Conservation of angular momentum in propeller planes and helicopters Consider a propeller plane with only one propeller in the front. If the propeller rotates, I would expect by conservation of angular momentum, that the body of the plane would spin in the opposite direction of the propeller but with much lower angular velocity because of the larger moment of inertia. However this doesn't happen in real world. Is it correct, that this would happen in empty space and that the air is responsible to prevent the spinning of the body of the plane?
If so, how does this mechanism exactly work? How can one estimate the order of magnitude of the effects? What's the difference between the propeller plane and a helicopter where one actually needs for example a tail rotor to stabilize the helicopter.
Would be great if your answer would contain some formulas and approximations which estimate the orders of magnitudes in those problems. 
 A: The effect you describe is called engine torque or propeller torque.  All that happens is that the pilot opposes this torque with aileron in the opposite direction.  Because the wings have a much a larger lever arm than the propeller, usually only very small deflections of aileron are needed to counteract the propeller torque.  Most times the pilot won't even be conscious of it.
There are exceptions, when one is flying a very powerfull plane at low speeds and one suddenly increases power, the engine torque can overcome the ability of ailerons to counteract it.  This is called an involuntary torque roll.  This was known to have killed many inexperienced pilots with the Corsair fighter in WWII, for example, because it had such a powerful engine with high torque.  Another example was the Japanese Zero, which had such high torque that it could not roll very effectively in the counter torque direction, giving American pilots an advantage.
A: I think the torque described in the answer is the result of the propeller doing work against a wind resistance, not really the angular momentum of the propeller itself, which is a different issue. A prop spinning in a vacuum would have high angular momentum, but no torque would be required to keep it spinning. What I wonder is how the mechanical stresses of changing the attitude of the propeller are handled, given the very high angular momentum of one or more spinning props. Shouldn't this make it almost impossible to steer the plane in any direction  ?   Doesn't this put stress on the wings  ?
A: Yeah, I think even if the propeller was spinning at constant RPM there would be the rolling moment induced into the aircraft to conserve angular momentum. In case the engine tries to accelerate the propeller to a different RPM, you would have the additional reaction torque that comes from accelerating the inertial of the propeller.
