A very important event is the collision between two objects or systems of objects. During a collision (or, equivalently, an explosion – sort-of a collision in reverse) the dominant force experienced by an object is the force exerted by the object with which it is colliding. For example, when two pool balls collide, they do indeed feel the normal force exerted by the pool table as well as the pull of the earth’s gravitational force, but during the very short time that they are in contact and colliding, the overwhelmingly dominant force is the force that each pool ball exerts on the other.  (Immediately before and after the collision the normal and gravitational forces resume their dominant roles.)

We may thus assume that, during a collision, the net external force is either zero or negligible.  It then follows that linear  momentum must be conserved in collisions.

There are three types of collisions with which we must be familiar.  Keep in mind that, for any collision, momentum is always conserved!

i) Elastic Collision

This means that, not only is momentum conserved, but so is kinetic energy.  Thus, for an elastic collision, we must have that

Keep in mind that kinetic energy is a positive scalar quantity, so there are no signs or directions to worry about!

ii) Inelastic Collision

This basically just means that the collision is not elastic, so that kinetic energy is not conserved.  Thus, we only have the conservation of momentum.

iii) Completely Inelastic Collision

This is a very special type of inelastic collision.  In this case, the objects colliding stick together after the collision, so there is only one object to worry about afterwards!

(Note that the “single object” which remains after the collision has a mass equal to the sum of the masses of the objects which collided.)