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Introduction to the Model

Description and Assumptions

This model is applicable to a single rigid body that is rotating about a fixed axis or else both rotating and translating in such a way that its angular momentum is a one-dimensional vector (usually taken to lie along the z-axis). As a special case, this model is also useful to constrain the forces acting on a static rigid body. It is a subclass of the Angular Momentum and External Torque about a Single Axis model defined by the constraint that the system consists of only one rigid body which has a fixed mass and a fixed moment of inertia for rotations about the fixed axis or its center of mass.

Learning Objectives

Students will be assumed to understand this model who can:

S.I.M. Structure of the Model

Compatible Systems

One rigid body whose moment of inertia calculated about the chosen axis of rotation is constant.

Relevant Interactions

Only external torques need be considered, as internal torques do not produce angular accelerations. Since torque is needed, forces must be specified not only by their magnitude and direction, but also by either their point of application or moment arm with respect to the axis of rotation. Allowed choices of the axis of rotation will depend upon the specific
circumstances of the problem:

Laws of Change

Mathematical Representation
Diagrammatic Representations

Relevant Examples

Examples Involving a Fixed Axis
Examples Involving a Rotating and Translating Rigid Body
Examples Involving a Static Rigid Body
All Examples Using this Model








Photos courtesy:
Wikimedia Commons by Johann H. Addicks
U.S. Navy by Mass Communications Specialist 3rd Class Walter M. Wayman

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