angular acceleration

Angular acceleration α is the rate at which angular velocity ω changes with time: α = dω/dt. For a body with angular velocity ω at one instant and ω + Δω a time Δt later, the average angular acceleration is Δω/Δt; the instantaneous value is the derivative. Units are radians per second squared (rad/s²).

In rigid-body mechanics angular acceleration stands to torque as linear acceleration stands to force: τ = I·α is the rotational version of Newton's second law, where I is the moment of inertia. A given torque produces more angular acceleration on a body with a smaller moment of inertia (e.g. a figure skater with arms drawn in versus arms out at the same applied muscle torque).

For rotational kinematics under constant angular acceleration, the formulas mirror linear kinematics: ω = ω₀ + α·t, θ = θ₀ + ω₀·t + ½·α·t², ω² = ω₀² + 2·α·Δθ. These are the equations engineers use to spin up flywheels, accelerate car wheels, and design electric motor starts. When α is not constant the integrals are done numerically or via energy methods.