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{table:align=right|cellspacing=0|cellpadding=1|border=1|frame=box|width=40%} {tr} {td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]* {td} {tr} {tr} {td} {pagetree:root=Model Hierarchy|reverse=true} {search-box} {td} {tr} {table} h2. 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. h2. Problem Cues Only used in problems involving a gyroscope. ---- || Page Contents || | {toc:style=none|indent=10px} | ---- h2. Prerequisite Knowledge h4. Prior Models * [1-D Angular Momentum and Torque] * [Uniform Circular Motion] h4. Vocabulary * [torque (one-dimensional)] * [angular momentum (one-dimensional)] ---- h2. System Technically, any number of [rigid bodies|rigid body]. In practice, only used in analyzing gyroscopes (single rigid body with a fixed pivot point). ---- h2. Interactions Only external torques need be considered. Internal torques do not change the system's angular momentum. ---- 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} \\ 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: \\ {latex}\begin{large}\[\sum_{\rm system}\frac{d\vec{L}}{dt} = \sum_{\rm external}\vec{\tau}\]\end{large}{latex} \\ ---- h2. Diagrammatic Representations * A delta-L diagram analogous to the [Delta-v diagram] of [Uniform Circular Motion]. ---- h2. Relevant Examples None yet. ---- {search-box} \\ \\ | !copyright and waiver^copyrightnotice.png! | RELATE wiki by David E. Pritchard is licensed under a [Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License|http://creativecommons.org/licenses/by-nc-sa/3.0/us/]. |
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System: Any. — Interactions: Any. — Note: This difficult model is only used for gyroscopes.
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Angular Momentum and External Torque
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 Description and Assumptions
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This model is generally applicable, but mathematically very complicated. In introductory mechanics it will only be used to describe the motion of a gyroscope.
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 Problem Cues
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Only used in problems involving a gyroscope.
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 Prior Models
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 Vocabulary
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Model
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Technically, any number of rigid bodies. In practice, only used in analyzing gyroscopes (single rigid body with a fixed pivot point).
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 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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 Relevant Definitions
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 Law of Change
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  • A delta-L diagram analogous to the  of .
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