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_{f}^{2} – v_{o}^{2} = 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

A merrygoround slows down from 6.5 radians/s to 2.5 radians/s, undergoing an angular acceleration of 1.0 radians/s^{2}. How many radians does the merrygoround go through while this is happening?
The correct answer is 18 radians.

Start with the equation:

Solve for theta:

Plug in the numbers:

Practice questions

A helicopter’s blades are speeding up. They go from 60 radians/s to 80 radians/s.
If the angular acceleration is 10 radians/s^{2}, what is the total angle the blades have gone through?

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/s^{2}, what is the total angle the ball has gone through during this acceleration?
Following are answers to the practice questions:

140 radians

Use this equation:

Solve for theta:

Plug in the numbers:


11 radians

Use this equation:

Solve for theta:

Plug in the numbers:
