You can connect angular displacement, angular velocity, and angular acceleration. The corresponding equation for linear motion is *v*_{f}^{2} – *v*_{o}^{2} = 2*as**. *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 merry-go-round 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 merry-go-round 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: