I took apart a couple of small motors and found that they all have the copper coils attach to the shaft and spin around stationary magnets, rather then the other way around.The reason I'm asking is because they also have those two copper prongs touching the shaft in order to transfer the electricity back and forth, which wouldn't be necessary if you had the magnets spin and the coils stationary.
Motors work by having the rotor poles constantly attracted toward the stator poles they are approaching, and repelled from the stator poles they are moving away from. This means either the rotor poles or the stator poles must have alternating magnetic polarity. In a motor designed to run on AC, you could have magnets in the rotor if the stator coils are driven by AC. However this would require that the rotor spin exactly at the AC rate. Instead, AC motors don't use permanent magnets at all, but use the magnetic induction effect, with no commutator necessary, to produce rotating polarity in the rotor that matches that of the alternations of the stator field. For DC, coils are needed in the stator so the rotation of the rotor can be used to switch its own polarity via the coil current reversal provided by the commutator. If you had PMs in the rotor of a DC motor, with only DC in the stator coil there'd be no rotation. I suppose you could design a DC motor with a PM rotor and a commutator that switches the stator polarity. I think you'd need slip rings plus a commutator. That should work and it could be an interesting project.
Will a spinning Neodymium Magnet induce a current in the copper coil which surrounds it? Yes, if the coil is oriented in such a way that it cuts the magnetic field lines. I am doing an experiment where i have a magnet inside of a copper coil which is connected to a voltage meter, and I am wondering if when the magnet is spun on its axis if it will induce a current in the coil. Does the axis on which it spins affect this or not? Yes, the axis is crucial. It is not really practical to set up a spin such that there is no current induced, but the orientation is important to get optimum results. Imagine that the Earth is a perfect magnet with north and south poles and perfectly aligned field lines, rotating as the Earth actually does. A coil of wire going around the equator would likely not have current induced, due to the fact that the coil would not be effectively cutting field lines. Making the earth rotate such that the poles went end over end would be an optimal orientation. Does the coil have to be bare wire or can it be insulated? It does not matter, but it helps to have lacquered wire and many loops of wire (instead of just one loop). The gauge of the wire does not really affect the result, but thinner wire is easier to loop multiple times in a small volume of space. I suppose that if you are generating high enough currents, the resistance in thinner wire and the heat generated may become a problem (generator windings usually breakdown because of overheating). Good luck!