Electromotor for large platform
There is no simple answer to your question. You need to at least put together the following data before any meaningful calculations can even be conceptualized:


What is the total weight of the load-bearing platform with all supporting hardware?
What is the mass distribution of this plate? This will affect the moment of inertia, hence the power required to spin up and spin down the platform.
What is the suspension mechanism? Friction at the bearings alone could consume over half of the motive power of the motor. Add to this the friction at the edge stabilization mechanism, be it a circular rail and wheels, pure cantilever (it'll oscillate out of control pretty quick) or a load-bearing drive mechanism. 
What is the spin-up rate required? How quickly does the platform need to spin up to the full rotation speed - 30 seconds? A minute? An hour? 
How will the platform be brought to a stop? Brake shoes? Motor dynamic braking? Regenerative braking?
What is your proposed drive mechanism for the motor? A belt-driven central shaft? Belt-drive around the outer circumference of the platform? A gear drive on the inner circumference of the platform? Multiple motors driving wheels distributed around the outer edge, running on a circular rail beneath the platform? All these mechanisms, and many others, have been used for designs similar to yours, and each mechanism requires very different motor sizing calculations.


Even with all this data, you're just making a start towards arriving at your answer.

Provided below are some broad assumptions and guidelines for your power sizing exercise.

Rotation Speed:
The circumference of your platform is approximately 12.6 meters.
Assume a driving gear-head of diameter 5 cm on your motor, directly driving the outer edge of the platform: Gear head circumference is around 0.15 meters.
To traverse 12.6 x 4 meters a minute, the gear-head must run at around 335 RPM.

This will help in computing the gear drive ratio required, based on available motor RPMs. If you use a 4000 RPM motor, then a 10:1 gear reduction more or less serves, providing you leeway for rotation speed fine-tuning. That's just one step.

Motive Power:
Assume average weight of a person to be 75 KGs (a mix of average weight male and female persons).
Thus the platform must carry 1,125 KGs of payload.

Assume that your platform itself weighs around 875 KGs - This is purely a number I picked for calculation convenience, you would need to compute the actual weight of the combination of plastic and steel construction of the load bearing platform plus central and stabilizing support mechanisms. 

Therefore total mass to be rotated is 2000 KGs.

Now plug in the spin-up time required, and you have an approximation of productive power of drive mechanism. 

Factor in friction losses to arrive at actual required motor power.

Double that number to account for sketchiness of computation ;-)

So finally you have it: A horsepower baseline and an RPM baseline for motor selection. Or, at least a vague starting point for product selection to begin.