Question 7

A thin square plate of mass $M$ with sides of length $a$ rotates freely about its centre-of-mass. Determine its principal axes and principal moments of inertia. Hence use Euler's equations to show that

(a) the component $\omega_3$ of the angular velocity about the axis perpendicular to the plate is a constant,

(b) the frequency of precession of $\hbox{{\boldmath$\omega$ }}$ in the body-fixed frame is equal to $\omega_3$.

[Hints can be found here, but do not follow this link until you have attempted the question on your own.]