A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means of storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 300 mile trip in a typical mid-sized car produces about 1.2x10^9 J of energy. How fast would a 13kg flywheel with a radius of 0.3m have to rotate to store this much energy? Give your answer in rev/min
Rotational Kinetic Energy (KEr) = (1/2)Iw^2
where I = mr^2
The Attempt at a Solution
So doing some basic algebra, and solving for w, I came up with:
w = sqrt(KEr/.5mr^2)
w = sqrt(1.2x10^9J / .5(13kg)(.3m^2)
w = 45291 rad/s
(45291 rad/s) / 2pi = 7208 rev/s * 60s = 432497 rev/min
The answer that the book is providing is: 6.1x10^5 rev/min
I'm not sure what I'm doing wrong, or If this is even the correct approach I should be taking to solve this problem.
Any help would be greatly appreciated.