Question 8

A thin circular disc rotates about its centre of mass. It is subject to a torque which damps rotations about any diameter. The components of this torque are related to to the components of the angular velocity $\hbox{{\boldmath$\omega$ }}$ along the principal axes by

$$\tau_1 = -k\omega_1$$

$$\tau_2 = -k\omega_2$$

$$\tau_3 = 0$$

where $k$ is a constant and the the ${\bf e}_3$ axis has been chosen to be the one perpendicular to the disc. If the initial angular velocity is not along a principal axis, determine how $\omega$ varies with time from the viewpoint of a body-fixed frame. Try to describe this motion from as seen by a space-fixed observer, and check this using a Frisbee.

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