Why is there are precession frequency here?

[simphys]

Homework Statement

A child's toy top consists of a uniform thin disk of radius 5.0 cm and mass
0.15 kg with a thin spike passing through its center. The lower part of the
spike protrudes 6.0 cm from the disk. If you stand this top on a table and start
it spinning at 200 rev/s, what will be its precession frequency?

Relevant Equations

.

so I need to use the eq.: omega_pr = $mgr / L_s$ with r = 6cm.
But from how I imagine/see it, the rod pierces the disk through the middle so how does this create precession if the weight will not cause a torque then and thus a hortizontal change in angular momentum?

Thanks in advance!

 

[kuruman]

What if the axis of rotation is slightly tipped when the toy is started spinning? What if the surface on which it is spinning is not exactly flat? You get the point.