9·1. So far we have been concerned with the motion of a single particle. When two or more particles are moving in such a manner that the motion of any one is affected by the presence of the others we have to make use of another law enunciated by Newton, viz. Action and Reaction are equal and opposite, or, the actions of two bodies on one another are always equal and opposite. In explicit terms this means that if a body A exerts a force F on a body B, then B exerts an equal force F on A but in the opposite direction. Consequently the momentum communicated to A by the action of B is equal and opposite to the momentum communicated to B by the action of A.

Consider the case of a system of bodies, attracting or repelling each other or acting on one another by contact, or through connections by means of strings or rods, either for a finite time or by instantaneous impulses. In this case any momentum which is produced or destroyed in any assigned direction is accompanied by the production or destruction of an equal momentum in the opposite direction.

Hence it follows that, if no external forces act on a system of bodies, the total momentum, of the system, in any assigned direction remains constant.