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h3.  Conservation of Momentum      [!copyright and waiver^SectionEdit.png!|Momentum (Conservation)]

One important feature related to the fact that the [Momentum and External Force] [model] can accomodate a [system] composed of several [constituents|system constituent] 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:

{latex}\begin{large}\[ \sum_{\rm sys} \vec{p}_{f} = \sum_{\rm sys} \vec{p}_{i} \]\end{large}{latex}

which says that the [system's|system] _total_ momentum is conserved, but _does not necessarily_ mean that the momentum of _each constituent_ is conserved (this is the "nontrivial" part).  

h3.  Approximate Conservation in Collisions     [!copyright and waiver^SectionEdit.png!|Momentum (Conservation)]

One of the most important types of problem involving a multi-object system is a collision problem.  A collision between [rigid|rigid body] 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|gravity (near-earth)] 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|internal force], the [net|net force] [external|external force] [impulse] during the collision will be approximately zero.  This allows the use of conservation of [momentum] to analyze the collision.

{panel:bgColor=#F0F0FF}!SAPimages^SAP.gif! *[Head-on Collision]* ({excerpt-include:Head-on Collision|nopanel=true}){panel}
{panel:bgColor=#F0F0FF}!SAPimages^SAP.gif! *[Out of Bounds]* ({excerpt-include:Out of Bounds|nopanel=true}){panel}
{panel:bgColor=#F0F0FF}!SAPimages^SAP.gif! *[A Walk on the Pond]* ({excerpt-include:A Walk on the Pond|nopanel=true}){panel}