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 for 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 midsize car produces about 1.2*10^9 J of energy. How fast would a 13-kg flywheel with a radius of 0.30m have to rotate to store this much energy? Give your answer in rev/min.

Question

I need some hints to do this problem. Please help. Thanks.

Answer 1

The kinetic energy stored in a rotating object is

(1/2) I w^2

I is the moment of inertia of the disk about an axis perpendicular to the disk at the center, which you can look up (If they want you to derive it reply to me that you need a derivation)
I = (1/2) M R^2 where R is the radius of the flywheel and M is the mass
w is the angular velocity in radians per second
w = 2 pi (revolutions per second)
so set your Joules equal to (1/2) I w^2 and solve for w
then change w from radians per second to revs per minute
revs/min = w in rad/sec * 1 rev/2pi radians * 60 seconds/1 minute

Answer 2

I did the same thing, but I can't get the right answer.
My answer is 4.3*10^5 rev/min

Answer 3

I agree with your answer

Answer 4

But the book says the right answer should be 6.0*10^5rev/min

Answer 5

That is pretty mysterious.