Do you remember what **Kinetic Energy** is, and how to calculate it?

- Jack is 150 cm tall and has a mass of 68 kg.
He runs down the street at a speed of 7 m/s.
**What is Jack's kinetic energy?**

What if the body in question is not TRANSLATING (moving in a straight line), but REVOLVING around some point? If you are given the linear velocity of the body, it's no different.

- Jack is 150 cm tall and has a mass of 68 kg.
He sits in the Whirl-a-Kid carnival ride,
which has an arm of radius
**R = 3 m**and spins him at a speed of 5 m/s.**What is Jack's kinetic energy?**

But what if you are given only the angular velocity?

- Jack is 150 cm tall and has a mass of 68 kg.
He sits in the Whirl-a-Kid carnival ride,
which has an arm of radius
**R = 3 m**and spins him at an angular speed of 0.5 revolutions per second.**What is Jack's kinetic energy?**

We can write the KE in terms of the angular velocity plus some other stuff ...

... but why should we bother?

The answer is -- if the rotating object is a complicated collection of pieces, then figuring out the linear velocity of each piece becomes tiresome.

- Jack has a mass of 68 kg,
and sits
**R**from the center of the ride. Fred has a mass of 55 kg, and sits_{1}= 3 m**R**from the center of the ride. Bob has a mass of 73 kg, and sits_{2}= 2 m**R**from the center of the ride. The Whirl-a-Kid spins at an angular speed of 0.5 revolutions per second._{2}= 4 m**What is the total kinetic energy of the boys?**

We can simplify the result down to a single, familiar-looking equation with just two variables

if we define a new quantity, the **moment of inertia**.
For a compact mass, it is simply a combination of
mass and distance-from-axis-of-rotation:

What IS this "moment of inertia"? You may recall that "inertia" is a fancy term which refers to the resistance of a body to a change in its motion. Items with large inertia -- like trucks and whales -- are hard to start moving, and hard to STOP moving once they get going. Items with small inertia -- like ping-pong balls and mice -- are easy to accelerate.

In a similar fashion, the "moment of inertia" measures
the **resistance of a body to a change in its rotation**.
A body with a large moment of inertia is hard to
get spinning ... but, once it is spinning, is hard to stop.
A body with a small moment of inertia is easy to
start spinning, and easy to stop.

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.