Connecting Angular Acceleration and Angular Displacement to Angular Velocity - dummies

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:

image0.png

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:

      image1.png

    2. Solve for theta:

      image2.jpg

    3. Plug in the numbers:

      image3.jpg

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:

      image4.png

    2. Solve for theta:

      image5.jpg

    3. Plug in the numbers:

      image6.jpg

  2. 11 radians

    1. Use this equation:

      image7.png

    2. Solve for theta:

      image8.jpg

    3. Plug in the numbers:

      image9.jpg