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Q & A: conservation of angular momentum

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Most recent answer: 01/10/2014
Q:
When a person jump on a rotating merry go round, its angular velocity increases as he or she moves close to the center.
Finally, it stops due friction.

Can we apply the law of conservation of angular momentum in this case ?

Thanks
- Jessie (age 15)
Auckland, New zealand
A:
Yes, if you’re careful. Obviously the angular momentum of the merry-go-round plus person has changed when things come to a stop. The missing angular momentum must have been transferred to the Earth as a whole, which will then spin a tiny bit differently. However, that transfer occurs slowly. On a shorter time scale, the merry-go-round+person angular momentum is approximately conserved. So when the person moves toward the middle, lowering the moment of inertia, the angular speed must go up to keep the product constant.

Mike W.

(published on 10/22/2007)

Follow-Up #1: Formation of Water Vortices in Tanks

Q:
If you have a tank full of still water, say at the equator to remove Coriolis forces due to the Earth's rotation, and you pull out a plug at the centre and bottom of the tank, the water will be rotating visibly before the tank is empty. Why? And how can this be compatible with the conservation of angular momentum?
- Jeff Moreland (age 66)
Peterborough England
A:

Hi Jeff,

A lot of experiments were done on similar topics many decades ago. Actually, most of these experiments were trying to detect the Coriolis force in water vortices, and in the process they answered your question.

The researchers* found that even if you leave a tank of water for many hours without bumping it, there still remains a bit of net angular momentum from the random motions in the water. When you drain the water, then, the water rotates faster and faster as it nears the plug hole in order to conserve angular momentum. (Actually, there are a few much more complicated theories about how vortexes form around plug holes, but the experimental consensus* agrees with my description above: conservation of angular momentum magnifies the small net rotation left over from when the tank was filled.)

These experiments showed that in order to get rid of this initial net rotation, you would have to let the water sit still for over a day in an isolated, vibration-stabilized and temperature-stabilized environment.

If you take care of these variables (as the experimenters did years ago), you shouldn't observe rotation at the equator, and you could observe the rotation induced by the Coriolis force as you moved away from the equator.

Cheers,

David Schmid


*See Shapiro (1962), Binnie (1964), etc.

 


(published on 01/10/2014)

Follow-up on this answer.