Power for POV display
Here's some instructions on building a rather ingenious slip ring using ball bearings.
You need to use some form of slip ring and carbon brushes. The slip rings are mounted on the spinning shaft which is a ring of brass that makes contact with sprung brushes that supply the power. They are similar to a commutator on a DC motor, except they are a continuous ring instead of segmented.
You'll need two slip rings for power and GND unless it's possible to use the shaft itself as GND. In that case, you can get away with just one. But this would mean you'd need to mount all of your control circuitry on the spinning assembly, otherwise you'd also have to have extra rings to supply individual LED circuits.
A neat and cheap alternative to using carbon brushes is to use tool clips that are mounted on a piece of insulating nylon that surround the rings.
If you are building a small display, you can also do it with a round circuit board with circular traces that rotates coaxially with your rotating part with two fixed "brushes" (small brass springs) that each drag on one of the circular traces. Like a flattened out version of how a DC motor commutator works.