Angular velocity
Rate of rotation, measured in radians per second: ω = dθ/dt. A vector aligned with the rotation axis (right-hand rule).
Definition
Angular velocity ω describes how fast something rotates. For a point moving in a circle of radius r, the linear speed and angular speed are locked by v = ωr — a single revolution covers 2πr in 2π radians. The connection is geometric, not dynamical: it holds whether the rotation is caused by gravity, a motor, a spring, or nothing at all.
Angular velocity carries a direction as well as a magnitude. By convention the vector ω points along the rotation axis, with sign given by the right-hand rule: curl the fingers of your right hand in the direction of rotation, and the thumb points along ω. For planar motion (a spinning record, a wheel on a car) the vector reduces to a single signed scalar along the axis perpendicular to the plane.
Newton's laws in their most familiar form (F = ma) refer to linear motion, but a parallel set of equations governs rotation: τ = Iα relates torque to angular acceleration exactly the way F = ma relates force to linear acceleration. Angular velocity is the rotational cousin of linear velocity, and most of the machinery of circular motion — centripetal acceleration ω²r, rotational kinetic energy ½Iω², angular momentum Iω — lives in its shadow.