When you put your hand over the mouth of the vacuum cleaner hose, you can hear an increase in the pitch of the motor hinting that the motor speed has increased. Why is this?
A friend of mine once heard that in this state the motor has no load in this condition, and hence it speeds up since there is no air load to resist the full strength of the motor. Is this correct? Also, in this condition are you starving the fan, and if so, how does the vacuum still maintain suction? - Jinx 
Your friend is nearly right. It’s working under reduced load. Here’s why. Normally, the fan motor takes air from the sweeper’s business end, and it throws it into the filter bag. That’s the work load the motor was designed to do. The ambient air pressure in the room continues to push air into the hose to replace the air thrown out by the motor. When you close off the intake, the fan hasn’t any new air to move. It speeds up; with no new air to throw, it is doing less work. It’s not “no load,” because the motor still has to spin itself and the fan rotor.
By the way, although we usually think in terms of a “vacuum” cleaner, and we speak of the machine “sucking” up dirt, it’s the other way around. The ambient air pressure (roughly 15psi) all around us is pushing the dirty stream of air into the machine when the pressure is slightly reduced inside the hose. There’s never a vacuum, because there is still pressure inside the hose.
I wouldn’t say there is no load but there is no airflow. That may account for a decreased load. To maintain a vacuum you don’t need to do anything but keep air from getting back in. That’s what the fan is doing with a blocked intake.
The strength of the suction depends only on the reduced air pressure at the hose inlet, and the size of the inlet. A inlet with a 1" area will lift at most 15 lbs, and that’s with the hose being completely evacuated. Whether the fan is still pushing air or not doesn’t affect the strength of suction at all.
This makes no sense to me at all; i’ve always thought that the rising pitch of the motor was due to increased load. Normally, the motor moves air with only a little pressure difference; block the inlet, and the motor is suddenly working against a rising pressure differential.
Once the inlet is evacuated, the only load on the motor is from the mass of the rotor and fan, and what air leaks back in through the exhaust vent. That leakage represents less mass per second for the fan to move than when the inlet is wide open; less load.