The only consideration is the ratio of the spindle speed to the motor speed. The ratio of the motor pulley to the drive sleeve pulley is 2.0 divided by 1.25 equals 1.6. So 10,000 RPM spindle speed would be 16,000 RPM auxiliary shaft speed. The ratio of the drive sleeve pulley to the motor pulley is 1.25 divided by 3.125 equals 0.4. therefore the motor RPM is 16,000 auxiliary shaft speed times 0.4 ratio equals 6400RPM.
I don't know why the DVR motor would be limited to 5500 RPM. Theoretically it should be able to run as fast as the microprocessor can switch as long as the motor's armature is properly balanced.
There are a couple of factors that limit the top speed of a motor.
First, motors all have a maximum “mechanical” speed. This is the limit above which the bearings may fail prematurely, or more likely that centrifugal forces exceed the structural strength of the rotor.
Second, high-frequency self-heating effects (from eddy currents) impose a thermal limit on motor speed. At some speed, to keep from overheating the motor, you have to reduce the motor current until the available output torque and power fall to zero. Running the motor that fast serves no useful purpose, of course, so the top rated speed is always somewhat less.
I have a Technatool DVR motor speed/torque curve that shows it can still produce about 0.9 hp continuously at 5000 RPM. So my educated guess is that Shopsmith chose to rate the motor for a higher speed, and settle for a lower continuous-power capability at top speed. This is entirely consistent with the reports of over-temperature alarms when routing at top speed for an extended period of time.