Since no specific shape is given, I will analyze a small square located a distance \( r \) from the axis (shown in red in the diagram).
Moment of inertia:
Pressure, force, and torque (let be the angular frequency):
Rotational Newton's 2nd Law:
This corresponds to exponential decay of the angular frequency:
The angle swept out over infinite time is:
And the number of revolutions is therefore: