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Old 10-13-2015, 09:35 AM
Ernst Ernst is offline
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Join Date: Jul 2012
Posts: 905
You are forgetting that when most of the mass is far from the axis, the whole will rotate slower than when it is near to the axis. THAT is "the LAW". Otherwise there would be an increase of energy in the system when the mass is at the far end.
Remember the orbital velocity is wr (w being the angular velocity), then the kinetic energy is mv/2 becomes mwr/2. So when r increases while w remains constant, the kinetic energy increases.
Thus, to keep a constant velocity you must add energy when the mass-centre to axis distance increases, and you must put a break on it when this distance decreases.
This externally REQUIRED force is the force that you thought to get for free....

Nice try though!

Ernst.
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