A thin uniform rectangular plate of length a, width b and mass m has a moment of inertia
1/12 m(a2 + b2)
about an axis through its centre and perpendicular to its plane. Identify the principal axes of inertia and give the values of the principal moments of inertia. What is the moment of inertia of the plate about an axis in the plane of the plate and forming a diagonal of the rectangle? If the plate is made to rotate about the diagonal, show that the angle between the angular velocity and the angular momentum is
arctan a/b – arctan b/a.