In a closed system (one that does not exchange any matter with the outside and is not acted on by outside forces), the total momentum is constant . This fact, known as the law of conservation of momentum, is implied by Newton's laws of motion. Suppose, for example, that two particles interact. Because of the third law, the forces between them are equal and opposite. If the particles are numbered 1 and 2, the second law states that
or
Therefore, total momentum (p1+p2) is constant. If the velocities of the particles are u1 and u2 before the interaction, and afterwards they are v1 and v2, then
This law holds regardless of the nature of the interparticle (or internal) force, no matter how complicated the force is between particles. Similarly, if there are several particles, the momentum exchanged between each pair of particles adds up to zero, so the total change in momentum is zero.
Newton's Second Law
Newton actually stated his second law of motion in terms of momentum: The net external force equals the change in momentum of a system divided by the time over which it changes. Using symbols, this law is
where
This statement of Newton's second law of motion includes the more familiar
Because Δv/Δt=a, we get the familiar equation
Momentum in a Closed System
In a game of pool, the system of entire balls can be considered a closed system. Therefore, the total momentum of the balls is conserved.