Rotation & Angular Dynamics · Physics

Describe rotation with angles, rates, and a clear sign convention.

Rotational kinematics is the language of spinning motion: angular position, angular velocity, angular acceleration, and how they map onto linear motion at a distance from the axis.

This topic

Rotational Kinematics

Set up the coordinate choices first, then connect angles and angular rates to tangential motion.

Foundations

Angular position and reference axes

Define an angle relative to a chosen axis and a reference line. Good rotational work starts with a consistent coordinate choice.

Reference line, axis, and “zero angle”
Radians as the natural angular unit
Positive direction as a convention
Angles can wrap: treating them modulo 2π

Direction

Right-hand rule for rotation

The right-hand rule turns “clockwise vs counterclockwise” into a 3D direction. This is the bridge to torque and angular momentum later.

Thumb gives the axis direction
Fingers curl in the positive rotation sense
Relating sign of ω and α to the axis
Common pitfalls in diagrams and projections

Link

Relating angular and linear motion

Points on a rotating body have linear speed and acceleration that depend on their distance from the axis. Use the geometry to connect θ, ω, α to s, v, a.

Arc length: s = rθ (r in meters, θ in radians)
Tangential speed: v = rω
Tangential acceleration: a_t = rα
Centripetal acceleration: a_c = rω²

Practice

Practice & Exercises

Build fluency converting between angular and linear quantities and applying a consistent sign convention.

Radians, revolutions, and unit conversions
Sign convention and right-hand rule checks
Compute v and a for points at different radii
Separate tangential vs centripetal acceleration
Exam-style mixed kinematics prompts (rotation)