Let’s start here by defining Impulse and Momentum.
Impulse (J) is defined as the product of the net force acting on an object and the duration of time that force is applied. So in short, it is the total area underneath the Force-Time curve (an integral, just like we talked about earlier). J=FΔt.
Momentum is defined as the product of an object’s mass and its velocity. .It represents how much “motion” an object carries. The main goal of a thrower, for example, is to change the implements momentum as much as possible. p=mv.
Impulse–Momentum Theorem states that the net impulse on an object is equal to its change in momentum: J=Δp=mv(final)−mv(initial). In the majority of non-contact sporting contexts, mass is constant, so we can write the formula like this-
FΔt= m(vf-vi).
This is a perfect example of forward dynamics at work, going from force (kinetics) to velocity (kinematics). So to be able to change the momentum of our center of mass, or the center of mass of a separate implement, the goal is to create as much positive impulse as possible.
Side Note- The fact that Impulse is a integral is exactly why it is so reliable, because it is a full look at the area under the force-time curve. This is why more derivative-based metrics like peak power are much more variable and not as reliable, because they only exist at one specific point on the force time curve. A longer write up on this by Dr. Jason Lake can be found here.