Conservation of Momentum: Introduction

The total momentum of a system consisting of N interacting objects is constant in time or is conserved. A system must meet two requirements for its momentum to be conserved:

1. The mass of the system must remain constant during the interaction. As the objects interact (apply forces on each other), they may transfer mass from one to another; but any mass one object gains is balanced by the loss of that mass from another. The total mass of the system of objects, therefore, must remain unchanged as time passes.
2. The net external force on the system must be zero. As the objects collide, or explode, and move around, they exert forces on each other. However, all of these forces are internal to the system, and thus each of these internal forces is balanced by another internal force that is equal in magnitude and opposite in sign. As a result, the change in momentum caused by each internal force is canceled out by another momentum change that is equal in magnitude and opposite in direction. Therefore, internal forces cannot change the total momentum of a system because the changes sum to zero. However, if there is some external force that acts on all of the objects (for example, gravity or friction), then this force changes the momentum of the system as a whole. That is to say, the momentum of the system is changed by the external force. Thus, for the momentum of the system to be conserved, the net external force must be zero.

A system of objects that meets these two requirements is said to be a closed system (or an isolated system), and the total momentum of a closed system is conserved. All experimental evidence supports this statement: from the motions of galactic clusters to the quarks that make up the proton and the neutron, and at every scale in between. Note that there can be external forces acting on the system, but for the system's momentum to remain constant, these external forces must cancel so that the net external force is zero. For instance, billiard balls on a table all have a weight force acting on them, but the weights are balanced (canceled) by the normal forces, so there is no net force.

This text is adapted from Openstax, University Physics Volume 1, Section 9.3: Conservation of Linear Momentum.