Conservation of momentum



If a body collides with another body, by using Newton's third law the two bodies will exert equal and opposite forces on one another. Also because their time of contact is the same the impulse Ft will be the same. As impulse is equivalent to the change of momentum, irrespective of the initial velocities of masses of the bodies the total momentum will be conserved. It follows from the impulse-momentum equation that the changes of momentum must be equal and opposite.

For bodies of mass m' and m, with initial velocities u' and u:

m'u' + mu = m'v' + mv

where v' and v'' are final velocities.

This important result is known as the principle of conservation of momentum, and was deduced by using Newton's laws. It is a universal law and applies in all situations. An example of the conservation of momentum is when someone fires a gun. The backward component of momentum equals the forward momentum of the bullet, so the total momentum equals zero, even though the momentum of each part changes. Due to the bullet being much lighter than the gun, the backwards velocity of the gun is much less than the forward velocity of the bullet.

No external agent must act on the interacting bodies otherwise momentum may be added to the system.

When bodies in a system interact the total momentum remains constant provided no external force acts on the system.