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{excerpt:hidden=true}*System:* Any. --- *Interactions:* Any. --- *Note:* This difficult model is only used for [gyroscopes|gyroscope].{excerpt}


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h2h1. Angular DescriptionMomentum and AssumptionsExternal Torque

{excerpt:hidden=true}*System:* Any. --- *Interactions:* Any. --- *Note:* This difficult model is only used for [gyroscopes|gyroscope].{excerpt}
h4. {toggle-cloak:id=desc} Description and Assumptions

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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.
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h2h4. {toggle-cloak:id=cues} Problem Cues

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Only used in problems involving a gyroscope.

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h1. Prerequisite Knowledge

h3. Prior Models{cloak}

h4. {toggle-cloak:id=pri} Prior Models

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

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h4. {toggle-cloak:id=vocab} Vocabulary

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


h1.{cloak}

h2. Model

h4. {toggle-cloak:id=sys} Compatible Systems

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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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h4. {toggle-cloak:id=int} Relevant Interactions

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Only external torques need be considered.  Internal torques do not change the system's angular momentum.
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h1. Model

h3.h4. {toggle-cloak:id=def} Relevant Definitions

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h6. Gyroscopic Approximation 
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{latex}\begin{large}\[ \vec{L} \approx \vec{\omega} I\]\end{large}{latex}
(_I_ is the moment of inertia of the gyroscope about the spin axis {latex}$\hat{\omega}${latex})
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h6. Angular Frequency of Gyroscopic Precession
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{latex}\begin{large}\[\displaystyle  \Omega = \frac{\displaystyle \left(\frac{dL}{dt}\right)}{L} \]\end{large}{latex}
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h3.h4. {toggle-cloak:id=law} Law of Change

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h6. Differential Form
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{latex}\begin{large}\[\sum_{\rm system}\frac{d\vec{L}}{dt} = \sum_{\rm external}\vec{\tau}\]\end{large}{latex}
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h1.h4. {toggle-cloak:id=diag} Diagrammatic Representations

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* 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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