There are two equations that you will find useful
1. T = I * alpha
This is the rotational equivalent of Newton's second law ( F = ma ). In this case T is torque, I is the moment of inertia, and alpha is the angular acceleration in radians per second squared.
2. T = Kt * i
This relation says that a motor will produce an amount of torque equal to some constant Kt which is a property of the motor times the current going through the windings.
It should be reasonably easy to find the formula for the moment of inertia of a disc,
https://en.wikipedia.org/wiki/List_of_moments_of_inertia
which will of course be an approximation of your system. Looks like Iz = (mr²)/2 After that you need to find the Kt for your motor and then you can pick a current that will give you an alpha that you require to move the platform.