Confused about the conservation of angular momentum

[Rick16]

TL;DR

confused about conservation of angular momentum

In his book "Take me to your leader", Neil deGrasse Tyson writes that rotating flying saucers cannot exist, because they would violate the conservation of angular momentum. I don't really understand this. If the thing rotates, it must have an engine, which produces a torque. When there is a torque, angular momentum is not conserved. Theoretically, the torque should be external to the system under consideration, but is the torque here really internal? The engine has to be powered by something. Let's say it is powered by a battery. This battery had to be charged beforehand, so energy entered the system from the outside. Can I still consider the flying saucer as an isolated system and analyse it as such?

Then deGrasse Tyson writes that helicopters have tail rotors for the same reason, i.e. conservation of angular momentum. I thought the tail rotors were there to stabilize the helicopter. Can one or should one really analyse this situation using conservation of angular momentum?

And what about my car? When I drive along the road my car's tires rotate, but since they are in contact with the road, I guess that they try to spin the earth in the opposite direction, which would take care of the momentum conservation. A flying saucer has no contact with the ground, but it has contact with the air and if it rotates it certainly would produces air currents, which could counter the rotational momentum of the saucer. I could then define my system to include the nearby air, and there would be no more momentum violation.

As you can tell, I don't see clearly at all in all this.

 

[A.T.]

Neil deGrasse Tyson writes that rotating flying saucers cannot exist, because they would violate the conservation of angular momentum. I don't really understand this.

Can you provide his full argument?

Theoretically, the torque should be external to the system under consideration, but is the torque here really internal? The engine has to be powered by something. Let's say it is powered by a battery. This battery had to be charged beforehand, so energy entered the system from the outside. Can I still consider the flying saucer as an isolated system and analyse it as such?

Energy and torque are different things, and a system can be isolated against one but not the other.

I thought the tail rotors were there to stabilize the helicopter.

Stabilize against the torque from the main rotor.

 

[Roberto Pavani]

For the car: your front is "lifted" and your rear is "lowered" under acceleration (think of motorcycles doing wheelies), that's the reaction torque from the wheels.

For the helicopter: the tail rotor generates a horizontal force that, since it is displaced from the helicopter's center of gravity, produces an opposite torque, cancelling the main rotor's reaction torque on the fuselage.

In space: satellites use reaction wheels to change orientation. Total angular momentum remains zero.

You can do a simple experiment: sit on a rotating office chair and spin a heavy book (or a bicycle wheel) by hand, you'll rotate in the opposite direction. That's conservation of angular momentum in action.

 

[Rick16]

Can you provide his full argument?

Here is the full paragraph:

All this leaves me saddened to report that smooth, rotating flying saucers are not a thing. They violate the conservation of angular momentum, which is physics-speak for declaring they cannot spontaneously spin up and spin down without some other thing to counter the rotational momentum. That's why helicopters have tail rotors. Damage it and the chopper spins out of control. Helicopters designed without a tail rotor otherwise sport two counter-rotating main rotor blades, to compensate for each other's angular momentum. You can also spin up via sideways jets that spew forth any kind of mass. Turn those same jets around by 180 degrees and they will slow down your rotation.

 

[Rick16]

Energy and torque are different things, and a system can be isolated against one but not the other.

I meant to say that the energy is ultimately responsible for the torque, and that therefore the torque might be considered external to the system, i.e. the saucer.

 

[Rick16]

For the car: your front is "lifted" and your rear is "lowered" under acceleration (think of motorcycles doing wheelies), that's the reaction torque from the wheels.

Very interesting, I never thought of it that way.

 

[Rick16]

cancelling the main rotor's reaction torque on the fuselage

So there would be a reaction torque on the fuselage similar to the reaction torque on the car. Very clear explanations, thank you.

 

[Rick16]

Okay, my idea about the external torque is pretty far-fetched. I think I am rather convinced that there is no external torque acting on the saucer.

Now I wonder what would happen if somebody built such a thing. It should not be difficult to build a rotating disc, it wouldn't even have to lift off, it could sit on a pole or be attached to a balloon. But in these cases I suppose that the pole or the balloon would experience the compensating effect. And if the rotating disc were not attached to anything -- what would happen to it?

 

[Filip Larsen]

Note that it perfectly fine for an isolated system at rest (e.g. a saucer) to spin up parts of the system as long as the total angular momentum (as a vector quantity) is conserved. For example, if the system is a gyro (a "bicycle wheel") with its axis attached coaxial inside an enclosing hollow ellipsoid (a "saucer") combined with an engine providing a torque between the two, then the outer ellipsoid can spin up just fine. This angular situation corresponds to the linear situation where two parts of an isolated system change speed relative to each other (and external observers) by exchanging linear forces.

This is also what deGrass seems to explain during the quote, even if his opening statement perhaps is a bit too categorical in the sense that conservation of angular momentum alone does not as such preclude the existence of "free flying saucers appearing to spin up". But on the other hand I am not aware of the context of his quote, so I do not know if he is aiming to explain physics (and just used saucers as a bad example) or if he felt the need to call bluff on some speculative observations at the time.

 

[A.T.]

But on the other hand I am not aware of the context of his quote, so I do not know if he is aiming to explain physics (and just used saucers as a bad example) or if he felt the need to call bluff on some speculative observations at the time.

Whatever his goal was, I don't think he is doing a good job on either front. Making things that look externally like they spin up in space, is possible even with our current technology. Either by ejecting something with opposite angular momentum, or by counter rotating internal parts. So declaring it impossible is rather silly, and counter productive to either potential goal.