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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)]
Compatible Systems
Technically, any number of rigid bodies. In practice, only used in analyzing gyroscopes (single rigid body with a fixed pivot point).
Relevant Interactions
Only external torques need be considered. Internal torques do not change the system's angular momentum.
Model
Definitions
Gyroscopic Approximation
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\begin
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[ \vec
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\approx \vec
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I]\end
(I is the moment of inertia of the gyroscope about the spin axis
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$\hat
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$
)
Angular Frequency of Gyroscopic Precession
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\begin
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[\displaystyle \Omega = \frac{\displaystyle \left(\frac
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\right)}
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]\end
Law of Change
Differential Form
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\begin
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[\sum_
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\frac{d\vec{L}}
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= \sum_
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\vec
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]\end
Diagrammatic Representations
- A delta-L diagram analogous to the Delta-v diagram of Uniform Circular Motion.
Relevant Examples
None yet.
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