Why is there no helicoptor with a single rotor?

[amberlyp]

All helicopters have two rotors. Some have both rotors on vertical axes but rotating in opposite directions, and the rest have one rotor on a horizontal axis perpendicular to the helicopter body at the tail. Why is a single rotor never used?

 

[cepheid]

To prevent the helicopter from spinning in circles, I believe.

 

[amberlyp]

i think i have to relate it to energy and momentum and all that great stuff...

 

[cepheid]

okay. What physical quantity does the motor "impart" to the rotor? (Hint: it puts it into rotational motion right? So how is that measured as a "quantity?") If so, does an equal and opposite amount of this quantity get "imparted" back to the helicopter?