[Model Hierarchy]
Description and Assumptions
This model is [generally applicable], but mathematically very complicated. In introductory mechanics it will only be used to describe the motion of a gyroscope.
Problem Cues
Only used in problems involving a gyroscope.
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Prerequisite Knowledge
Prior Models
- [1-D Angular Momentum and Torque]
- Uniform Circular Motion
Vocabulary
- [torque (one-dimensional)]
- [angular momentum (one-dimensional)]
System
Constituents
A single point particle (or a system treated as a point particle with position specified by the center of mass).
State Variables
Time (t), position (x) , and velocity (v).
Interactions
Relevant Types
Some time-varying external influence that is confined to one dimension.
Interaction Variables
Acceleration (a(t)).
Model
Laws of Change
Differential Forms:
\begin
[ \frac
= a]\end
\begin
[ \frac
= v]\end
Integral Forms:
\begin
[ v(t) = v(t_
)+\int_{t_{0}}^
a\;dt]\end
\begin
[ x(t) = x(t_
)+\int_{t_{0}}^
v\;dt]\end
Diagrammatical Representations
- Acceleration versus time graph.
- Velocity versus time graph.
- Position versus time graph.
Relevant Examples
None yet.
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