By Zencalcy Editorial TeamLast reviewed About us
The equations of rotational motion mirror the linear SUVAT equations, with angle replacing distance, angular velocity replacing speed and angular acceleration replacing acceleration. They apply when angular acceleration is constant, which is a good approximation for many machines during a short interval.
Angular velocity and angle under constant angular acceleration.
ω_f = ω_i + α t θ = ω_i t + ½ α t²
ω is in rad/s, α in rad/s², t in seconds and θ in radians. For a time-free solution use ω_f² = ω_i² + 2αθ.
| Symbol | Meaning |
|---|---|
| ω_i, ω_f | Initial and final angular velocity, in rad/s. |
| α | Constant angular acceleration, in rad/s². |
| t | Time, in seconds. |
| θ | Angle turned, in radians. |
The final angular velocity is 0 + 5 × 4 = 20 rad/s, and the angle turned is ½ × 5 × 4² = 40 rad, just over six full turns.
Continue with the Rotational Power Calculator, SHM Acceleration Calculator, or the SHM Displacement Calculator — or browse more rotational and periodic motion tools and all physics calculators.
Only while angular acceleration stays constant. If torque varies, the motion must be integrated or split into short intervals.
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.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026