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 148-mile trip in a typical
midsize car produces about 1.28 x 10^{9} J of energy. How
fast would a 34.5-kg flywheel with a radius of 0.463 m have to
rotate to store this much energy? Give your answer in rev/min.

Answer #1

Rotaional kinetic energy=1/2*I*2, where I is moment of inertia and is angular velocity.

Now, for a disc, I=mr2/2, where m is mass and r is radius.

Here, m=34.5 kg and r=0.463 m.

So, I= 34.5*0.463*0.463/2 = 3.69786525 kg-m2.

Also, kinetic energy = 1.28*109 J.

So, 1/2*3.69786525*2 = 1.28*109

=>2 = (1.28*2/3.69786525)*109 = 6.92291315*108

=>=2.631142936*104 rad/sec = 2.631142936*104*60/(2) rev/min = 251255.6 rev/min.

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