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 490-mile trip in a typical midsize car produces about 4.39 x 109 J of energy. How fast would a 6.31-kg flywheel with a radius of 0.500 m have to rotate to store this much energy? Give your answer in rev/min.

Explanation / Answer

first we calcualte the moment of inertia

I = 0.5 * m * r^2 =

I = 0.5 * 6.31 * 0.5^2

I = 0.78875 kg m^2

then we calculate the angular velocity

E = 0.5 * I * w^2

w = sqrt [2E / I]

w = sqrt [2 * 4.39 * 10^9 / 0.78875]

w = 105506 rad/sec

rpm = w*[60 / 2*pie ] = 1007508

so the speed is 1007508 rev / min

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