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 350-mile trip in a typical midsize car produces about 1.90 109 J of energy. How fast would a 20-kg flywheel with a radius of 0.39 m have to rotate to store this much energy? Give your answer in rev/min.

Explanation / Answer

from

Rotational kinetic energy is :

KE = 1/2 I²

I is moment of inertia. For a solid disk, this is 1/2 mr², so :

KE = 0.5(0.5mr²)²
² = KE / (0.25mr²)
= [KE / (0.25mr²)]^0.5
= (1.90*10^9/ (0.25*20* (0.39)^2))^(0.5)
= 5*10^4rad/s

This is :

5*10^4rad/s(1.0rev/2pi rad)(60s/ 1.0min) = 477707rev/min

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