You can connect angular displacement, angular velocity, and angular acceleration. The corresponding equation for linear motion is vf2 – vo2 = 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 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.
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/s2, 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/s2, 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:
