To answer your question, let's first remember some basic ideas about magnetism. A common way to think about a magnet and the magnetic field corresponding to it is using flux lines, which are lines that indicate the direction of the magnetic field (by their direction) and its strength (by their density). These lines (per convention) originate at the north pole of a magnet and point towards the South Pole. A compass is a small suspended magnet, which will align itself with the flux lines of the much bigger magnet, i.e. the earth. If you look at a picture of the magnetic flux lines of the earth (or even a staff-like magnet), you can see that they will point pretty much vertically downward at the North Pole. So rather than spinning, I'd think that a compass needle might lock up at the (magnetic) North Pole, because it will want to point downward. Maybe that confusion of the needle combined with small fluctuations in its position or the earths magnetic field could make it spin or just make it behave irrationally. In principle, however, a static magnetic field (which doesn't change over time) can not make a compass needle spin, which is quite evident when you think about the question based on the flux line picture. So to make it spin, you'd have to generate a magnetic field that changes direction with time. This could be as simple as using one of those magnetic stir plates (in essence, a staff-shaped magnet attached to a motor) and placing the compass on top. In fact, that's how these magnetic stirrers work, you add a smaller staff-shaped (and glass- or Teflon-covered) magnet to the solution you want to stir, and it will rotate with the big magnet of the stirplate. Other than via a magnetic field that changes with time, it is not possible to make the compass rotate continuously.
The simplest method I can think of to cause a compass needle to spin would be the interaction of the compass needle with a bar magnet that is rotated around the compass in close proximity.As all permanent magnets have a north pole and south pole - the circular magnet I believe you are envisioning is actually an electromagnet made by passing an electric current through a coil of wire wrapped around a metallic core to create a magnetic field. In this case, assuming a constant current, the compass would initially spin until it is aligned with the new field and then would point in the direction of the new field.
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