# How would one lose angular momentum in a vacuum?

## Main Question or Discussion Point

Hey all, I've been puzzling about this one for a while, and can't intuitively reach a conclusion about it. Although perhaps some law would provide a definite ruling...

In short: How can a system floating in vacuum lose angular momentum?

Longer, fun mental illustration: You awake to find yourself on a house-sized artifact in an empty universe. You only deduce that the artifact is rotating because you feel the centrifugal force (or centripetal acceleration, whichever one isn't an illusion) as you get further away from its apparent axis of rotation. The artifact is made of girders, planks and tethers, and you can restructure it however you wish. There are flywheels, cog wheels, springs, magnets, containers of liquid and gas, and a pressurizable cabin in which to manipulate them without loss. You also realize that you are not dying from lack of oxygen or hunger, and can invest as much mechanical energy into the artifact as your eternally able body can produce. How do you shed angular momentum without losing any mass (including the liquid and gas) into space?

Perhaps the conservation-of-angular-momentum law immediately rules this as impossible...does this still apply to a system in wich we can invest energy/manipulate mass in the manner described?

If not, how would you go about shedding momentum? I had three approaches in mind:

1) Set up the gas and/or liquid so that the centripetal acceleration causes friction. In this case, we lose kinetic energy to heat (temperature, thermal energy, I think you know what I'm saying. Not the scientific meaning of heat) until all kinetic energy is gone. But I can't figure out if such a scenario is possible.

2) Standing at the artifact's "equator", throw tethered masses out in the direction of rotation, and then pull them back from the other side. Both actions exert a force against the direction of rotation...but the angle at which we throw and pull will be slightly different, and would we regain all the angular momentum upon catching the tethered mass?

3) Would something as simple as this work?
http://www.xkcd.com/162/

If you need equipment for another approach, it's probably there, hidden away in some cranny of the artifact. Feel free to retrieve it and use it :) Only don't lose any mass!

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Hello,

What a delightful question!

First about the xkcd cartoon: it would work, as long as you kept spinning ;) As soon as you stop, everything goes back to how it was.

Well first of all, conservation of angular momentum says what it says :) it will be conserved.
My proposal would be to build a tiny box and with a mechanism that can store all the angular momentum present and hide it in a closet. I'm not even sure if it's possible, because I can't imagine how, but then again I can't find a law which it breaks.

Aw, shucks. That's kinda disappointing. It seems strange that one could immediately determine that their system was rotating, and yet do nothing about it. Anyway, you could probably store all the rotation in a flywheel, right? With magnetic bearings to minimize friction.

When a molecule emits a photon, the internal energy of the molecule (including both the kinetic energy of rotation and the kinetic energy of vibration/libration) is reduced by an amount equal to the energy of the photon. Thus, real-world molecules are continually losing angular momentum. You don't need a hypothetical construct. Every cooling substance is losing angular momentum. When that photon is absorbed by another molecule, there is no guarantee that the original angular momentum of rotation is restored. The partition of that photon's energy between kinetic energy of rotation and kinetic energy of vibration/libration will depend on the energy level of the absorbing molecule and its molecular makeup.

Hm. That's interesting, but at a macro level, wouldn't all these tiny changes cancel out? What are the chances that all the brownian-ish motion loss would all be in the same direction? Forgive me if my understanding is off...

K^2
Angular momentum is a conserved quantity. To lose it, you must get rid of it. Radiation is the most seamless way to do so. Note that one of the ways a large system can lose angular momentum is by radiating gravitational waves.

Hm. That's interesting, but at a macro level, wouldn't all these tiny changes cancel out? What are the chances that all the brownian-ish motion loss would all be in the same direction? Forgive me if my understanding is off...
They would cancel out if there were a spinning house in every point of the universe, but if you're the only one, only you send out light, so you can't also receive light (carrying angular momentum). So things can't cancel out. Maybe you're not clear about how the angular momentum is carried away? Radiation is (in this sense) electromagnetic radiation (of which light is one form), and electromagnetic radiation carries angular momentum (google "EM radiation angular momentum").

But notice! This breaches one of your demands: you didn't want to lose any mass, but light has energy and thus mass, according to $$E = mc^2$$, so don't be mistaken, by getting rid of angular momentum this way you'll be losing mass (but maybe the ratio angular momentum/lost mass is greater with light than with matter, I'm not sure, I haven't calculated it)

Hm. That's interesting, but at a macro level, wouldn't all these tiny changes cancel out? What are the chances that all the brownian-ish motion loss would all be in the same direction? Forgive me if my understanding is off...
The mean direction of angular momentum would be unaffected by photon emission from a macroscopic mass, but the magnitude (both total and mean) would be diminished.

I have seen no studies that suggest that the absorption of a photon by a molecule reproduces either the direction or the magnitude of the angular momentum lost by the emitting molecule. My guess is that the consequent angular momentum would be entirely independent of the antecedent angular momentum.

But notice! This breaches one of your demands: you didn't want to lose any mass, but light has energy and thus mass, according to $$E = mc^2$$, so don't be mistaken, by getting rid of angular momentum this way you'll be losing mass (but maybe the ratio angular momentum/lost mass is greater with light than with matter, I'm not sure, I haven't calculated it)
Good point, mr.vodka.

Although, by that logic, shedding angular momentum in any way will be losing energy and therefore mass - making the problem impossible by definition, unless we convert 100% of the artifact's kinetic energy into some storable form!

Though the total angular momentum must remain constant, there is a sense in which the direction of it's spin can be changed.

