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.