When a ball rolls down a cliff, it gains momentum. When a car speeds up on a racing track, it gains momentum. In both cases, the velocity of the object is changing.

Momentum is often described as mass times velocity of a particle. In everyday cases, mass stays constant for any given object. Hence, when velocity changes, so does momentum.

Momentum = Mass x Velocity

Momentum is important, because it turns out that it is related to the force applied on the particle, as:

momentum

i.e. force on a particle is equal to the rate of change of its momentum. If you assume the mass to be constant, you get:

momentum2

Since dv/dt or the rate of change of velocity is just acceleration a, you can write

momentum3

This is Newton’s Second law of motion and works really well in the domain of Newtonian Mechanics.

A very important property of momentum is that, given there are no external forces on a body, its momentum is conserved. This property is known as the “law of conservation of momentum” and is never violated.

What we have discussed above is the linear momentum. There is yet another form of momentum, called the Angular Momentum which has a conservation law of its own.

Momentum
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