angular acceleration
Angular acceleration measures how quickly a spin rate is changing — the rotational version of ordinary acceleration. When you flick a ceiling fan on and its blades climb from still to a fast whir, or when a bicycle wheel gradually slows to a stop, its angular velocity is changing over time, and angular acceleration is the number that captures how fast that change happens.
Precisely, it is the rate of change of angular velocity: the average is alpha = delta-omega / delta-t, and the instantaneous value is the derivative domega/dt; the units are radians per second squared (rad/s^2). Just as force causes linear acceleration, a net torque (a twist) causes angular acceleration. And it links to the everyday acceleration of a point on the object: a point a distance r from the axis has a tangential acceleration a_t = r alpha.
Watch out for a common mix-up: even an object spinning at a perfectly steady rate — zero angular acceleration — still has its individual points accelerating, because their velocity keeps changing direction (that is centripetal acceleration, a different thing). Angular acceleration is only about the spin rate itself speeding up or slowing down.
A fan spins up from rest to 60 rad/s in 4 seconds at a steady rate. Its angular acceleration is alpha = delta-omega / delta-t = 60 / 4 = 15 rad/s^2.
Angular acceleration is positive while spinning up and negative while slowing down.
Zero angular acceleration means a constant spin rate — but a point on the object is still accelerating toward the centre; that centripetal acceleration is separate.