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 270-mile trip in a typical midsize car produces about 1.60 109 J of energy. How fast would a 14-kg flywheel with a radius of 0.27 m have to rotate to store this much energy? Give your answer in rev/min.

Explanation / Answer

Rotational kinetic energy is : KE = 0.5I?² I is moment of inertia. For a solid disk, this is 0.5mr², so : KE = 0.5(0.5mr²)?² ?² = KE / (0.25mr²) ? = [KE / (0.25mr²)]^0.5 = [1.1 x 10^9J / {0.25 x 11kg x (0.35m)²]^0.5 = 5.7 x 10^4rad/s This is : 5.7 x 10^4rad/s(1.0rev/2pi rad)(60s/ 1.0min) = 540,000rev/min

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