A DC motor, though, should be able to run at the exact speed required every time it's turned on-so with the correct pulley and platter size, and belt thickness, 33 1/3 rpm should be easily maintained, minus the effects of wear, dirt, belt slippage, etc.
If that were the case we'd all be using DC motors and none of us would be concerned with speed. ;-) Unfortunately, it doesn't seem to work that way.