A dist-shaped flywheel, of uniform density , other radius R, and thickness w, rotates with an angular

A dist-shaped flywheel, of uniform density ρ, other radius R, and thickness w, rotates with an angular velocity ω, in rad/s.
(a) Show that the moment of inertia, I= ∫vol ρr2 dV, can be expressed as I= πρwR4/2 and the kinetic energy can be expressed as KE= Iω2/2.
(b) For a steel flywheel rotating at 3000 RPM, determine the kinetic energy, in N. m, and the mass, in kg, if R= 0.38m and w= 0.025 m.
(c) Determine the radius, in m, and the mass, in kg, of an aluminum flywheel having the same width, angular velocity, and kinetic energy as in part (b).