Wiki Markup |
---|
{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} {search-box} {td} {tr} {table} h2. Description and Assumptions {excerpt}This model is [generally applicable], but mathematically very complicated. In introductory mechanics it will only be used to describe the motion of a gyroscope.{excerpt} h2. Problem Cues Only used in problems involving a gyroscope. ---- || Page Contents || | {toc:style=none|indent=10px} | ---- h2. Prerequisite Knowledge h4. Prior Models * [1-D Angular Momentum and |
...
...
Torque]
* [Uniform Circular Motion]
h4. Vocabulary
* [torque (one-dimensional)]
* [angular momentum (one-dimensional)]
----
h2. System
h4. Constituents
A single [point particle|point particle] (or a system treated as a point particle with position specified by the center of mass).
h4. State Variables
Time (_t_), position (_x_) , and velocity (_v_).
----
h2. Interactions
h4. Relevant Types
Some time-varying external influence that is confined to one dimension.
h4. Interaction Variables
Acceleration (_a_(_t_)).
----
h2. Model
h4. Laws of Change
Differential Forms:
\\
\\
{latex}\begin{large}\[ \frac{dv}{dt} = a\]\end{large}{latex}\\
\\
{latex}\begin{large}\[ \frac{dx}{dt} = v\]\end{large}{latex}\\
\\
Integral Forms:
\\
{latex}\begin{large}\[ v(t) = v(t_{0})+\int_{t_{0}}^{t} a\;dt\]\end{large}{latex}\\
\\
{latex}\begin{large}\[ x(t) = x(t_{0})+\int_{t_{0}}^{t} v\;dt\]\end{large}{latex}\\
----
h2. Diagrammatical Representations
* Acceleration versus time graph.
* Velocity versus time graph.
* Position versus time graph.
----
h2. Relevant Examples
None yet.
----
{search-box}
\\
\\
| !copyright and waiver^copyrightnotice.png! | RELATE wiki by David E. Pritchard is licensed under a [Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License|http://creativecommons.org/licenses/by-nc-sa/3.0/us/]. | |