Conservation of angular momentum in helicopter
I have a small RC-controlled toy helicopter with removable tail rotor.
Suppose I remove the tail rotor, hold the tail with my hand, start the rotor until it moves with constant angular velocity and then let it go. Suppose that the heli remains on the floor all the time.
Then the body of the helicopter begins to turn into the opposite direction of the rotor.
My problem is to explain this in terms of angular momentum. At first this seemed to contradict angular momentum conservation because I assumed that the helicopter is a closed system and there is no external torque, but the rotor keeps the same angular velocity while the body starts to turn into the other direction.
My second thought was that I have to take the air into account. If I do that it seems plausible to me to explain it as follows:
The rotor transfers angular momentum from to the surrounding air. However to keep it running at constant angular velocity, the motor has to transfer angular momentum to the rotor, which is only possible if the body of the helicopter gets the same amount of angular momentum as goes to the rotor, but into the opposite direction.
But then I thought, the body should turn faster and faster to infinity which obviously doesn't happen. 782
So I guessed I should also take the friction with the floor into account where the angular momentum of the body is transferred to.
This leads me to the following three questions:
1. Is my reasoning described above correct or I am completely wrong?
2. If I would do the experiment on an almost frictionless turntable (which I don't have available at the moment), would the body of the helicopter indeed become faster and faster almost to infinity?
3. If I would do the same thing in a vacuum, what would happen? I guess (see my first thought above), that the body wouldn't turn at all. Is that correct?
So it would be great if someone could clarify this in terms of angular momentum.
Since the same problem should occur in real helicopters, I guess that there should be some detailed literature about it's physics, but I didn't find any resources about this. So if you have any references for more details or further reading on this problem, it would be also great if you could post it. 621