Versions Compared

Old Version 18

changes.mady.by.user Andrew E Pawl

Saved on

compared with

New Version Current

changes.mady.by.user David E Pritchard

Saved on

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.
Comment: Migration of unmigrated content due to installation of a new plugin
{
Wiki Markup
Composition Setup
 HTML Table
border1
cellpadding8
cellspacing0
rulescols
framevoid
}{composition-setup}
{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. Motion, Acceleration and Net Force
{excerpt:hidden=true}*System:* One [point particle|point particle]. --- *Interactions:* Any.{excerpt}

h4. {toggle-cloak:id=desc} Description and Assumptions

{cloak:id=desc}
This model is technically applicable to any [point particle] system.  In practice, however, the vector equations in this model are usually split into three one-dimensional equations, so that the [One-Dimensional Motion (General)] model is nearly as general, and more easily used.
{cloak}

h4. {toggle-cloak:id=cues} Problem Cues

{cloak:id=cues}

This model is rarely needed in introductory mechanics, and is presented principally for intellectual completeness of the hierarchy.

{cloak}

h4. {toggle-cloak:id=prior} Prior Models

{cloak:id=prior}

* [1-D Motion (Constant Velocity)]
* [1-D Motion (Constant Acceleration)]
* [One-Dimensional Motion (General)]

{cloak}

h4. {toggle-cloak:id=vocab} Vocabulary

{cloak:id=vocab}

* [position]
* [velocity]
* [acceleration]

{cloak}

h2. Model

h4. {toggle-cloak:id=sys} {color:red}Compatible Systems{color}

{cloak:id=sys}

A single [point particle|point particle] (or a system treated as a point particle with position specified by the center of mass).

{cloak}

h4. {toggle-cloak:id=int} {color:red}Relevant Interactions {color}

{cloak:id=int}

Only knowledge of the [net|net force] [external force|external force] is required to determine the motion of the system.

{cloak}

h4. {toggle-cloak:id=laws} {color:red} Laws of Change {color}

{cloak:id=laws}

{section}{column}
h5. Differential Forms
{latex}
 Table Row (tr)
valigntop
 Table Cell (td)
 Excerpt
hiddentrue
System: One point particle. — Interactions: Any.
Description and Assumptions
This model is technically applicable to any point particle moving in three dimensions, and involves vector calculus. Except for circular and rotational motion, however, one generally treats the vectors in Cartesian coordinates, so they split into three one-dimensional equations, allowing a solution with three applications of the One-Dimensional Motion (General) model.
Problem Cues
This model is needed only for problems that clearly involve motion in three dimensions, and is not often used in introductory mechanics.
Model
Compatible Systems
A single point particle (or a system treated as a point particle with position specified by the center of mass).
Relevant Interactions 
Only knowledge of the net external force is required to determine the acceleration of the system. 
Laws of Change
The laws of change are simply the laws of calculus for vectors. 
 Section
 Column
Differential Forms
 Latex
\begin{large}\[ \frac{d\vec{v}}{dt} = \vec{a}\]\end{large}
{


 Latex
}\\
\\
{latex}\
\begin{large}\[ \frac{d\vec{x}}{dt} = \vec{v}\]\end{large}
{latex}\\
\\
{column}{column}{color:white}


 Column
_____
{color}{column}{column}
h5. Integral Forms
{latex}
 Column
Integral Forms
 Latex
\begin{large}\[ \vec{v}(t) = \vec{v}(t_{0})+\int_{t_{0}}^{t} \vec{a}\;dt\]\end{large}
{latex}\\
\\
{latex}\


 Latex
\begin{large}\[ \vec{x}(t) = \vec{x}(t_{0})+\int_{t_{0}}^{t} \vec{v}\;dt\]\end{large}
{latex}\\
{column}{section}

{cloak}

h2. Relevant Examples

None yet.
\\
\\
\\
{search-box}
\\
\\
{td}
{tr}
{table}

{live-template:RELATE license}

Relevant Examples
None yet. 


 Search Box