Diagonal of a thin rectangular foil, inertial principal axis

[bznm]

I'd like to know if the diagonal of a rectangular thin foil is an inertial principal axis.I know that if an axis isn't a symmetry axis then it isn't a principal axis. In the rectangle the diagonal isn't a symmetry axis, so it shouldn't be a principal axis. Is it correct?

So, if I consider that the angle between the rotation axis and x-axis is $\theta$ and $\vec{\omega}$ is on xy-plane, I can't understand why

$\tau_z=\omega_x \omega_y(I_{xx}-I_{yy})$

 

[gtoguy97]

Because the angular momentum is conserved, it means that $\tau_z=I_{zz}\omega_z$So, the answer to your question is no, the diagonal of a rectangular thin foil is not an inertial principal axis.