Connecting Angular Acceleration and Angular Displacement to Angular Velocity

By Steven Holzner

You can connect angular displacement, angular velocity, and angular acceleration. The corresponding equation for linear motion is vf2vo2 = 2as. Substituting omega for v, alpha for a, and theta for s gives you:


Use this equation when you want to relate angle to angular velocity and angular acceleration.

Sample question

  1. A merry-go-round slows down from 6.5 radians/s to 2.5 radians/s, undergoing an angular acceleration of 1.0 radians/s2. How many radians does the merry-go-round go through while this is happening?

    The correct answer is 18 radians.

    1. Start with the equation:


    2. Solve for theta:


    3. Plug in the numbers:


Practice questions

  1. A helicopter’s blades are speeding up. They go from 60 radians/s to 80 radians/s.

    If the angular acceleration is 10 radians/s2, what is the total angle the blades have gone through?

  2. Your ball on a string is traveling around in a circle.

    If it goes from 12 radians/s to 24 radians/s and the angular acceleration is 20 radians/s2, what is the total angle the ball has gone through during this acceleration?

Following are answers to the practice questions:

  1. 140 radians

    1. Use this equation:


    2. Solve for theta:


    3. Plug in the numbers:


  2. 11 radians

    1. Use this equation:


    2. Solve for theta:


    3. Plug in the numbers: