A children\'s toy spins rapidly with angular speed along its axis with the botto

Question

A children's toy spins rapidly with angular speed along its axis with the bottom point of its axle resting in a shallow frictionless depression that allows it to spin without resistance. When it is spun at a slight angle vertical it will precess: the bottom point of contact will remain in place, but the top of the axle will rotate along a circular path that lies in a horizontal plane. For clarity, the direction of the angular velocity vector, a, has been shown at a particular moment in time when the axle is tilted to the right by an angle 6 relative to the vertical. The central axle of the toy has length t, and there is a disk of radius R located a distance t/3 from the bottom. The mass of the disk is much larger than the mass of the axle, so the axle does not contribute appreciably to the moment of inertia.

Explanation / Answer

There are two possible questions.

1) what is precession angular velocity, given moment of inertia of disc about it's natural axis.

2) what is minimum required coefficient of friction or
   what is horizontal component of reaction force acting on toy at the point of rest

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