What would happen if a rotatable ferromagnetic rod were placed beside a magnet?

Question

If one were to place a rotatable shaft (green circle), made of plastic with ferromagnetic material (grey circles inside green circle), right beside an electromagnet, what would happen? I am trying to exclude the case where the shaft has magnets on it as a thought experiment.

For instance if the green circle were the rotatable shaft in this picture, would the shaft rotate due to the magnetic force?

Alternatively, is there an orientation that will cause the shaft to rotate? This would seem to be a perpetual motion machine (which doesn't make sense).

Answer 1

Assuming that the shaft is constrained only to rotate, the shaft would rotate by a certain angle to settle at the point of stable equilibrium. This point of stable equilibrium would correspond to the one where the flux lines are offered the path of least reluctance. This is similar to what happens in a switched reluctance motor. Of course, there won't be perpetual motion since there is going to be only a single position of equilibrium (depending on the orientation, shape, and sizes of the ferromagnetic material).

From an engineering point of view, it may be noted that the reluctance offered by the plastic part is more or less the same as that offered by an air gap of the same length (same permittivity). The speed and the associated oscillation rate at which the rod would settle at equilibrium would depend upon the above factors, the strength of the magnet and the friction coefficient. The system can be modeled mathematically in s-domain to obtain the dynamics. However, as for the steady state, the rod would settle at an equilibrium position and move no further.

Answer 2

If the shaft can not move an any direction except to rotate the magnet will have little effect. If the shaft were to rotate due to some other force, there would be a braking force due to eddy currents induced in the shaft. The resistance of the shaft would tend to minimize that effect. The effect would be maximized if the shaft would be copper plated.

Added re change of question:

Making the rotating object non-homogeneous doesn't change the answer much, whatever the internal details and position of the rod, the equilibrium net force will be to displace the rod rather than making it rotate. Only a continuously moving magnetic field can make an object move continuously. The magnetic field must move in a way that will not allow the object to reach an equilibrium position. I think you can analyze any system of magnets and ferromagnetic objects by diagraming the forces and resulting motions and determining that the object will only move to an equilibrium position. You know the outcome because of the conservation of energy principle, but you can probably demonstrated it also.

Added re comment

Switching magnets on and off in a way that avoids getting stuck in equilibrium is essentially making a switched reluctance motor. That will work.