Solve the following problem:
Q: A dist-shaped flywheel, of uniform density other radius R, and thickness w, rotates with an angular velocity W in rad/s.
(a) Show that the moment of inertia, I= vol∫pr2dv an be expressed as I= ΠpwR4/2 and the kinetic energy can be expressed as KE= Iw2/2.
(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 par