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{composition-setup}{composition-setup}
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h1. IntroductionMomentum and External Force

h4. Description and Assumptions

{excerpt:hidden=true}*[System|system]:* Any. --- *[Interactions|interaction]:* Any. --- *Note:* Linear [momentum|momentum] evolves separately from [angular momentum|angular momentum (one-dimensional)], so all system constituents are treated as [point particles|point particle] in this [model|model].{excerpt}

This [model|model] is [generally applicable|generally applicable model] (assuming knowledge of the external [forces|force] and [system|system] [constituents|system constituent]).

h4. Problem Cues

This [model|model] is especially useful when describing the [momentum|momentum] of [systems|system] where [external forces|external force] are absent ([system|system] [momentum|momentum] will be constant) or estimating the [force|force] in a process that occurs in a very short time interval as in collisions ([impulse|impulse] will be easier to determine than [force|force]).


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h1. Prerequisite Knowledge

h4. {toggle-cloak:id=prior} Prior Models

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* [Point Particle Dynamics]

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h4. {toggle-cloak:id=vocab} Vocabulary

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* [system]
* [force]
* [impulse]
* [momentum]
* [velocity]

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h1. Compatible Systems

The system must be effectively composed of [point particles|point particle], though rigid bodies may be treated as point particles with positions specified by the center of mass positions of the rigid body when this model is used.


h1. Relevant Interactions

Only [external forces|external force] need be considered, since [internal forces|internal force] do not change the system's momentum.

h1. Model

h3. Relevant Definitions
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{latex}\begin{large}\[ \vec{p} = m\vec{v}\]\end{large}{latex}


h3. Laws of Change
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h6. Differential Form
{latex}\begin{large}\[ \sum_{\rm system}\frac{d\vec{p}}{dt} = \sum_{\rm external} \vec{F}\]\end{large}{latex}
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h6. Integral Form
{latex}\begin{large}\[ \sum_{\rm system}\vec{p}_{f} = \sum_{\rm system}\vec{p}_{i} + \sum_{\rm external} \vec{J} = \sum_{\rm system}\vec{p}_{i} + \int \sum_{\rm external} \vec{F}\:dt  \]
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h1. Diagrammatic Representations

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h1. Relevant Examples

h4. {toggle-cloak:id=const} Examples Involving Constant Momentum

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h4. {toggle-cloak:id=imp} Examples Involving Impulse

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h4. {toggle-cloak:id=oned} Examples Involving 1-D Collisions

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h4. {toggle-cloak:id=twod} Examples Involving 2-D Collisions

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h4. {toggle-cloak:id=elas} Examples Involving Elastic Collisions

{cloak:id=elas}{contentbylabel:elastic_collision|showSpace=false|showLabels=true|excerpt=true|maxResults=50}{cloak}

h4. {toggle-cloak:id=inel} Examples Involving Totally Inelastic Collisions

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h4. {toggle-cloak:id=flux} Examples Involving Continuous Momentum Flux

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h4. {toggle-cloak:id=all} All Examples Using this Model

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