Momentum (Conservation)

Conservation of Momentum     

One important feature related to the fact that the Momentum and External Force model can accomodate a system composed of several constituents is the fact that, in the absence of external impulse acting on such a system, the momentum will be nontrivially conserved.

For a multi-object system experiencing no net impulse, the Law of Change for the model becomes:

which says that the system's total momentum is conserved, but does not necessarily mean that the momentum of each constituent is conserved (this is the "nontrivial" part).

Approximate Conservation in Collisions     

One of the most important types of problem involving a multi-object system is a collision problem. A collision between rigid objects is a very rapid process. Because the time of a collision is so short, and because the definition of impulse involves a time integral, everyday forces like gravity or friction usually contribute a negligible impulse during the collision. Thus, if a system is chosen that includes all the colliding objects so that the (often very large) collision forces are purposely made internal, the net external impulse during the collision will be approximately zero. This allows the use of conservation of momentum to analyze the collision.