When a collision occurs in an isolated system, the total momentum of the system doesn’t change with the passage of time. Instead, it remains constant both in magnitude and in direction. The momenta of the individual objects in the system may change, but the vector sum of all the momenta will not change. The total momentum is therefore said to be conserved. In this section, we will see how the laws of motion lead us to this important conservation law.

The concept of momentum is particularly important in situations in which we have two or more bodies that interact. To see why, let’s consider first an idealized system of two bodies that interact with each other but not with anything else— for example, two astronauts who touch each other as they float freely in the zero-gravity environment of outer space (Figure 15). Think of the astronauts as particles.

Each particle exerts a force on the other; according to Newton’s third law, the two forces are always equal in magnitude and opposite in direction. Hence, the impulses that act on the two particles are equal in magnitude and opposite in direction, as are the changes in momentum of the two particles.