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h3.  Multi-Object Systems     [!copyright and waiver^SectionEdit.png!|Momentum (Multi-Object)]

The linear form of [Newton's Second Law] when written in terms of [momentum] implies that it is easily generalized to allow for a [system] consisting of many objects.  Simply add the contributions from all the objects within the [system]:

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

It is important to realize that although we are now allowing multiple objects within the [system], the relevant [impulse] to add on the right hand side of [Newton's Second Law] is still only the _[external|external force]_ [impulse].  Impulses applied to one [system constituent] by another [system constituent] end up canceling out of the equation by [Newton's Third Law].

It is also worth noting that technically the concept of linear [momentum] applies only to collections of [point particles|point particle]. The momentum of a [rigid body], then, must technically be thought of as the sum of the [momentum] of each of the atoms in the body.  This sum turns out to be the body's [mass] times its [center of mass] [velocity]. The [momentum] of a [system] composed of many [rigid bodies|rigid body] and [point particles|point particle] is then the sum of their individual momenta, which again can be expressed as the total [mass] of this [system] times the [velocity] of the [system's|system] [center of mass].