change in momentum of an object due to the impulse Favg is the average force exerted on an object t is the time interval over which the force was exerted over

This equation can actually be used to derive Newton’s 2nd Law. By solving for the force, you get ${F_{avg}=\frac{\Delta p}{\Delta t}}$. Assuming mass is constant, ${\Delta p}$ is just ${m \Delta v}$, making the equation ${F_{avg}=\frac{m \Delta v}{\Delta t}}$. By definition ${\frac{\Delta v}{\Delta t}=a}$, and also, the average force at an instant is just the net force on a system, so you get the equation ${F_{net}=ma}$.

The change in momentum of an object is just an object’s final momentum minus its initial momentum.