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h2. Description
{table:align=right|cellspacing=0|cellpadding=1|border=1|frame=box|width=40%}{tr}{td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]*{td}{tr}{tr}{td}{pagetree:root=Model Hierarchy|reverse=true}{td}{tr}{table}
{excerpt}This model is applicable to a system of [point particles|point particle] (or [rigid bodies|rigid body] treated as point particles located at the position of the body's center of mass).{excerpt}
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h2. Assumed Knowledge

h4. Prior Models
* [Point Particle Dynamics]
* [One-Dimensional Motion with Constant Acceleration|1-D Motion (Constant Acceleration)]

h4. Vocabulary
* [force]
* [impulse]
* [momentum]
* [acceleration]

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h2. Model Specification

h4. System Structure

Internal Constituents:  [Point particles|point particle].
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Environment:   Only [external forces|external force] need be considered, since [internal forces|internal force] do not change the system momentum.

h4. Descriptors

Object Variables:  Mass for each object (_m_^j^), unless momentum is given directly.

State Variables:   Velocity (_v_^j^) or momentum (_p_^j^) for each object.

Interaction Variables:   External forces (_F_~ext,k~) or, alternately, impulses may be specified (_J_~ext,k~).

h4. Laws of Interaction

{latex}\begin{large}\[ \vec{J}_{ext,k} = \int \vec{F}_{ext,k}\:dt \]
\[ \frac{d\vec{p}_{\rm system}}{dt} = \:\sum_{k=1}^{N_{F}} \vec{F}_{ext,k} \]
\[ \vec{J}_{ext,k} = \int \vec{F}_{ext,k}\:dt \]\end{large}{latex}


where the system momentum is the vector sum of the constituent momenta:

{latex}\begin{large}\[ \vec{p}_{\rm system} = \sum_{j=1}^{N} \vec{p}^{j} \]\end{large}{latex}

where _N_ is the number of system constituents.

h4. Laws of Change

{latex}\begin{large}\[ \vec{p}_{\rm system,f} = \vec{p}_{\rm system,i} + \sum_{k=1}^{N_{F}} \vec{J}_{ext,k} \]\end{large}{latex}

where the system momentum is the (vector) sum of the constituent momenta:

{latex}\begin{large}\[ \vec{p}_{\rm system} = \sum_{j=1}^{N_{const}} \vec{p}^{j}\]\end{large}{latex}

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h2. Relevant Examples

{contentbylabel:example_problem,momentum_force|showSpace=false|showLabels=true|excerpt=true|operator=AND|maxResults=50}
{contentbylabel:example_problem,constant_momentum|showSpace=false|showLabels=true|excerpt=true|operator=AND|maxResults=50}
{contentbylabel:example_problem,impulse|showSpace=false|showLabels=true|excerpt=true|operator=AND|maxResults=50}


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