Past exam of the physics B course of the University of Cambridge / 2018 / Paper 1 / Section C / C10 / b / Solution

Put $I_1=I_2=I_{\perp }$, with $I_3\ne I_{\perp }$. ThenRotation about the symmetry axis is stable whether that axial moment is larger or smaller than the transverse moment. In fact ${\omega }_3$ and ${\omega }_1^2+{\omega }_2^2$ are exactly constant for a torque-free axisymmetric body: the transverse components rotate into one another at the stated body-frame frequency. Stability here means bounded wobble, not relaxation back to perfect axial rotation.