You are designing a rotating metal flywheel that will be used to store energy. T

Question

You are designing a rotating metal flywheel that will be used to store energy. The flywheel is to be a uniform disk with radius 29.0 cm. Starting from rest at t = 0, the flywheel rotates with constant angular acceleration 3.00 rad/s^2 about an axis perpendicular to the flywheel at its center. If the flywheel has a density (mass per unit volume) of 8600 kg/m^3, what thickness must it have to store 800 J of kinetic energy at t = 8.00 s? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

Ef = 1/2 I w^2

I of uniform disk is 0.5 mr^2

at t= 8 ,

w = wo+ at

w =0 + 3*8 = 24 rad/s

so

800 = 0.5 * (0.5 mr^2) (24)^2

mass = density *volume , = density * base area *thickness = 8600 * pi * (0.29)^2 * t

800 = 0.5 * (0.5 * 8600 * pi * (0.29)^2 * t *(0.29)^2)*(24)^2

solving , we have

t = 0.029 m -----ANSWER

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