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You are isolated ( no bodies around you except the wheel) . enter image description here

Now you(orange) spin the blue wheel ( torus) with an $\omega$ in the direction of axis and then let go of the wheel . Now how will you move ? Will you keep moving in the brown circle ? ( Because by conservation of angular momentum you must also have an opposite $\omega '$ of some different value .

Edit1: Okay i have neglected something very basic , gravitational force ,which makes it even harder to imagine what will happen and how angular momentum will stay conserved

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  • $\begingroup$ Does the brown ring represent an object, or do you only intend it to indicate a possible path for the orange object? $\endgroup$ – S. McGrew Jun 10 at 14:15
  • $\begingroup$ Indeed .just the path , not a real object. $\endgroup$ – soutrik das Jun 10 at 16:04
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Assuming that the brown circle in your drawing only indicates a possible path and nothing physical, then an interaction between the orange cylinder and the blue torus that causes the blue torus to spin will do several things: 1) it will cause the blue torus and the orange cylinder separately to spin about their own centers of mass; and 2) it will give the blue torus and the orange cylinder each a velocity in opposite directions. If all the angular momenta are added up, the change adds up to zero. If all the linear momenta are added up vectorially, the net change in linear momentum is zero.

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  • $\begingroup$ the brown ring is indeed just the path. also by the orange cylinder i wanted to represent a human like me . If i spin the blue torus using coupled forces ( like how you open a bottle cap with two fingers ,similarly doing that using two hands , I think i will not have any linear momentum ( and torus will also have 0 linear momentum) but now The torus is spinning about its com ( which is indeed the axis in my diagram) but I am spinning along my own COM ? in opposite direction. So even if the axis are different ( ie spaced apart ) they still can be added to find the net agular momentum of a $\endgroup$ – soutrik das Jun 10 at 16:02
  • $\begingroup$ system ? ( This misconception is probably because i always though two angular momentums always have to be along the same axis to be added or substracted ) $\endgroup$ – soutrik das Jun 10 at 16:03
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you transfer angular momentum to the wheel, so you lose angular momentum. the system (you and the wheel) angular momentum is conserved.

hence your orbit around the wheel will decay or you will lose some of your spin.

L=R×Mv+Σr_i×m_iv_i

where the first component is total system angular momentum about center of mass and the second is the individual particles angular momentum about center of mass.

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  • $\begingroup$ "I transfer angular Momentum"? . At the beginning neither did i have any angular momentum nor did the blue wheel. So if i give it angular momentum , i get the same amount of angular momentum (but opp dirn) . Also why will it decay ( if its in an ideal space ) $\endgroup$ – soutrik das Jun 10 at 12:57
  • $\begingroup$ how did you get to be there in the first place? $\endgroup$ – ryaron Jun 11 at 7:59
  • $\begingroup$ Thats not the question... $\endgroup$ – soutrik das Jun 12 at 0:23
  • $\begingroup$ gravitational force will you pull you together. $\endgroup$ – ryaron Jun 12 at 2:39
  • $\begingroup$ so you can only be in this position if you orbit one another. $\endgroup$ – ryaron Jun 12 at 2:39

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