Relating Linear and Angular Motion

In physics, just as you can use formulas to calculate linear velocity, acceleration, displacement, and motion, you can also use equivalent formulas for angular (rotational) movement.

You can think of the angle, theta, in rotational motion just as you think of the displacement, s, in linear motion. This is great, because it means you have an angular counterpart for many of the linear motion equations. Here are the variable substitutions you make to get the angular motion formulas:

  • Displacement. Instead of s, which you use in linear travel, use

    image0.png

    the angular displacement;

    image1.png

    is measured in radians.

  • Velocity. In place of the velocity, v, use the angular velocity,

    image2.png

    angular velocity is the number of radians covered per second.

  • Acceleration. Instead of acceleration, a, use the angular acceleration,

    image3.png

    the unit for angular acceleration is radians per second2.

The table compares the formulas for both linear and angular motion.

image4.png

Say, for example, that you have a ball tied to a string. What’s the angular velocity of the ball if you whirl it around? It makes a complete circle,

image5.png

in 0.5 seconds, so its angular velocity is

image6.png

Another demonstration of the usefulness of radians in measuring angles is that the linear speed can easily be related to the angular speed. If you take the equation

image7.png

And multiply both sides by the radius, r, you get

image8.png

The term

image9.png

is simply the distance traveled by an object moving in a circle of radius r, so this equation becomes

image10.png

You may recognize the right side of this equation as the equation for speed. So you can see that linear speed and angular speed are related by

image11.png

2 seconds, what would its average angular acceleration be? Work it out by plugging in the numbers:

image12.png
  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
Advertisement

Inside Dummies.com

Dummies.com Sweepstakes

Win $500. Easy.