Rotation & Angular Dynamics · Physics

Model a spinning object as one connected whole.

In a rigid body, distances between points stay fixed. That lets one angular description (θ, ω, α) determine the motion of every point on the object.

This topic

Rigid Body Rotation

Understand what “rigid” means, then learn how fixed-axis rotation connects rotational and translational motion.

Definition

What makes a body “rigid”

A rigid body keeps fixed distances between all pairs of points. It’s an idealization that is excellent when deformations are small.

Rigid vs deformable: what is ignored
When the approximation is valid in practice
Internal forces can be complex but cancel in many balances
Why rigidity simplifies rotational motion descriptions

Fixed axis

Rotation about a fixed axis

When the axis is fixed in space, every point moves in a circle around that axis. One angular coordinate describes the whole body.

All points share the same θ, ω, α
Different radii produce different linear speeds
Identifying the axis in diagrams and real devices
Common examples: wheels, disks, pulleys

Compare

Rotation vs particle motion

Particle kinematics tracks one point. Rigid-body rotation tracks many points linked together, so geometry matters as much as time-dependence.

Particle: x(t) or r(t) for one point
Rigid body: one θ(t) describes many points
Why r enters linear quantities (v = rω)
Separating tangential and radial accelerations

Link

Translational vs rotational motion

Many real motions combine translation and rotation. Learn the core idea: you can describe a rigid body as a translation of a reference point plus a rotation about that point.

Center of mass translation + rotation about COM
Rolling: combining forward motion and spin
Instantaneous center of rotation (intro idea)
Choosing a convenient point for analysis

Practice

Practice & Exercises

Practice identifying axes, applying rigid-body assumptions, and converting rotational descriptions into point-by-point linear motion.

Identify fixed axes in diagrams and devices
Compute v and a at different radii for a given ω, α
Describe combined translation + rotation scenarios
Spot when “rigid” is a good approximation
Exam-style rigid-body rotation prompts