A flywheel is a solid disk that rotates about an axis that is perpendicular to t

Question

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 340 mile trip in a typical midsize car produces about 1.80 109 J of energy. How fast would a 12 kg flywheel with a radius of 0.22 m have to rotate in order to store this much energy? Give your answer in rev/min.

__________________rev/min.

Explanation / Answer

Look the energy produced s readable as 1.8 * 10^9 J

I'll take this as E and proceed.
Let the velocity of the fly wheel be

I = moment of inertia = 1/2 *m*r^2 = 0.5 *12 * 0.22 *0.22 = 0.2904 kg-m2

Hence energy stored = 1/2 *I * 2

E = 1/2 * 0.2904 *  2

1.8 *10^9 = 1/2 * 0.2904 *  2

Hence  2 = 2 * 1.8 *10^9 /0.2904 = 1.24 *10^10

Hence   = 111340 rad/sec

1 Rev = 2 radian

Hence = 111340/2 = 35440.76 RPM

Hope this will do.

If the energy is different let me know before rating I'll correct it. :)

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