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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

{cloak:id=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 such as collisions ([impulse|impulse] will be easier to determine than [force|force]).
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h4. {toggle-cloak:id=prior} Prior Models

{cloak:id=prior}

* [Point Particle Dynamics]

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

{cloak:id=vocab}

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

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h1. Model 

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

{cloak:id=sys}
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

{cloak:id=int}
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

{cloak:id=def}
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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

{cloak:id=laws}

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h6. Differential Form
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Introduction to the Model
Description and Assumptions
 Excerpt
hiddentrue
System: Any. — Interactions: Any. — Note: Linear momentum evolves separately from angular momentum, so all system constituents are treated as point particles in this model.

 This model is generally applicable (assuming knowledge of the external forces and system constituents). The model is especially useful when describing the momentum of systems where external forces are absent (system momentum will be constant) or estimating the force in a process that occurs in a very short time interval such as collisions (impulse will be easier to determine than force).
Learning Objectives
Students will be assumed to understand this model who can:
Relevant Definitions

 Latex
\begin{large}\[ \vec{p} = m\vec{v}\]\end{large}
S.I.M. Structure of the Model
Compatible Systems
The system must be effectively composed of point particles, 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.
Relevant Interactions
Only external forces need be considered, since internal forces do not change the system's momentum.
Laws of Change
Mathematical Representation
 Section
 Column
 
Differential Form
 

 Latex
\begin{large}\[ \
sum_{\rm system}\
frac{d\vec{p}}{dt} = \sum
_{\rm external}
 \vec{F}^{\rm ext}\]\end{large}
{latex}
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h6. Integral Form
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width40px
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Integral Form
 

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\begin{large}\[
 \sum_{\rm
 
system}
\vec{p}_{f} =
 \sum_{\rm
 
system}
\vec{p}_{i} + \sum
_{\rm external}
 \vec{J}
 = \sum_
^{\rm 
system}
ext}_{fi} = \vec{p}_{i} + \int_{t_{i}}^{t_{f}} \sum
_{\rm
 
external} 
\vec{F}^{\rm ext}\:dt  \]
\end{large}
{latex}
{column}
{section}

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h4. {toggle-cloak:id=diag} Diagrammatic Representations

{cloak:id=diag}
{contentbylabel:representation,momentum|showSpace=false|showLabels=false|excerpt=true|operator=AND|maxResults=50}
{cloak}

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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Diagrammatic Representations
Relevant Examples
 
 Toggle Cloak
idconst
 Examples Involving Constant Momentum
 
 Cloak
idconst
 falsetruetrue50constant_momentum
 
 Toggle Cloak
idimp
 Examples Involving Impulse
 
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idimp
 falsetruetrue50impulse
 
 Toggle Cloak
idoned
 Examples Involving 1-D Collisions
 
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idoned
 falsetruetrue501d_collision
 
 Toggle Cloak
idtwod
 Examples Involving 2-D Collisions
 
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idtwod
 falsetruetrue502d_collision
 
 Toggle Cloak
idelas
 Examples Involving Elastic Collisions
 
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idelas
 falsetruetrue50elastic_collision
 
 Toggle Cloak
idinel
 Examples Involving Totally Inelastic Collisions
 
 Cloak
idinel
 falsetruetrue50totally_inelastic
 
 Toggle Cloak
idflux
 Examples Involving Continuous Momentum Flux
 
 Cloak
idflux
 falsetruetrue50momentum_force
 
 Toggle Cloak
idall
 All Examples Using this Model
 
 Cloak
idall
 falsetruetrueOR50constant_momentum,momentum_force,impulse
 
 
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