3.1.2 Newton’s 2nd Law

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 2nd Law, the rate of change of momentum of an object subjected to a net external force Fnet can be calculated by

\displaystyle {{F}_{{net}}}=\frac{{dp}}{{dt}}

Note that \displaystyle \frac{{dp}}{{dt}} is also a vector: the direction of momentum change is in the direction of Fnet.

\displaystyle {{F}_{{net}}}=\frac{{dp}}{{dt}} can be expressed in a few different forms that are suitable for different scenarios.

For a constant mass:{{F}_{{net}}}=ma
Averaged:\displaystyle {{F}_{{ave}}}=\frac{{\Delta p}}{{\Delta t}}
Impulse:J=F\Delta t=\Delta p
Continuous flow:F={{M}_{t}}\Delta v

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

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