Newton’s second law of motion states that “the net force applied on an object is equal to the rate of change (the derivative) of its linear momentum in a reference frame”. This law is a continuation of the Newton’s first law of motion.

Mathematically, this law can be put as:

Where the dp/dt refers to the derivative of the momentum. The momentum of a body is given by the product of the mass of the body and its velocity (i.e. mV).

However, this Newton’s second law of motion is only applicable to bodies with a constant mass since if the mass of the object/body varies, the momentum of the body will change and this change will not be as a result of the net force applied, which is not governed by this Newton’s second law of motion. As a result of this argument, Newton’s second law of motion can also be expressed as:

Therefore, according to this law, the time derivative of the momentum is not equal to zero when the direction of the momentum changes. This applies even when there is no change in its magnitude (this is the case with uniform circular motion which is covered in our JC Physics tuition classes; the direction of the momentum of the circulating object changes and hence the momentum is non-zero).

Also according to this law, there is the conservation of momentum in that when the net force applied on the body is zero, the momentum of the body is constant (doesn’t change over time) and any net force applied to the object is equal to the rate of change of the momentum of the object.

Practical applications of the Newton’s second law of motion

Let’s take an example of a skydiver. When a skydiver jumps from a plane, he or she will accelerate downwards due to gravity until he or she attains the heist speed that he can attain and from there he will maintain a constant speed downwards. When the diver is coming down at a constant speed, then there is no net force acting upon him since the air resistance acting upwards is equal to the downwards force acting on the diver.

Another practical application is when you drop a ball into a viscous fluid, let’s say glycerin. The ball’s velocity downwards through the glycerin at first will increase unto a point where it becomes constant. The constant velocity is a result of the drag acting on the ball being equal to the downwards force acting on the ball.