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