It has been argued that power plants should make use of off-peak hours (such as

Question

It has been argued that power plants should make use of off-peak hours (such as late at night) to generate mechanical energy and store it until it is needed during peak load times, such as the middle of the day. One suggestion has been to store the energy in large flywheels spinning on nearly frictionless ball-bearings. Consider a flywheel made of iron, with a density of 7800 kg/m3 , in the shape of a uniform disk with a thickness of 14.8 cm .

What would the diameter of such a disk need to be if it is to store an amount of kinetic energy of 12.4 MJ when spinning at an angular velocity of 85.0 rpm about an axis perpendicular to the disk at its center?

What would be the centripetal acceleration of a point on its rim when spinning at this rate?

Explanation / Answer

density of flywheel , p = 7800 Kg/m^3

thickness , t = 0.148 m

let the diameter of the disk is d

angular speed , w = 85 rpm

w = 8.89 rad/s

Using conseravtion of energy

0.5 * I * w^2 = E

12.4 *10^6 = 0.5 * (0.5 * 7800 * pi * R^2 * 0.148) * R^2 * 8.89^2

solving for R

R = 3.63 m

diameter of wheel = 2 * 3.63

diameter of wheel = 7.26 m

the diameter of wheel is 7.26 m

centripetal acceleration = w^2 * r

centripetal acceleration = 8.89^2 * 3.63

centripetal acceleration = 286.9 m/s^2

the centripetal acceleration is 286.9 m/s^2

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