Newton's Second Law

Momentum

A motion of a body is described by its momentum. Momentum is the product of a body's mass and its velocity. Momentum has both magnitude and direction. Newton showed that bodies only change their motion when a force is applied, Newtons first law. The change in the momentum is equal to the applied force.

Derivation of Newton's second law

Consider a snooker ball of mass m moving with a velocity v₁. The ball hits the cushion and bounces off, it now has a velocity v₂. The change in momentum is mv₁ − mv₂ = m(v₁ − v₂). The change in velocity is the acceleration, and so the change in momentum and hence force F is mass times acceleration, F = ma. Thus Action and Reaction are equal but opposite in direction.