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h4. Introduction to the Model

h5. Description and Assumptions

{excerpt:hidden=true}*[*System*|system]**:* Any. --- *[*Interactions*|interaction]**:* Any. --- *Note:* Linear [momentum|momentum] evolves separately from [angular momentum|angular momentum about a single axis], so all system constituents are treated as [point particles|point particle] in this [model|model].{excerpt}
This [model|model] is generally applicable (assuming knowledge of the external [forces|force] and [system|system] [constituents|system constituent]).  The [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]).

h5. Learning Objectives

Students will be assumed to understand this model who can:
* Define the momentum of a [point particle].
* Define [impulse] in terms of [momentum] or in terms of [force].
* Give an expression for the time-average [force] on a [system] in terms of its [momentum].
* Calculate the net [external force] on a [system] containing several objects.
* Describe the conditions required for the [momentum] of a [system] to be [conserved].
* Describe the [system] that must be considered and the assumptions that lead to approximate conservation of momentum in a collision.

h5. Relevant Definitions
\\
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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}
{latex}

h4. 
S.I.M. 
 
 Structure 
 
 of 
 
 the 
 
 Model


h5. 
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.


h5. 
Relevant 
 
 Interactions



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


h4. 
Laws 
 
 of 
 
 Change


h5. 
Mathematical 
 
 Representation


{section}
{column}

h6. Differential Form

\\
{latex}
 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}
{column}
{column:width=40px}
{column}
{column}

h6. Integral Form

\\
{latex}
 Column
width40px
 Column
 
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}
ext}_{fi} = \vec{p}_{i} + \int_{t_{i}}^{t_{f}} \sum
_{\rm external}
 \vec{F}^{\rm ext}\:dt  \]
\end{large}
{latex}
{column}
{section}

h5. Diagrammatic Representations

* [
Diagrammatic Representations
 
 
]
* [
 
 diagram]

h4. Relevant Examples


h6. {
Relevant Examples
 Toggle Cloak
:
id
=
const
} 
 Examples 
 
 Involving 
 
 Constant 
 
 Momentum


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

h6. {toggle-cloak:id=imp} Examples Involving Impulse

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

h6. {toggle-cloak:id=oned} Examples Involving 1-D Collisions

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

h6. {toggle-cloak:id=twod} Examples Involving 2-D Collisions

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

h6. {toggle-cloak:id=elas} Examples Involving Elastic Collisions

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

h6. {toggle-cloak:id=inel} Examples Involving Totally Inelastic Collisions

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

h6. {toggle-cloak:id=flux} Examples Involving Continuous Momentum Flux

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

h6. {toggle-cloak:id=all} All Examples Using this Model

{cloak:id=all}
{contentbylabel:
const
 falsetruetrue50constant_momentum
 
 Toggle Cloak
idimp
 Examples Involving Impulse
 
 Cloak
idimp
 falsetruetrue50impulse
 
 Toggle Cloak
idoned
 Examples Involving 1-D Collisions
 
 Cloak
idoned
 falsetruetrue501d_collision
 
 Toggle Cloak
idtwod
 Examples Involving 2-D Collisions
 
 Cloak
idtwod
 falsetruetrue502d_collision
 
 Toggle Cloak
idelas
 Examples Involving Elastic Collisions
 
 Cloak
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
|showSpace=false|showLabels=true|excerpt=true|operator=OR|maxResults=50}
{cloak}

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Photos courtesy:
* [Wikimedia Commons|http://commons.wikimedia.org] by user [No-w-ay|http://commons.wikimedia.org/wiki/User:No-w-ay] in collaboration with H. Caps
* [Wikimedia Commons|http://commons.wikimedia.org] by user [Uwe Langer|http://commons.wikimedia.org/wiki/User:Uwe_Langer]
* [NASA Johnson Space Center (NASA-JSC)|http://images.jsc.nasa.gov]
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