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Angular Momentum and External Torque
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.
Prior Models
Vocabulary
Model
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.
Relevant Definitions
Gyroscopic Approximation
The gyroscopic approximation assumes that the angular momentum due to precession of the gyroscope is negligible compared to the angular momentum of the spinning gyroscope. If Ω is the angular velocity of precession and ω is the angular velocity of the gyroscope's spin, then the gyroscopic approximation holds when
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and
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I is the moment of inertia of the gyroscope about the spin axis
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See Spinning Top and Delta-v diagram for more details.
Angular Frequency of Gyroscopic Precession
Under the gyroscopic approximation, the angular velocity of the precession is given by Ω
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This result is independent of the tipping angle of the gyroscope.
Law of Change
Differential Form
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Diagrammatic Representations
Relevant Examples
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Photos courtesy:
Wikimedia Commons by user Kiko2000
NASA
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