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An ice skater is in a spin, she pulls her arms in and she spins faster, she lets her arms extend outward and then she starts to slow down. She will probably weigh on a weigh scale about the same weight during this spin cycle.

Now let us connect an electric motor to her to make her spin faster as she extends her arms outward. Would angular momentum still be conserved? It seems to me that it would not.

Also would she still have the same weight? I think she will weigh less as she is being accelerated by the electric motor.

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Angular momentum is still conserved in the system consisting of the skater, the motor, and whatever the motor is attached to (probably the planet). Why do you think the skater will weigh less? –  Keith Thompson Aug 14 '12 at 3:15
    
Yes Kieth I believe she will weigh a little less if she lets her arms float freely upward as she is spinning. Is there anyone out there who has access to a small portable centrifuge, just weigh it when its not in motion and loaded with someting heavy like mercury for example, then weigh it again when it is spinning under power. –  George Jones Aug 18 '12 at 1:24
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@ George Jones : I don't think that she will weigh less. She is rotating about an axis perpendicular to the Earth's surface (or along the line of Gravity) so there is no centrefugal force to counter gravity. –  Swapnanil Saha Aug 20 '12 at 16:20
    
I made some edits, since otherwise the question would have been off topic. –  David Z Aug 20 '12 at 17:00
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1 Answer 1

The problem will become clear to you once you consider the mechanism of the elctric motor you will use to make her spin faster.

Motor used for spinning

The vertical bars you can see is providing the torque, so angular momentum is conserved. If you ever feel that angular momentum is not being conserved, look deeply into the situation. You will find it being conserved.

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I should have described the situation better. The motor would be connected at the feet, it would be part of the total weight before spinning, and again weighed during the spin. Sort of imagine a large surface like a very sensitive truck weigh scales and the ice, skater, motor and everything is weighted. It is important to have the arms as free floating or falling, the connection of the skater would be made at the feet or head closest to the center of gravity ( spin). Now I think there will be a reduction of the weigh scales as the froce of gravity is shifted to centrifical force. –  George Jones Aug 21 '12 at 2:32
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