[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
Only external torques result in a changing angular momentum.
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
[\displaystyle \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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