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[Model Hierarchy]

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The root page Model Hierarchy could not be found in space Modeling Applied to Problem Solving.
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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)]

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

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$\hat

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$

):

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\begin

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[ \vec

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\approx \vec

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I]\end


Angular frequency of gyroscopic precession:

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\begin

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[\displaystyle \Omega = \frac{\displaystyle \frac

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{dt}}

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]\end

Law of Change

Differential Form:

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\begin

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[\frac{d\vec

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^{sys}}

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= \sum\vec

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^

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]\end



Diagrammatical Representations


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.

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