}{composition-setup}
{excerpt:hidden=true}*System:* Any system can be treated as a [point particle] located at the [center of mass]. --- *Interactions:* Any.{excerpt}
{table:rules=cols|cellpadding=8|cellspacing=0|border=1|frame=void}
{tr:valign=top}{td:width=355px|bgcolor=#F2F2F2}
{live-template:Left Column}
{td}
{td}
h1. Point Particle Dynamics
h4. Description and Assumptions
This [model|model] is applicable to a [point particle] (or to a [system|system] of objects treated as a [point particle|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.
h4. Problem Cues
This [model|model] is typically applied to find the [acceleration|acceleration] in cases where the [forces|force] 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|model], such as when finding the [normal force|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]).
h4. Learning Objectives
Students will be assumed to understand this model who can:
* State and explain the significance of Newton's Laws of Motion.
* Define [normal force] and describe its relationship to [weight].
* Discriminate between [static|static friction] and [kinetic|kinetic friction] friction.
* Explain the role of the [coefficient of friction] in both the [kinetic|kinetic friction] and [static|static friction] cases.
* Construct a [free body diagram] for an object subject to [contact forces|contact force], [gravity|gravity (near-earth)], [elastic forces|Hooke's Law for elastic interactions], and/or [tension forces|tension].
* Construct and solve a system of equations describing the dynamics of more than one object that interact with one another.
h1. Model
h4. Compatible Systems
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. Relevant Interactions
[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. Law of Change
{latex}| Table Row (tr) |
|---|
| | Table Cell (td) |
|---|
Introduction to the ModelDescription and AssumptionsThis 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 ObjectivesStudents will be assumed to understand this model who can: S.I.M. Structure of the ModelCompatible SystemsA 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 InteractionsExternal 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 ChangeMathematical Representation |
|
\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}
h4. Diagrammatical Representations
* [Free Body Diagram|free body diagram]
h1. Relevant Examples
h4. {toggle-cloak:id=vec} Examples Involving Vector Components
{cloak:id=vec}
{contentbylabel:dynamics,vector_components|showSpace=false|showLabels=true|maxResults=50|exerpt=true|operator=AND}
{cloak}
h4. {toggle-cloak:id=norm} Examples Involving Normal Force
{cloak:id=norm}
{contentbylabel:dynamics,normal_force|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
{cloak}
h4. {toggle-cloak:id=appw} Examples Involving Apparent Weight
{cloak:id=appw}
{contentbylabel:dynamics,apparent_weight|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
{cloak}
h4. {toggle-cloak:id=tens} Examples Involving Tension
{cloak:id=tens}
{contentbylabel:dynamics,tension|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
{cloak}
h4. {toggle-cloak:id=incl} Examples Involving Inclined Planes
{cloak:id=incl}
{contentbylabel:dynamics,inclined_plane|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
{cloak}
h4. {toggle-cloak:id=stat} Examples Involving Static Friction
{cloak:id=stat}
{contentbylabel:dynamics,static_friction|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
{cloak}
h4. {toggle-cloak:id=kin} Examples Involving Kinetic Friction
{cloak:id=kin}
{contentbylabel:dynamics,kinetic_friction|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
{cloak}
h4. {toggle-cloak:id=cen} Examples Involving Centripetal Acceleration
{cloak:id=cen}
{contentbylabel:dynamics,centripetal_acceleration|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
{cloak}
h4. {toggle-cloak:id=all} All Examples Using this Model
{cloak:id=all}
{contentbylabel:dynamics,example_problem|showSpace=false|showLabels=true|maxResults=50|excerpt=true|operator=AND}
{cloak}
\\
\\
{search-box}
\\
\\
{td}
{td:width=235px}
!pull.jpg!
\\
\\
!helicopter.jpg!
\\
Photos courtesy:
[US Navy|http://www.navy.mil] by Mass Communication Specialist 3rd Class James R. Evans
[US Army|http://www.army.mil] by Spc. Michelle Waters
{td}
{tr}
{table}
{live-template:RELATE license}
\\
Diagrammatical RepresentationsRelevant Examples Examples Involving Vector Components | Cloak |
|---|
| | falsetrue50trueANDdynamics,vector_components |
Examples Involving Normal Force | Cloak |
|---|
| | falsetrue50trueANDdynamics,normal_force |
Examples Involving Apparent Weight | Cloak |
|---|
| | falsetrue50trueANDdynamics,apparent_weight |
Examples Involving Tension | Cloak |
|---|
| | falsetrue50trueANDdynamics,tension |
Examples Involving Inclined Planes | Cloak |
|---|
| | falsetrue50trueANDdynamics,inclined_plane |
Examples Involving Static Friction | Cloak |
|---|
| | falsetrue50trueANDdynamics,static_friction |
Examples Involving Kinetic Friction | Cloak |
|---|
| | falsetrue50trueANDdynamics,kinetic_friction |
Examples Involving Centripetal Acceleration | Cloak |
|---|
| | falsetrue50trueANDdynamics,centripetal_acceleration |
All Examples Using this Model | Cloak |
|---|
| | falsetrue50trueANDdynamics,example_problem |
|
| Table Cell (td) |
|---|
|  Image Added
 Image Added
Photos courtesy:
US Navy by Mass Communication Specialist 3rd Class James R. Evans US Army by Spc. Michelle Waters |
|
|