To study motion we have to quantify it. So how do we quantify motion? Perhaps the kinetic energy is the first thing that comes to many people’s mind. But Isaac Newton had a better idea. He chose to quantify an object’s motion by its momentum, which is the object’s mass m times its velocity v.

Unlike KE, momentum is a vector quantity. The direction of the momentum (of an object) is in the direction of the velocity (of the object).

According to Newton’s 2^{nd} Law, the rate of change of momentum of an object subjected to a net external force F_{net} can be calculated by

Note that is also a vector: the direction of momentum change is in the direction of F_{net}.

can be expressed in a few different forms that are suitable for different scenarios.

For a constant mass:

Averaged:

Impulse:

Continuous flow:

Each form will be discussed in detail in separate sections under Chapter 3.2.