Conservation of linear momentum

Consider the direct collision of two spheres A and B shown in Figure 4.3

When the spheres collide, then by Newton's third law, the force F exerted by A on B is equal and opposite to the force exerted by B on A.

The time for contact is the same for both. The impulse of A on B is thus equal and opposite to the impulse of B on A. It then follows that the change in momentum of A is equal in magnitude to the change in momentum in B - but it is in the opposite direction. The total change in momentum of the whole system is thus zero.

This means that the total momentum before and after a collision is equal, or that linear momentum is conserved. This is called the principle of conservation of linear momentum and in summary this may be stated:

The total momentum of a system, in any direction, remains constant unless an external force acts on the system in that direction.