Work out angular displacement instantly with clear inputs, formula shown and shareable results.
Rotational kinematics mirrors the linear case with angle replacing distance: theta = omega.t + alpha.t^2/2. Spinning up from 10 rad/s at 2 rad/s2 for 5 s sweeps 75 rad, which is just under 12 full turns, and ends at 20 rad/s. Dividing by 2 pi converts radians into revolutions.
Angular displacement
theta = omega x t + 0.5 alpha t^2
Revolutions
revolutions = theta / (2 pi)
Because arc length is simply r.theta in radians. Degrees would inject a conversion factor into every formula.
Multiply the angular displacement in radians by the radius.