Do you have such an experience when you skate? When your friend skates faster than you and pushes you at the back, you will speed up but your friend will slow down. The contact is actually a collision. In the collision your friend exerts a force on you to speed you up. By Newton's Third Law, he will experience an equal and opposite reaction that slows him down. When two objects collide, one object may gain speed while the other may lose speed. Somehow a physical quantity of motion is transferred from one object to the other. We shall see that this quantity is the momentum that we have defined previously.

Conservation of momentum

Fig. 2-1 The process of a collision

Suppose two objects labeled 1 and 2 undergo a collision. The masses of the objects are and , and they move with the velocities and before the collision (Fig. 2-1a).

During the collision, there is a short duration of contact between the objects (Fig. 2-1b). Object 1 exerts an average force on object 2, and by Newton's Third Law, object 1 also experiences an equal and opposite reaction force (the force is negative because it acts in the opposite direction). These forces cause accelerations and hence a change in velocities of the objects.

Suppose after the collision, the objects move apart and have the velocities and (Fig. 2-1c). Applying Newton's Second Law to object 1, we have:

......(1)

where is time of contact. Similar relation applies for object 2:

......(2)

Summing up equations (1) and (2) gives

or

The result shows that the sum of momentum of the objects before the collision is equal to the sum of momentum after the collision. In other words, the total momentum of the system is unchanged or conserved. This is known as the principle of Conservation of Momentum.