Law of conservation of momentum

The law of momentum conservation can be stated as follows. For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.

According to newton’s 2nd law, the rate of change of momentum is equal to external force applied.

So, Fexternal = Fresultant = dp/dt

We already know that change of momentum of a body is due to internal forces is equal to “0”, because the internal forces are mutual forces and cancel out each other.

So, Fexternal = dp/dt

When the external force doesn’t act on a body  

dp/dt = 0

So, therefore P is a constant.

So, we can also say that when only internal force are acting momentum of a system is conserved.

This is called conservation of momentum.