Final angular velocity, angular displacement and revolutions for rotation at constant angular acceleration.
Constant angular acceleration only, for a rigid body spinning about a fixed axis. One revolution equals 2π radians.
Final angular velocity
How to use this tool
Type the initial angular velocity in radians per second — use 0 for a wheel starting from rest.
Enter a positive value for speeding up or a negative value for slowing down, in rad/s².
Enter how many seconds the acceleration acts for.
The headline result is the final angular velocity, with total displacement, revolutions and average velocity below.
Formula & worked example
A wheel starting from rest with angular acceleration 2 rad/s² reaches 10 rad/s after 5 seconds, having turned through 25 radians — about 3.98 revolutions.
Limitations — read this before you rely on it
This is the constant-acceleration model for a rigid body about a fixed axis. It ignores friction, changing torque and flexible-body effects, so real spin-up may differ slightly.
Frequently asked questions
It is the rate of rotation, measured in radians per second. One full revolution per second equals 2π ≈ 6.28 rad/s.
Multiply rpm by 2π/60 (about 0.10472). So 100 rpm is about 10.47 rad/s.
Yes — a negative value means the rotation is slowing down, exactly like linear deceleration.
Then this simple model does not apply; the motion must be integrated over time with the varying torque.
It is the total angle turned, in radians. Divide by 2π to get revolutions, or multiply by 180/π for degrees.