How this calculator works
Average angular acceleration is the signed change in angular velocity divided by elapsed time. Tangential acceleration is the same angular acceleration multiplied by distance from the axis. The endpoint equations describe constant acceleration, or an average over the interval. Choose one positive rotation direction and retain signs when an object slows or reverses.
Formula
alpha = (omega_f - omega_i)/t; a_t = alpha r. Angular velocities are converted to rad/s before calculation.
Worked example
An increase from 2 to 14 rad/s in 3 s gives 4 rad/s². A tangential acceleration of 6 m/s² at radius 2 m gives 3 rad/s².
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Frequently asked questions
Can angular acceleration be negative?
Yes. Its sign indicates direction, so negative acceleration can slow positive rotation or speed up negative rotation.
Is tangential acceleration centripetal acceleration?
They are perpendicular components. Tangential acceleration changes speed; centripetal acceleration changes direction.
What if the angular speed does not change?
Average angular acceleration is zero. Solving elapsed time from zero acceleration and zero speed change is indeterminate.