Question: What are the Physics laws and what math describe them for the situation below?

The object in the above display consists of a thin red disk and attached thin blue disk. They have radii 1.0 and 0.2 and masses 1.0 and 0.2 respectively.

Starting from rest at the above position they are given an initial angular velocity of Omega radians/second which starts the object rolling along the positive x axis.

If Omega is great enough that, at some time during the roll, the vertical component of the centrifugal force on the blue disk exceeds the downward force of gravity on the object, will the object begin a spinning projectile motion above the x axis?

Assuming both disks have negligible thickness, what Physics laws will govern the rolling and (possible) spinning projectile motions and what mathematics describes these motions? 

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