Conservation of Linear Momentum

Two billiard balls, labeled A and B,

are approaching each other head on

mass of ball A

mass of ball B

velocity of ball A before the collision

velocity of ball B before the collision

velocity of ball A after the collision

velocity of ball B after the collision

Let:

force on A due to being struck by B

force on B due to being struck by A

Newton’s third law tells us that

(1)

for A (2)

for B (3)

or (4) using (1)

adding (2) and (4):

putting the terms with a minus sign on the left side of the equation

This is the equation for conservation of momentum in one dimension.

It says that the total momentum before the collision is equal to the total momentum after the collision.