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 250-mile trip in a typical midsize car produces about 1.85 x 109 J of energy. How fast would a 6.53-kg flywheel with a radius of 0.219 m have to rotate to store this much energy? Give your answer in rev/min.

Explanation / Answer

radius = r = 0.219 m

mass = m = 6.53 kg

Conservation of energy

Rotational Kinetic energy = Chemical energy

0.5 I w^2 = 1.85 x 10^9 J

0.5 * 0.5 * m * r^2 *w^2 = 1.85 x 10^9

0.25 * 6.53 * 0.219^2 * w^2 = 1.85 x 10^9

w = sqrt( 1.85 x 10^9 /(0.25 * 6.53 * 0.219^2)) = 153714.612 rad/s

=  153714.612 * (60/(2*pi)) = 1467866.4 rev/min

Speed = 1467866.4 rev/min

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