Answer to Question #151385 in Classical Mechanics for Isurini Sirisena

Question

Explain how the principle of conservation of momentum
in collisions is a consequence of Newton’s third law of
motion.

Answer 1

Conservation of momentum is actually a direct consequence of Newton's third law.

Consider a collision between two objects, object A and object B. When the two objects collide, there is a force on A due to B ​but because of Newton's third law, there is an equal force in the opposite direction, on B due to A.

The forces act between the objects when they are in contact. The length of time for which the objects are in contact depends on the specifics of the situation. For example, it would be longer for two squishy balls than for two billiard balls. However, the time must be equal for both balls.

Consequently, the impulse experienced by objects A and B must be equal in magnitude and opposite in direction.

If we recall that impulse is equivalent to change in momentum, it follows that the change in momenta of the objects is equal but in the opposite directions. This can be equivalently expressed as the sum of the change in momenta being zero.