**Conservation of momentum**

Tanusri Gururaj, Academic content writer of Physics at Edumarz

If two or more bodies are in an isolated system, the total momentum of the objects before colliding is equal to the total momentum after colliding unless acted upon by an external force.

Proof of conservation of momentum:

Let us assume that there are two balls A and B travelling in the same direction on a straight path with different initial velocities.

For ball A:

Mass = mA

Initial velocity = uA

For ball B:

Mass = mB

Initial velocity = uB

Suppose the two balls collide together.

The force exerted by ball A on ball B is FAB and, the force exerted by ball B on ball A is FBA.

Now the final velocity of ball A becomes vA and, the final velocity of ball B becomes vB.

Rate of change of momentum of ball A = mA(vA – uA)/t = FAB (according to newton’s second law of motion )

Rate of change of momentum of ball B = mB(vB – uB)/t = FBA (according to newton’s second law of motion )

Where t is the time for which the collision between the two balls lasts.

According to Newton’s third law of motion,

FAB = -FBA

On equating these equations we get,

mAuA + mBuB = mAvA + mBvB

In the above equation, the left side represents the total momentum of the two bodies before the collision and, the right side represents the total momentum of the two bodies after the collision.

This example proves the law of conservation of momentum.