How to Calculate Rotational Kinetic Energy

The best way to spice up your understanding of rotational kinetic energy is to apply the formulas to interesting situations. Here is the setup: Jack is an evil little booger who tricks his sister Suzy into putting a noose around her waist. Once Jack cinches the rope up tight, he spins in place, flinging his sister around him a little like a yo-yo. Here's how to calculate rotational kinetic energy generated by this mean little prank.

Difficulty: Easy

Instructions

Things You'll Need:

• Calculator
• Pencil
• Paper

1. Assume that friction does not matter, and air resistance is not a factor, because that adds a heck of a lot of math. Here are the facts about the rope, Jack and Suzy: The rope is magical and weighs nothing. Suzy masses 25 kg and can be considered a point mass. The rope stretches 2 m from Jack to Suzy. Jack is spinning Suzy around three times every second.

2. Read the formula for rotational kinetic energy. KE (rotational) equals 1/2 I (moment of inertia) times w (angular momentum) squared. You will have to derive all of these values from the example values.

3. Find the moment of inertia. This is the easy part. For a point mass going round in circles, the moment of inertia is the mass of the object times the squared radius of the circular path upon which it travels. From the given information, you see that Suzy masses 25 kg and the radius of the circular path is 2 m. Plug in the numbers and you should get 100 kg/m squared.

4. Calculate the angular momentum. Angular momentum is equal to the distance traveled around the circular path per second. Since Jack is flinging Suzy around three times per second, you take the formula for the diameter of a circle, two times Pi times radius, and find that Suzy's angular momentum is equal to 18.8 m per second. Squared, that's 353.44 m squared per second squared.

5. Multiply the moment of inertia times the squared angular momentum. You should get 35,344. Divide by two to get the final answer of 17,672 joules, or about 10 times as much energy as that generated by a high-powered assault rifle.

Tips & Warnings

• The formulas for rotational energy vary according to the shape and axis of rotation of the objects being studied. Please consult a physics text for more information about rotational kinetic energy.

Resources

• Overview of Rotational Kinetic Energy
• More Formulas for Rotational Kinetic Energy

[alfadog]

on 11/2/2009 Whoops.
1. w is angular speed, not angular momentum. Very different (momentum must include mass).
2. w is in radians/sec and has nothing to do with the radius. Even though you explained it wrong, you got the right answer. 2 x pi radians per rev and 3 rev/sec = 6 x pi = 18.85. Radius has nothing to do with it.