# Need help with physics problem?

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 1.80 * 10^9 J of energy. How fast would a 12-kg flywheel with a radius of 0.33 m have to rotate to store this much energy? Give your answer in rev/min.

I just cant figure out what exactly I'm doing incorrectly.

### 1 Answer

- 1 decade agoFavorite Answer
Alright, obviously for this problem we are using rotational kinetic energy, given by K = 1/2 * I * w^2 where I is the moment of inertia (angular mass) and w is the angular velocity.

We also know that for any solid, uniform disk on an axis of rotation through its center of mass the moment of inertia is I = 1/2 * M * R^2 , where M is the mass of the disk and R is the radius.

We also know from the given statements that the kinetic energy this flywheel must store is 1.80 * 10^9 J.

Thus

w = sqrt(2 * K / I ) = sqrt(4 * K / ( M * R^2) )= sqrt(4 * (1.80*10^9 J)/( [12kg]*[0.33m]^2))

= 74,230 rad/s

Now we simply have to convert this rad/s to rev/min:

1 rev = 2*pi rad, 1 min = 60 sec

thus,

w = (74,230 rad/s) * (1 rev/ 2*pi rad) * (60 sec/ 1min)

...= 708,840 rev/min

which is REALLY freakin' fast...

- but on a side note this could easily be decreased by limiting the range. I know that they have actually made successful vehicles using this technology, but they often go only 100 miles (also they are buses which can support a heavier flywheel or simply make the flywheel with a larger radius (this will have the greater impact))

EDIT: I accidentally left out a square root earlier, I fixed it now...sorry :P

Hope this is understandable :)

Source(s): I'm a physics tutor at Iowa State University