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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.


Page Contents

Prerequisite Knowledge

Prior Models

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

Relevant Examples

None yet.


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