h2. Description and Assumptions

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{excerpt:hidden=true}*System:* Any system can be treated as a [point particle] located at the [center of mass]. --- *Interactions:* Any.{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 a subclass of the model [Momentum and External Force] defined by the constraint _dm/dt_ = 0.

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, such as when finding the normal force exerted on a passenger in a roller coaster at the top of a loop-the-loop (in which case, it would be combined with [Mechanical Energy and Non-Conservative Work]).

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h2. Prerequisite Knowledge

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. System

h4. Constituents

A single [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.

h4. State Variables

Mass (_m_) (must be constant in this model).

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h2. Interactions

h4. Relevant Types

[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. Interaction Variables

External forces (_F_^ext^), acceleration (_a_).

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h2. Model

h4. Law of Change

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

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

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

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h2. Diagrammatical Representations

* [Free body diagram|free body diagram].

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h2. Relevant Examples

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