Determine the direction of spin using Coriolis. Paint some arrows around the perimeter of artifact. Construct a flywheel and spin it up on the axis of rotation until the rest of the structure is no longer spinning.

Putting leverage on the flywheel, turn the rest of the artifact over 180 degrees.

Now spin down the flywheel. The direction of spin of the artifact relative to the painted arrows is now reversed.

I was actually trying to figure out if something along those lines could be used to stop it entirely, but I think gyroscopic precession ruins it.

Instead of one, suppose we build two magnet-bearing flywheels into boxes, and stack them on top of each other, so that the plane of one flywheel is above the plane of another and they share the same axis of rotation. They are also on the same axis of rotation as the artifact itself.
Now, using a bicycle-powered magnetic drag, we begin to accelerate both flywheels equally in the direction of the artifact's rotation. The act of doing this necessarily accelerates the artifact itself in the opposite direction, ie. against its own rotation. Eventually we reach the point where the artifact is at rest, and all its angular momentum is stored inside the two spinning flywheels (along with a heck of a lot more angular momentum, from the energy invested into the system by the bicycle-drag). But the point is that it's equally distrubuted between the two.

Now flip one over, so that they are on top of each other but spinning in opposite directions, and let them drag each other down to a stop. I figure the problem is the point where we flip one over (or even just flip both 90 degrees in opposite directions, and then move them sideways) - that this would somehow impart torque on the artifact and bring it up to speed.

Cleonis
Gold Member
Hey all, I've been puzzling about this one for a while, and can't intuitively reach a conclusion about it. Although perhaps some law would provide a definite ruling...

In short: How can a system floating in vacuum lose angular momentum?
You mention the following attempt: get some internal friction going, so that kinetic energy dissipates. If you can sustain dissipation then your angular velocity must go down.

So, is there anything in the laws of physics that says you can't keep dissipating energy?

I'm thinking now two flywheels, connected by an axle, with bearings so they spin freely on that axle. If the two flywheels are initially co-rotating, can you dissipate their kinetic energy? What if you transfer kinetic energy from one flywheel to another, so they have different velocity, and then you use friction to bring the two flywheels to co-rotating motion again.

Clearly, that last step dissipates energy. So: can you repeat that, and reduce the angular velocity of the flywheels more and more.

I don't think you can.
When two flywheels are co-rotating then there is a cost in transferring kinetic energy from one flywheel to another.
This energy cost is analogous to energy cost that corresponds with change of entropy.

When the two flywheels have different velocity, and friction is introduced then there is only one way in which the system will develop, to a state of co-rotating motion. The state of co-rotating is analogous to a state of highest possible entropy.

When a system is in a state of highest possible entropy, then there is an energy cost in moving the system to a state of lower entropy. For the case of the two flywheels: the energy dissipated during the friction stage is only the energy that was pumped in in the first place, to induce difference in angular velocities

I think this generalizes to anything you might try to dissipate energy. Example: a star that is forming loses rotational kinetic energy because there is convection inside. Could you set up something like that in a fluid filled vessel? Well, I think that in order to get convection going you need to heat the liquid. I think that the energy that eventually dissipates will never exceed the energy that is pumped in in the first place.

Hence a system in vacuum cannot reduce it's own angular momentum.

~~~~~~~~~~~LATER~~~~~~~~~~~~~~~~~

So sorry to resurrect this long-dead thread for something that I know won't change the outcome, but I must know why!

I was just posting elsewhere about something related to weather, and ended up thinking about coriolis force.

The coriolis force is a fictitious force, but any movement caused by it represents a real transfer of energy. Where does this energy come from? If it doesn't come out of the planet's rotation, then where does it come from?

New scenario: suppose the empty universe has a single, large, rocky planet with an atmosphere of some gas/liquid that really doesn't like to freeze. It is spinning, but there is no light source shining on it from anywhere. Does the coriolis force cause friction in the atmosphere? If so, doesn't that mean this will slowly kill its rotation? If not, what is different about earth such that we observe the effects of coriolis force here?

The Coriolis force on an object also acts perpendicularly to the velocity of the object. This means that it does not change the object's speed, only its direction of motion. This means that it does not impart any new energy to the objects on which it acts.

Also, the Coriolis force on an object is proportional to the speed of the object as seen in the rotating frame. So if the atmosphere of a planet is everywhere at rest with respect to the planet's surface, no part of it experiences a Coriolis force.

Ah, thank you very much. So the Coriolis force on the planet would not induce friction in the atmosphere, and earth's atmosphere experiences coriolis force due to the pre-existing motion of the atmosphere. Thanks!

D H
Staff Emeritus
By bringing up the atmosphere you are getting close to an answer to your original question, "How would one lose angular momentum in a vacuum?"

The length of an earth day is gradually increasing. 2.45 billion years ago, a solar day was 17 to 19 hours long. 4.5 billion years ago, some estimate that a day was only six hours long. So right under our feet there is an example of an object that is losing angular momentum in a vacuum.

This change in length of a day is not due to coriolis forces. It is primarily the ocean tides, and possibly the earth tides. Another mechanism that acts on satellites in low earth orbit is gravity gradient torque.

Yes, but the question is how the system can lose angular velocity without ejecting mass, specifically. (Oops, I guess that's not clear from the title...)

My understanding is that the very same process that slows the Earth's rotation is also increasing the Moon's orbital distance. Taken to its conclusion, the Earth loses its angular velocity, but it also loses the Moon. And the system as a whole still hasn't lost its angular momentum, it's just transferred between bodies such that one isn't rotating on its axis...so yes, you're right, it's a solution in a sense, but just not with all the impossible constraints I had in mind. :)