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{td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]*
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Hello

h2. Description and Assumptions

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

h2. Problem Cues

This 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 as in collisions (impulse will be easier to determine than force).

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h2. Prerequisite Knowledge

h4. Prior Models

* [Point Particle Dynamics]

h4. Vocabulary

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

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h2. System

h4. Constituents

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.

h4. State Variables

Mass (_m{_}) and velocity (_v{_}) for each object or, alternately, the momentum (_p{_}) may be directly specified.

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h2. Interactions

h4. Relevant Types

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

h4. Interaction Variables

External forces (_F{_}{^}ext^) or, alternately, impulses may be specified (_J{_}{^}ext^).  

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h2. Model

h4. Relevant Definitions

{latex}\begin{large}\begin{alignat*}{1}& \vec{p} = m\vec{v}\\
 &\vec{p}^{\;\rm sys} = \sum_{\rm constituents} \vec{p} \end{alignat*}\end{large}{latex}

h4. Laws of Change

h5. Differential Form
{latex}\begin{large}\[ \frac{d\vec{p}^{\;\rm sys}}{dt} = \:\sum \vec{F}^{\;\rm ext} \]\end{large}{latex}
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h5. Integral Form
{latex}\begin{large}\[ \vec{p}^{\;\rm sys}_{f} = \vec{p}^{\;\rm sys}_{i} + \sum \vec{J}^{\;\rm ext} = \vec{p}^{\;\rm sys}_{i} + \int \sum \vec{F}^{\;\rm ext}\:dt  \]
\end{large}{latex}

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h2. Diagrammatical Representations

* [Free body diagram|free body diagram].
* [Initial-state final-state diagram].

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h2. Relevant Examples

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