AC vs DC. While I fundamentally agree with Dover, a few points he raises need expansion.
Not all AC motors lock on to the field frequency. What we should be talking about is synchronous motors. In this design the rotor follows the rotating field in the stator at the same speed, but not the same phase angle. IOW the rotor is running slightly behind the rotating field in the stator, but at the same speed. There is an angular displacement between the two. No displacement, no torque. This angle is determined by the load the motor is seeing and the motors design. More load equals greater angle, where the motor momentarily slows until the torque it produces equals the higher torque demand. Maintain that higher load and the angle will stay at this higher figure. Reduce the load and the angle will similarly decrease and momentarily the rotor's speed will increase. The rotor maintains an average speed dictated by the rotating field, but when driving a dynamic load, its real-time speed is changing at microscopic rates. Some synchronous motors are very stiff. This means that the increase in displacement angle is very small for any given increase in load, others are comparatively loose where the angle increase with load is correspondingly larger.
Further adding to the mix, the change in angle vs load is not linear. As the angle increases the motor draws more current to self correct, but it first needs to increase the angle, thus slow momentarily. It has go wrong to correct. It is feedback. The correction is sinusoidal so we can assume that this is more benign. But, as above, the point to point speed can be changing when playing a record. There is no free lunch.
Most synchronous motors used in TTs are 2 phase. We need a way to generate a phase shift between the two phases in order to make the motor rotate. This can be done with something as simple as a capacitor all the way up to sophisticated regenerator controllers. If you are targeting smooth, ultra low torque ripple you want to use a 3 phase synchronous motor. Well designed 3 phase synchronous motors are virtually linear torque devises. Of course the controller needs to be capable of driving such a motor by generating three phases, 120 degrees apart
If one was designing a TT today, where we were aiming for great dynamic speed stability. A logical strategy would be to use a 3 phase synchronous motor that is very stiff and of sufficient intrinsic torque to dominate the platter. Then wrap a very high speed, but gentle, feedback loop around this to make the drive even more speed stable.
Cheers