Angular Kinematics
ω = ω₀ + αt, θ = ω₀t + ½αt² — see disk spin with live ω(t) and θ(t) plots.
Key Notes
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.
Formulas
Angular velocity
Rate of change of angular position.
Angular acceleration
Rate of change of ω.
Constant α kinematics
Direct analog of v = u + at.
Linear-angular link
Tangential vs centripetal acceleration.
Important Points
Angular kinematics is structurally identical to linear — just replace symbols.
ω in rad/s, NOT rpm or rev/s. Convert: ω(rad/s) = 2π × rev/s = (π/30) × rpm.
All points of a rigid body share the SAME ω and α; their linear v and a differ by their distance r from axis.
Centripetal acceleration always exists in circular motion (a_c = rω²). Tangential acceleration only if α ≠ 0.
Direction of ω is along the rotation axis (right-hand rule).
Period T = 2π/ω. Frequency f = ω/(2π) = 1/T.
Angular Kinematics notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.