Angular Momentum and Torque

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[Model Hierarchy]

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The root page Model Hierarchy could not be found in space Modeling Applied to Problem Solving.

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Description and Assumptions

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

Problem Cues

Only used in problems involving a gyroscope.

Page Contents
Description and Assumptions Problem Cues Prerequisite Knowledge Prior Models Vocabulary System Constituents State Variables Interactions Relevant Types Interaction Variables Model Law of Change Diagrammatical Representations Relevant Examples

Prerequisite Knowledge

Prior Models

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

Vocabulary

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

System

Constituents

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

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).

Interactions

Relevant Types

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

Interaction Variables

Torque (τ).

Model

Law of Change

Differential Form:

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\begin

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[ \frac{d\vec{L}}

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= \sum\vec

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]\end

Diagrammatical Representations

A delta-L diagram analogous to the Delta-v diagram of Uniform Circular Motion.

Relevant Examples

None yet.