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:

If

_ext = 0,

then

and therefore

= constant

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

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

The total momentum of a system is always conserved, if the net external force acting on it is 0.

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.