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 360-mile trip in a typical midsize car produces about 1.20 109 J of energy. How fast would a 20-kg flywheel with a radius of 0.36 m have to rotate to store this much energy? Give your answer in rev/min.

This is what I got: 5.3e5 Incorrect: Your answer is incorrect. rev/min

Explanation / Answer

Given rotational energy = 1.20 * 10^9 J

mass m = 20 kg

radius r = 0.36 m

the moment of inertia of a disk is I = m * r^2 / 2

I = 20 * (0.36)^2 / 2

I = 1.296 kg-m^2

the rotational energy is

1/2 * I * (omega)^2 = 1.20 * 10^9

1/2 * 1.296 * (omega)^2 = 1.20 *10^9

omega = 43033.148 rad/s

we know 1 rev = 2pi rad

and 1 minute = 60 s

omega = 43033.148 * 60 / 2pi rev/min

omega = 4.109 * 10^5 rev/min-------------------------------Answer

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