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h2. KeysDescription toand ApplicabilityAssumptions

{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|external force] are known or needed.  It is often a subclass of the model [Momentum and Impulse] defined by the constraint _dm/dt_ = 0.{excerpt}

h2. Problem Cues

This model is typically applied to find the acceleration in cases where the forces will remain constant, such as an object moving along a flat surface like a ramp or a wall.  It is also useful in combination with other models, thatsuch requireas quantitativewhen knowledgefinding ofthe forcesnormal forforce theirexerted application.on a Itpassenger isin a subclass roller coaster at the top of a loop-the model [Momentum and Impulse] defined by the constraint _dm/dt_ = 0.{excerpt}-loop (in which case, it would be combined with [Mechanical Energy and Non-Conservative Work]).

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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], or a system of constant mass that is treated as a point particle located at the system's center of mass.

*[Interactions|interaction]:* [External forces|external force] must be understood sufficiently to draw a [free body diagram] for the system.  [Internal forces|internal force] will always cancel from the equations of Newton's 2nd Law for the system and can be neglected.

h4. Descriptors

*[State Variables|state variable]:* Mass (_m_) (must be constant in this model).

*[Interaction Variables|interaction variable]:* External forces _F_^ext^~k~ (k = 1,2,...,N where N is the number of external forces acting), acceleration (_a_).

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h2. Model Equations

h4. Mathematical Statement of the Model

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

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

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

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h2. Relevant Examples

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