And controlling it with an arduino is no problem. You've got to main options for the sensor - either an optical tracker that is pointed at the shaft and detects the presence of a striped/marked point which appears once every revolution, or the (cheaper but just as reliable, really) solution of an iR sender/receiver pair monitoring the turning of something (imagine a motor shaft turning a fan. The iR pair would be positioned perpendicular to the fan blades, each time a blade crosses the path of the iR, a signal is generated).
iR is cheaper.
An arduino (or just about any other microcontroller) has an operating frequency way over the rotational speed of the motor. Both optical and iR sensors can easily handle the relatively-slow rotational speed of the shaft. I've used an MC68k from, what, 20 or 30 year old production lines(?) to pull this off. The code is dead simple, just connect the iR/optical output to a counter (which comes built-in in several of the arduino input ports) (you'll need to run it through an inverter first, if you're doing the iR approach) and then loop over the count until it's moved as far as you need it to.
The human hand isn't crazy fast the way you're thinking. If you've ever seen a stepper motor snap from one position to another, that is real acceleration. Basic DC motors typically have lower acceleration than that - their acceleration and speed will vary greatly depending on the model chosen.
2KG is not a light weight. I would have recommended the stepper approach, but you'll need motors about the size of your fist running at 12V and a relatively high current to rotate an object of that size. Basic statics says that the farther away from the point of rotation a weight is applied, the stronger its force. You've got 2KG distributed (I assume) evenly across the 30cm surface, it's going to be quite the weight to turn against gravity, so stepper motors are out.
Servos, which are basically your run-of-the-mill DC motors with their own close-lood feedback system will work. But you'll have better luck with the larger variety of DC motors available online or in your local electronics store.