[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.
Page Contents |
|---|
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), the distance from the pivot point to the center of mass (R) and the angle of inclination of the axle above the horizontal (θ).
Interactions
Relevant Types
The weight of the gyroscope is assumed to be the only interaction that produces torque about the pivot point.
Interaction Variables
Weight (W).
Model
Laws of Change
Differential Forms:
Diagrammatical Representations
- A delta-L diagram analogous to the Delta-v diagram of Uniform Circular Motion.
Relevant Examples
None yet.
null |
RELATE wiki by David E. Pritchard is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License |
