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Well I think if I were in a gravity free space and was rotating then will I be able to stop myself completely by moving my hands away from my body and hence increasing moment of inertia($I $) and decreasing the the angular velocity as angular momentum would be conserved?

My doubt is that whether I would be able to stop completely or just be able to decrease my angular velocity( $\omega $)

cause if angular momentum is conserved then $I\omega $should be constant. But then if $\omega $ is 0 then I should be rather infinity , so does it mean that I would never be able to stop ?

Am I thinking correctly ? Or is there any other way round?

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  • $\begingroup$ You're right. On the other hand, you can stop completely if you can throw objects away... $\endgroup$ – GCLL Feb 26 '17 at 14:40
  • $\begingroup$ GCLL , how would I be able to stop my rotational motion do I have only one choice of throwing my own material ?But that too in I am in confusion whether linear fashion or in a rotating fashion opposite to my rotation? $\endgroup$ – Physicsapproval Feb 26 '17 at 14:43
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    $\begingroup$ As the angular momentum of the system 'you+the objects you cant trow away' is conserved, you must throw the objects in such a way that they carry away all the angular momentum of the system. So it does not work to throw them in a radial direction. An example: take two balls in your hands, far from the center of your body, and throw them in two opposite directions parallel to your body (a sketch could help here... :) ) $\endgroup$ – GCLL Feb 26 '17 at 14:49
  • $\begingroup$ Pardon my naivety but it is common when overbalancing, to windmill our arms in the opposite direction. Surely this or even rotating a hand held flywheel or agyroscope would do the job. $\endgroup$ – chasly - supports Monica Nov 24 '18 at 13:07
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You are thinking largely correctly. $I\omega$ is conserved. You can increase $I$ by moving your hands away from your body. This would decrease $\omega$.

To stop completely, you would have to increase $I$ to an infinite value. You might do this if you had infinitely long arms.

Another approach that almost works is used by a spinning ice skater. She spins on a point of a skate. To stop spinning, she puts the other skate down, which digs into the ice. The ice exerts a force on her, which slows her spin to match the Earth. Likewise, she exerts a force on the ice, which speeds up the spin of the Earth. The Earth has an almost infinite $I$. So the change in $\omega$ of the Earth is almost $0$.

Of course, the Earth is spinning on its axis. One rotation per day is close enough to $0$ for most purposes. If it isn't, you would have to try this on a planet that doesn't rotate.

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  • $\begingroup$ "So the change in $\omega$ of the earth is almost zero"... And the change simply cancels out the tiny change in the earth's angular velocity when the skater started spinning... $\endgroup$ – DJohnM Feb 26 '17 at 16:28
  • $\begingroup$ @DJohnM - Angular momentum = $I\omega$ is conserved. The skater's $\Delta(I\omega)$ cancels the Earth's $\Delta(I\omega)$. The skater has a small $I$ and a large $\Delta \omega$. The Earth has a giant $I$ and a tiny $\Delta \omega$. And yes. The skater made a tiny change to the Earth's $I\omega$ when she started spinning, and set it back to what it was when she stopped. $\endgroup$ – mmesser314 Feb 26 '17 at 18:22
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You will just able to decrease the angular $w$ and also stop yourself because the energy or the momentum will get converted into stopping by increasing, Your $I$ so hence your muscular resistance will make the momentum conservation.But on contrary the weight will be very negligible on you.So the $w$ will get larger hence YOU will not able to decrease the $w$. So answer can be contradictory.

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