h1. Description and Assumptions
{excerpt:hidden=true}*System:* Any. --- *Interactions:* Any. --- *Note:* This difficult model is only used for [gyroscopes|gyroscope].{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.
h1. Problem Cues
Only used in problems involving a gyroscope.
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h1. Prerequisite Knowledge
h3. Prior Models
* [1-D Angular Momentum and Torque]
* [Uniform Circular Motion]
h3. Vocabulary
* [torque (one-dimensional)]
* [angular momentum (one-dimensional)]
h1. Compatible Systems
Technically, any number of [rigid bodies|rigid body]. In practice, only used in analyzing gyroscopes (single rigid body with a fixed pivot point).
h1. Relevant Interactions
Only external torques need be considered. Internal torques do not change the system's angular momentum.
h1. Model
h3. Definitions
h6. Gyroscopic approximation (in this equation, Approximation
{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}):
{latex}\begin{large}\[ \vec{L} \approx \vec{\omega} I\]\end{large}{latex}
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Angular frequency of gyroscopic precession:\
h6. Angular Frequency of Gyroscopic Precession
{latex}\begin{large}\[\displaystyle \Omega = \frac{\displaystyle \left(\frac{dL}{dt}\right)}{L} \]\end{large}{latex}
h3. Law of Change
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. Diagrammatic Representations
* A delta-L diagram analogous to the [Delta-v diagram] of [Uniform Circular Motion].
h1. Relevant Examples
None yet.
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