The mass of the platter has nothing to do with speed control other than it is the "m" in the equation, F=ma or T=J(Omega). The motor controls the speed. Its that simple. As shown by the equation, more mass means the motor must generate more torque to provide the same acceleration. How much acceleration is enough? Well, it depends on how well the designer wants to hold the exact rotational speed under dynamic conditions. I stated as a rule of thumb based on my knowledge and experience designing dynamic systems, (not turntables) that a tt motor should be able to accelerate the platter from 0 rev/s to 0.5556 rev/s within the first rotation. Some motors may be able to do better than that, but if it takes a motor more than one rotation to get the platter up to speed, then I think it might lack sufficient torque to maintain a stable speed. I could be wrong here, I've never designed a tt myself. But to carry it further, the motor is designed to spin at a certain speed. That control system for the motor can be as simple as being clocked to the 60Hz sine wave of the AC power to a very sophisticated electronic servo feedback control system. However it is done, the resolution and rate of response of this control system results in the level of stability of the platter speed. The system design dictates how much speed error can occur before it corrects it and how fast it can correct the speed. At this point I could get into the impact of an underdamped or over damped system, but the point is the tt designer must come up with a system that includes the motor torque, speed, resolution of the control loop, platter inertia.
I might be wrong here, but I have observed that DD turntables tend to have lower mass platters versus later BD tables. I'm guessing that the torque available from DD motors is less than for BD considering BD motors get a mechanical advantage from the pulleys. Higher mass platters offer a nice stable sink for the vinyl record to minimize vibrations. The added inertia of high mass platters is probably more of a problem for tt designers in terms of speed control- just because it requires more torque from the motor.
I'm starting to think the rhythm and pace might be linked more to the tonearm and stylus. The runout of the vinyl record, as I showed before, has more impact on Wow than does the tt. But the swaying of the tonearm, which is part of the Wow problem must also influence the tempo of the music I think. Couldn't the side to side movement of the stylus in the groove alter the tempo? Is that what tonearm damping is all about? I don't have damping. Does anyone have experience that says tonearm damping improves the tempo of the music?