Collisions

A collision is any brief, forceful interaction between two (or more) bodies -- carom, billiards and marbles are everyday examples -- and collisions can happen with or without the bodies physically touching (e.g. two charged particles or two planets can "collide" gravitationally/electrically without contact).

Linear momentum is always conserved in every collision. During the brief collision time $\Delta t$, the first body exerts an impulsive force $\vec F_{12}$ on the second, and by Newton's third law the second body exerts an equal and opposite force $\vec F_{21} = -\vec F_{12}$ on the first. Each force produces a change of momentum in the body it acts on:

Adding these two equations and using $\vec F_{12}=-\vec F_{21}$ gives $\Delta \vec p_1 + \Delta \vec p_2 = 0$, i.e. $\Delta(\vec p_1+\vec p_2)=0$. Taking the limit $\Delta t \to 0$, this says the total momentum of the two-body system does not change during the collision:

$\vec p_1 + \vec p_2 = \text{constant}$ …