Any constant-speed motor will work fine for spinning the platters.
The sculptures seen in this first image were made by 3dscanning and 3dprinting my head.
Step 1: Phonograph Turntable and Strobe
It has a knob that adjusts the rate at which the strobe flashes.
The turntable you want is one that spins at 78rpm.
That's the old victrola speed which is 1.3 revolutions per second.
If you draw 8 evenly spaced cels of animation and adjust your strobe til it flashes about 10 times/second you'll see 8 copies of your animation all going at once, each at a different phase of the sequence.