Rotation and Translation of a Rigid Body

Description

This model is applicable to a single rigid body constrained to move only in a plane (taken to be the xy plane). Such a motion can generically be divided into a sum of pure translation of the center of mass and pure rotation about an axis that is perpendicular to the plane of motion and passes through the center of mass. (Thus, this model is essentially a combination of Point Particle Dynamics and [Fixed-Axis Rotation of a Rigid Body].) It is a subclass of the [1-D Angular Momentum and Torque] model defined by the constraint that the system consists of only one rigid body.

Assumed Knowledge

Prior Models

• Point Particle Dynamics
• [Fixed-Axis Rotation of a Rigid Body]

Vocabulary

• force
• free body diagram
• [torque]

Model Specification

System Structure

Internal Constituents:  One rigid body.
Environment:  Forces must be specified not only by their magnitude and direction, but also by either their point of application or [lever arm] with respect to the center of mass of the rigid body.

Descriptors

Object Variables:  Mass (m), moment of inertia about the center of mass (I_cm). The moment of inertia may not be explicitly given, but there must be sufficient information to calculate it (often the mass plus some parameters of the rigid body's shape such as radius, length, etc.).

State Variables:  None.

Interaction Variables:  Acceleration of the center of mass (a_cm), angular acceleration about the center of mass (α_cm), forces (F) and torques about the center of mass (τ_cm).

Laws of Interaction

Laws of Change

None.

Relevant Examples