h2. Keys to Applicability
{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 point particle (or to a system of objects treated as a point particle located at the system's center of mass) when the external forces are known or needed.  It is a subclass of the model [Momentum and Impulse] defined by the constraint _dm/dt_ = 0.{excerpt}
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h2. Assumptions and Limitations

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

h4. Vocabulary
* [Newton's First Law]
* [Newton's Second Law]
* [Newton's Third Law]
* [mass]
* [acceleration]
* [force]

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h2. Model Specification

h4. System Schema

*[Constituents|system constituent]:* [Point particle|point particle]. 

*[Interactions|interaction]:* External influences must be understood sufficiently to draw a [free body diagram] for the system.

h4. Descriptors

*[Object Variables|object variable]:* {latex}\begin{large}\[m\]\end{large}{latex}.

*[State Variables|state variable]:* None.

*[Interaction Variables|interaction variable]:* {latex}\begin{large}\[\vec{F}^{\rm ext}_{i}\]\end{large}{latex} (i = 1,2,...,n where n is the number of external forces acting), {latex}\begin{large}\[\vec{a}\]\end{large}{latex}.

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h2. Model Equations

h4. Mathematical Statement of the Model

{latex}\begin{large} \[ \sum_{i} \vec{F}^{\rm ext}_{i} = m\vec{a} \]  \end{large} {latex}

{note}As with all vector equations, this Law of Interaction should really be understood as three simultaneous equations:\\

{latex}\begin{large}\[ \sum_{i} F^{\rm ext}_{i,x} = ma_{x}\]
\[ \sum_{i} F^{\rm ext}_{i,y} = ma_{y}\]
\[\sum_{i} F^{\rm ext}_{i,z} = ma_{z}\]\end{large}{latex}{note}

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h2. Relevant Examples

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