The law of conservation of momentum says In the absence of outside force, the momentum of a system must not change.

A "collision" occurs whenever momentum is exchanged between two or more bodies who are approaching each other. For collisions the law of conservation of momentum can expressed one of two ways.

1. The sum of each body's momentum before a collision equals the sum of each body's momentum after a collision.
2. During a collision/interaction, the momentum lost by one body equals the momentum gained by another.

Mathematically these two laws look like this:

This section will look mathematically at the first expression for solving problems. It is equally correct to use the second expression.

s a vector. So vector addition can be used to see the 1st law of conservation of momentum. Try the example below to see how vectors can be used. Remember, adding up the vectors associated with the bodies' momentums before the collision equals the adding up the momentum vectors after the collision.