Angular Kinematics

Angular kinematics describes rotation: θ (angle), ω (angular velocity), α (angular acceleration).

Same form as linear kinematics with substitutions: x → θ, v → ω, a → α.

Units: θ (rad), ω (rad/s), α (rad/s²). 1 rev = 2π rad = 360°.

For uniform angular acceleration: ω = ω₀ + αt; θ = ω₀t + ½αt²; ω² = ω₀² + 2αθ.

Linear-angular relations (for rigid body, distance r from axis): v = rω, a_tangential = rα, a_centripetal = rω² = v²/r.

Total acceleration of a point in circular motion: a = √(a_t² + a_c²).

Sign convention: counter-clockwise positive (by right-hand rule, ω points along rotation axis).

Used in: rotating machinery, wheels, planets, gyroscopes.