It's aaaaaages since I did this kind of calculation, but the torque T required depends on the Moment of Inertia I of the disk and the required acceleration a, and :

T = Ia

The Moment of Inertia of a disk on mass m and radius r is

I= mr^{2} / 2

(Let's check those units....

units of I will be kg m^{2}

units of a are rad / s^{2} or just 1/s^{2}

So units of T are kg m^{2} / s^{2}

(Which is right since T=Fd and units of force at kg m / s^{2}) )

I think... it's been a long time, as I say