Law of conservation of momentum:

The momentum of an isolated system of two or, more two interacting bodies remains constant.

Example:

Consider the example of an air-filled balloon as described under the third law of motion. In this case, the balloon and the air inside it form a system. Before releasing the balloon, the system was at rest and hence the initial momentum of the system was zero. As soon as the balloon is set free, air escapes out of it with some velocity. The air coming out of it possesses momentum. To conserve momentum, the balloon moves in a direction opposite to that of air rushing out.

 

Explanation: 

Law of conservation of momentum applies to all objects in the universe. A rocket and jet engine are taking off. The recoil of a gun is an example that demonstrates the importance of the law of conservation of momentum.

 

Case I:

Consider an isolated system of two spheres of masses m₁ and m₂. They are moving in a straight line with initial velocities u₁ and u₂ respectively such that u₁ is greater than u₂. The sphere of mass m₁ approaches the sphere of mass m₂ as they mThe initial

The initial momentum of mass m₁ =m₁u₁

The initial momentum of mass m₂ =m₂u₂

The total initial momentum of the system before collision = m₁u₁+m2u2 ………(i)

 

 

Case II:

After sometimes mass m₁ hit m₂ with some force. According to newton's third law of motion, m₂ exerts an equal and opposite reaction force on m₁. Let their velocities become v₁ and v₂ respectively after the collision. Then

Final momentum of mass m₁ = m₁u₁

Final momentum of mass m₂ = m₂u₂

Total final momentum of the system before collision = m₁u₁+m₂u₂ ………(ii)

 

According to the Law of conservation of momentum:

 [ total initial momentum of the system before collison] = [ total initial momentum of the system before system]

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂......... (iii)

 

Equation (iii) shows that the momentum of an isolated system before and after collisions remains the same which is the law of conservation of momentum. The Law of conservation of momentum is important and has vast applications.