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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

A single [point particle|point particle] (or a system treated as a point particle with position specified by the center of mass).

h4. State Variables

Time (_t_), axial angular momentum (_L_), axial angular velocity (ω), precessional angular velocity (Ω), axial moment of inertia (_I_), mass (_m_), the distance from the pivot point to the center of mass (_R_) and the angle of inclination of the axle above the horizontal (θ).

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h2. Interactions

h4. Relevant Types

The weight of the gyroscope is assumed to be the only interaction that produces torque about the pivot point.

h4. Interaction Variables

Torque (τ).

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h2. Model

h4. Law of Change

Differential Form:
\\
{latex}\begin{large}\[ \frac{d\vec{L}^{sys}}{dt} = \sum\vec{tau}^{ext}\]\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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