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

h4. {toggle-cloak:id=desc} 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}

{cloak:id=desc} This [model|model] is [generally applicable|generally applicable model] (assuming knowledge of the external [forces|force] and [system|system] [constituents|system constituent]).{cloak}

h4. {toggle-cloak:id=cues} Problem Cues

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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 such as collisions ([impulse|impulse] will be easier to determine than [force|force]).
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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. Model 

h4. {toggle-cloak:id=sys} Compatible Systems

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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.
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h4. {toggle-cloak:id=int} Relevant Interactions

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Only [external forces|external force] need be considered, since [internal forces|internal force] do not change the system's momentum.
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h4. {toggle-cloak:id=def} Relevant Definitions

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{latex}\begin{large}\[ \vec{p} = m\vec{v}\]\end{large}{latex}
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h4. {toggle-cloak:id=laws} 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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h4. {toggle-cloak:id=diag} Diagrammatic Representations

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{contentbylabel:representation,momentum|showSpace=false|showLabels=false|excerpt=true|operator=AND|maxResults=50}
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h1. Relevant Examples

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

{cloak:id=const}{contentbylabel:constant_momentum|showSpace=false|showLabels=true|excerpt=true|maxResults=50}{cloak}

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

{cloak:id=imp}{contentbylabel:impulse|showSpace=false|showLabels=true|excerpt=true|maxResults=50}{cloak}

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

{cloak:id=oned}{contentbylabel:1d_collision|showSpace=false|showLabels=true|excerpt=true|maxResults=50}{cloak}

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

{cloak:id=twod}{contentbylabel:2d_collision|showSpace=false|showLabels=true|excerpt=true|maxResults=50}{cloak}

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

{cloak:id=inel}{contentbylabel:totally_inelastic|showSpace=false|showLabels=true|excerpt=true|maxResults=50}{cloak}

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

{cloak:id=flux}{contentbylabel:momentum_force|showSpace=false|showLabels=true|excerpt=true|maxResults=50}{cloak}

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

{cloak:id=all}{contentbylabel:constant_momentum,momentum_force,impulse|showSpace=false|showLabels=true|excerpt=true|operator=OR|maxResults=50}{cloak}

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