Double spinning

A uniform, solid cone of height $h = 4\text{ m}$ is leaning against a vertical axis, forming an angle of $\alpha=30^\circ,$ as shown. The angle between the lateral surface and the axis of the cone is also $\alpha=30^\circ.$

The cone rotates about the vertical axis as well as about its own axis with their respective angular speeds $\omega_1$ and $\omega_2,$ as marked in the diagram.

If the cone does not slip at points $B,$ find $\dfrac{\omega_1}{\omega_2}.$