Calculating Rotational Kinetic Energy

Rotational kinetic energy is the amount of energy that an object has while going around in a circle. To calculate it, you will need to know two things: its angular velocity (i.e., how fast it's going around in a circle) and its moment of inertia (i.e., inertia while going in a circle).

Step 1: Weigh the object to get its mass in kilograms. We'll call it "m."

Step 2: Measure the distance between the object and the center of rotation. The center of rotation is the point that the object is circling. For example, if you have a ball on the end of a string that you're twirling over your head, the center of rotation would be your hand and the distance would be the length of string between your hand and the ball. We'll call this distance "r." You'll want this in meters.

Step 3: Calculate moment of inertia. Multiply mass by distance squared: I = m * r².

Step 4: Measure how long it takes, in seconds, for the object to make one complete circle around the center of rotation. This is angular velocity in revolutions per second. For simple objects like a ball on the end of a string, you can use a stopwatch. If you prefer to make the measurement in revolutions per minute (RPM), you will need to divide by 60 to convert to seconds.

Step 5: Convert angular velocity into radians per second. A full circle is 2 * π radians, or about 6.28318 radians. If it takes one second for the object to make one full circle, the angular velocity would be 6.28318 radians per second. One RPM would be 6.28318 divided by 60, or 0.1047 radians per second. We'll call this "w."

Step 6: Multiply moment of inertia by angular velocity squared, then divide by two to arrive at the answer: RKE = I * w² * 1/2. This gives you the rotational kinetic energy in joules. One joule is equal to one (kilogram * meter²) / second².


Tips

You can weigh the object in pounds and ounces, and measure the distance in feet and inches, then convert to kilograms and meters before continuing.

Warnings

This is the generalized form of the equation. It assumes that all of the object's mass is at the same distance from the center of rotation. This works well for items at the end of a string or hoop objects like bicycle wheels. If different parts are at different distances, you will need to calculate moment of inertia separately for each, then add them all together for a total. If it's a solid object spinning around an axis rather than lots of parts circling a point, you will need to use calculus--however, there are some equations for the more common types of objects in the third reference listed.

Additional resources from C.R. Nave's Hyperphysics:
Rotational Kinetic Energy
Angular Velocity
Moment of Inertia