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Suppose a bar (black) sitting on a suspended ball (blue) has two rigid loads attached to it (red, green):

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Because the bar sits on a ball, the bar can swing clockwise or anti-clockwise. Suppose the red load can be shifted left and right. When the bar swings clockwise, will moving the red load to the right dampen the swing by decreasing the swung height? That is, would shifting the red load to the right increase the moment of inertia? Or should it be the other way around?

Any thought appreciated.

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  • $\begingroup$ moving the red load to the center will decrease the moment of inertia. also increase the torque in the clockwise direction. Thus assuming the red load start at the same distance than the green one, moving it to the right will increase the clockwise motion, moving it to the left will result in a counterclockwise angular acceleration $\endgroup$ – user83548 Jun 1 '16 at 15:42
  • $\begingroup$ So, does it mean that moving the red load toward the centre will dampen anti-clockwise rotation instead? That is, if the bar is already rotating in anti-clockwise, moving the red load to the centre could slow down the rotation or even stop it? $\endgroup$ – John M. Jun 1 '16 at 16:23
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    $\begingroup$ Yes and not only stop it, but start moving in the opposite direction. the problem is that if you move the loads to positions other than equal distance (assuming same mass) the equilibrium position will be vertical, not horizontal, with the load most distant from the center at the bottom. $\endgroup$ – user83548 Jun 1 '16 at 16:30

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