Conservation of Linear Momentum

Suppose there is no external force acting on an object, = 0. Then we have from our new formulation of Newton's Second Law:


ext = 0,


and therefore

= constant

This equation is the law of momentum conservation, stating that the linear momentum is conserved (constant) in time.

If we have a system of particles, then we can generalize this statement to:

If the net external force acting on it is zero, the total momentum of a system is always conserved.

The internal forces acting between objects in a system do not change the total momentum of the system. Basically this is due to Newton's Third Law.

We can state the same law of momentum conservation without the use of calculus, but the result is exactly the same again.