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 Excerpt
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System: Any system can be treated as a point particle located at the center of mass. — Interactions: Any.
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h2. Description and Assumptions

{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}
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Introduction to the Model
Description and Assumptions
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 External Force defined by the constraint dm/dt = 0.
Learning Objectives
Students will be assumed to understand this model who can:
S.I.M. Structure of the Model
Compatible Systems
A single point particle, or a system of constant mass that is treated as a point particle located at the system's center of mass.
Relevant Interactions
External forces must be understood sufficiently to draw a free body diagram for the system. Internal forces will always cancel from the equations of Newton's 2nd Law for the system and can be neglected.
Law of Change
Mathematical Representation
 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}
 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

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h2. Relevant Examples

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Diagrammatical Representations
Relevant Examples
 
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idvec
 Examples Involving Vector Components
 
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idvec
 falsetrue50trueANDdynamics,vector_components
 
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idnorm
 Examples Involving Normal Force
 
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idnorm
 falsetrue50trueANDdynamics,normal_force
 
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idappw
 Examples Involving Apparent Weight
 
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idappw
 falsetrue50trueANDdynamics,apparent_weight
 
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idtens
 Examples Involving Tension
 
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idtens
 falsetrue50trueANDdynamics,tension
 
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idincl
 Examples Involving Inclined Planes
 
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idincl
 falsetrue50trueANDdynamics,inclined_plane
 
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idstat
 Examples Involving Static Friction
 
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idstat
 falsetrue50trueANDdynamics,static_friction
 
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idkin
 Examples Involving Kinetic Friction
 
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idkin
 falsetrue50trueANDdynamics,kinetic_friction
 
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idcen
 Examples Involving Centripetal Acceleration
 
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idcen
 falsetrue50trueANDdynamics,centripetal_acceleration
 
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idall
 All Examples Using this Model
 
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idall
 falsetrue50trueANDdynamics,example_problem


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Image Added 

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Photos courtesy:
 US Navy by Mass Communication Specialist 3rd Class James R. Evans
US Army by Spc. Michelle Waters
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