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{td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]*
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h2. Description and Assumptions

{excerpt}This model is [generally applicable|generally applicable model], but mathematically very complicated.  In introductory mechanics it will only be used to describe the motion of a gyroscope.{excerpt}


h2. Problem Cues

Only used in problems involving a gyroscope.

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h2. Prerequisite Knowledge

h4. Prior Models

* [1-D Angular Momentum and Torque]
* [Uniform Circular Motion]


h4. Vocabulary

* [torque (one-dimensional)]
* [angular momentum (one-dimensional)]

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h2. System

h4. Constituents

Technically, any number of [rigid bodies|rigid body].  In practice, only used in analyzing gyroscopes (single rigid body with a fixed pivot point).
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h2. Interactions

h4. Relevant Types

Only external torques result in a changing angular momentum.

h4. Interaction Variables

Torque (τ).

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h2. Model

h4. Definitions

Gyroscopic approximation (in this equation, _I_ is the moment of inertia of the gyroscope about the spin axis {latex}$\hat{\omega}${latex}): 
{latex}\begin{large}\[ \vec{L} \approx \vec{\omega} I\]\end{large}{latex}
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Angular frequency of gyroscopic precession:
{latex}\begin{large}\[\displaystyle  \Omega = \frac{\displaystyle \left(\frac{dL}{dt}\right)}{L} \]\end{large}{latex}

h4. Law of Change

Differential Form:
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{latex}\begin{large}\[\sum_{system}\frac{d\vec{L}^{sys}}{dt} = \sum_{external}\vec{\tau}^{ext}\]\end{large}{latex}
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h2. Diagrammatical Representations

* A delta-L diagram analogous to the [delta-v diagram] of [Uniform Circular Motion].

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h2. Relevant Examples

None yet.
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