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Where does the top's angular momentum get transferred to? Does it very slightly change the angular momentum of the table, and then the angular momentum of the Earth?

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Conservation of Angular momentum applies only when you don't have any net torque on the system. For a spinning top, the frictional force between the top and the floor would give it enough torque in the opposite direction so as to make the top stop (this is much like how a block loses its linear momentum due to friction when it slides down a plank). As far as the energy goes, it gets converted into heat, sound etc. Of course if you took an atomic point of view, you'd see that the angular momentum of the top slightly changed the angular momentum of the molecules of the table. It would also have changed the angular momentum of the earth. But such effects are hardly noticeable. This xkcd comic is relevant:

xkcd162

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Well, the XKCD comic's physics is wrong. The first turn robs the Earth of angular momentum, depending on your latitude. The subsequent turns simply fail to return the angular momentum. –  Mark Eichenlaub Jul 24 '11 at 18:16
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@Mark, you interpreted the comic incorrectly. The comic doesn't say that each turn goes on robbing the planet of its angular momentum. But to keep the planet's angular momentum reduced, you'll have to go on spinning. Sure, only the first turn robs the Earth of its angular momentum. But soon frictional forces between you and the earth's surface would take over and would give back the earth its angular momentum. So to permanently rob the earth of angular momentum, you'd have to constantly keep spinning. –  Bernhard Heijstek Jul 24 '11 at 18:31
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@Mark: She's actually turning faster and faster. –  Seth Jul 24 '11 at 19:44
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Does it very slightly change the angular momentum of the table, and then the angular momentum of the Earth?

Yes, it does.

Exactly the same amount but opposite direction of the momentum earth received when the top was accelerated first.

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