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 420-mile trip in a typical midsize car produces about 3.16 x 109 J of energy. How fast would a 10.5-kg flywheel with a radius of 0.375 m have to rotate to store this much energy? Give your answer in rev/min.

Explanation / Answer

Energy of a rotating body = I2/2

= angular velocity (rad/sec)

I for a fly wheel (through an axis passing perpendicular to the plane through the centre) = 1/2 mr2

=1/2 x 10.5 x 0.3752 = 0.738 kgm2

So energy of the rotating fly wheel = [(1/2 x10.5 x 0.3752)x2]/2

3.16x109=  [(1/2 x10.5 x 0.3752)x2]/2

=> 2 = 3.16x4x109/(10.5x0.3752) = 8560423280

=> = 92522.55 rad/sec

=> rate of rotation of wheel = 92522.55/2 = 14725.4 rev/sec

= 14725.4*60 rev/min 883525.3 rev / min

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