By Zencalcy Editorial TeamLast reviewed About us
Angular acceleration is the rotational counterpart of linear acceleration: the rate at which angular velocity changes. A motor that reaches its running speed quickly has a large angular acceleration even if its final speed is modest.
Rate of change of angular velocity.
α = (ω_f − ω_i) / t
α is angular acceleration in rad/s², ω_i and ω_f are the initial and final angular velocities and t is the time in seconds. The sign follows the direction of rotation.
| Symbol | Meaning |
|---|---|
| α | Angular acceleration, in rad/s². |
| ω_i, ω_f | Initial and final angular velocities. |
| t | Time over which the change occurs, in seconds. |
The change is 20 rad/s over 4 s, so α = 5 rad/s². If the same rotor then stopped in 2 s, the angular acceleration would be −10 rad/s².
Continue with the Angular Momentum Calculator, Angular Velocity Calculator, or the Circular Motion Period Calculator — or browse more rotational and periodic motion tools and all physics calculators.
A net torque. Newton's second law for rotation is τ = Iα, so the same torque produces less angular acceleration when the moment of inertia is larger.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Content updated: September 2026