A flat rectangular plate with sides a and b has the mass M homogeneously distributed with density ρ. Use the Z axis perpendicular to the plane of the plate, and the X, Y axes in the plane of the plate.
Calculate:
a) The main moments of inertia for the plate.
b) The torque necessary to rotate it about an axis perpendicular to the plane of the plate, with constant angular velocity ω = ωẑ.
c) Clearly explain your calculations.
d) Identify the axis with the greatest stability of rotation.