You are designing a rotating metal flywheel that will be used to store energy. The flywheel is to be a uniform disk with a radius of 23.0 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?