[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), axial angular momentum (L), axial angular velocity (ω), precessional angular velocity (Ω), axial moment of inertia (I), mass (m).
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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