With a stepper motor you can control both speed and distance/angle.
You do need at least a home sensor to find the starting position before you start stepping, and depending on the application, you may need a 2nd limit sensor. Once your software knows the starting position, the software can easily keep track of the steps so it always knows the position.
The downside might be that a stepper motor takes 1.8 degree steps so it's not "smooth". But, it can be smoothed to some extent by gearing-down (or with belts & pulleys) or with microstepping.
A servo motor may be another option if you don't need to rotate it in a full circle. Servo motors are angular motors. They typically have range of 180 degrees (they don't "spin" in a circle like a regular motor). They have a built-in position sensor and a built-in motor driver. You supply power and then a pulse that's proportional to the desired angle, and the servo knows which way to move and how far to move. If you push it out of position it "fights you" and returns to the set position when you release it (as long as the control pulse continues). The only way to control the speed of a servo is to "step" it by sending a series of commands to "walk" it to the desired angle.
With a DC motor it's harder to precisely control the speed, particularly at slow speeds. Again, you need some sort of speed/position sensor. Typically, you are finding the RPM in a feedback loop in order to control the speed.
AC motors are similar to DC motors in that you need external sensors to control the speed & position. The exception is synchronous AC motors that lock-into the AC power line frequency. Synchronous motors are used in (analog) electric clocks and in some turntables (record players). The speed-control electronics are more complicated for (non-synchronous) AC motors, and of course they are usually running on power line voltage.
The downside might be that a stepper motor takes 1.8 degree steps so it's not "smooth".
How heavy is your disc?
Does it have other things attached to it?
Is it vertical or horizontal orientation?
You maybe be able to use these low-cost stepper motors; they are geared down and so a very small rotation per step. See THIS page. They have 2048 steps per revolution.
Thank you all.
The plate is horizontal it weighs 3.5 pounds but I want to change that to aluminum half the thickness of the steel plate much less mass to start and stop.
I bought Stepper motor - NEMA-17 size - 200 steps/rev, 12V 350mA from ebay it's a adafruit motor.
I see a hole in the shaft but no threads. where do I find gears chain or pulleys and belts?
If you ask a question about parts suppliers, you need to explain where you live, since people here from
all over the globe... I'd say beltingonline.co.uk, but that won't help if you don't like in the UK!