Connecting Angular Acceleration and Angular Displacement to Angular Velocity

You can connect angular displacement, angular velocity, and angular acceleration. The corresponding equation for linear motion is v_f² – v_o² = 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: