Consider a flat piece of sheet metal located on the (x, y) plane and rotating about the z axis. Do not take the thickness into

Consider a flat piece of sheet metal located on the (x, y) plane and rotating about the zˆ axis. Do not take the thickness into account. (a) Which entries of the inertia tensor are equal to zero?(b) Verify that the following relation holds: Izz = Ixx + Iyy. (c) Verify that ˆz is a principal axis. Hint: show that if the angular velocity is aligned with zˆ the same goes for the angular momentum. (d) Now assume that the sheet metal has the shape of a thin disk with uniform mass density, radius R, mass m and compute Ixx, Iyy and Izz.