If there is no external force acting on a system, the total *momentum* of a system is always conserved. In addition, if a collision is *elastic*, the total kinetic energy before a collision is equal to the total kinetic energy after the collision i.e kinetic energy is also conserved. In other words, in an elastic collision between two particles of mass and ,

- momentum is conserved:
- kinetic energy is conserved:

If the particle with mass is stationary, i.e , we can derive the following two expressions,

If , we can neglect in our expressions and we get

Which makes sense. For example, imagine a tennis ball colliding with a wall.

If , we get

which also makes sense. Imagine two snooker balls colliding.

If a collision is *inelastic* its kinetic energy is not conserved (but the momentum is still conserved). However, if a collision is *completely inelastic* i.e the colliding particles get stuck together after the collision, we can still derive an easy expression to figure out their combined velocity simply from conservation of momentum:

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