Motors to Power a Potato Slicer

Personally, I think we would be doing you a disservice to provide many answers here, until you've done some of the basic work. You should know the calculations for synchronous speeds, should have a pretty good idea of what motors can be found in single phase vs three phase, and should know which is typically used in industry, and why. Calculations for torque and power are things you should be able to do in your sleep.

As you progress in your project, doing your own research, you may get to the point where you have a question like this: "I've decided I need a 4 Kw motor for my potato slicer, and I've found that it needs to be of variable speed. I can see advantages to both DC drives and AC VSD's. I know that slicing potatoes will throw off some water. Should that have any impact on my design decision, or are there likely to be other variables that should drive the decision?"

At that point, there are loads of people here who would be very happy to help. I think short of that point, then we would just be doing your homework for you.