If no net external force acts on a system of particles, the total linear momentum P of the system cannot change. This is the law of conservation of linear momentum.
See pages 214-215 in the text book.
Caution: Momentum should not be confused with energy. In the sample problems of section 9-7, momentum is conserved but energy is definitely not.
The law of conservation of linear momentum stems from Newton's third law. In a collision of two objects (or when two objects push off each other), each object experiences the same force but in the opposite direction, and they experience that same force for the same amount of time. Therefore they each experience the same change in momentum magnitude but opposite in sign. (refer to equation 9-31 on p.211) The net change of momentum is therefore zero. Also, we consider our system of particles to contain the colliding objects, so that the forces they exert on one another are internal forces and cannot change the net momentum of the system.
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