[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
Technically, any number of rigid bodies. In practice, only used in analyzing gyroscopes (single rigid body with a fixed pivot point).
Interactions
Relevant Types
The weight of the gyroscope is assumed to be the only interaction that produces torque about the pivot point.
Interaction Variables
Torque (τ).
Model
Definitions
Gyroscopic approximation (in this equation, I is the moment of inertia of the gyroscope about the spin axis
\hat
):
\begin
[ \vec
\approx \vec
I]\end
Angular frequency of gyroscopic precession:
\begin
[ \Omega = \frac{\frac
{dt}}
]\end
Law of Change
Differential Form:
\begin
[ \frac{d\vec
^{sys}}
= \sum\vec
^
]\end
Diagrammatical Representations
- A delta-L diagram analogous to the Delta-v diagram of Uniform Circular Motion.
Relevant Examples
None yet.
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RELATE wiki by David E. Pritchard is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License |
