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Consider the following situation:

You are locked inside a cylindric container allowing you to move around freely without being in contact with any of the items or surfaces aboard. The container is floating in space, far from any gravitational field, and is spinning around - like a washing machine would do, at a constant speed.

My question is: Is there any speed limit that would make air resistance inside the container substantial enough so that you would start spinning also? How about the same situation, but in vacuum? Are there any factors that could cause you to start the spinning motion at all?

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If the container full of air is spinning around you, the drag will eventually set you spinning as well, regardless of the rotational speed or the air density. Low air density just means that it will take much longer. Eventually the air and you will share the same rotation, so that as you speed up, the air and the container will slow down.

Only in (complete) vacuum will you never start spinning. But there is no such thing as a complete vacuum, there are always at least some atoms or molecules around. When the density gets too low, quantum effect will start to take over, as individual particles push you one way or the other.

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    $\begingroup$ It's worth adding that even if there were a complete vacuum, you would start spinning eventually (e.g. maybe after trillions of years) due to Doppler-shifted thermal radiation emitted by the container walls. $\endgroup$ – Nathaniel Feb 19 '13 at 4:36
  • $\begingroup$ And, also due to Mach's principle/frame dragging. en.wikipedia.org/wiki/Mach's_principle $\endgroup$ – user12029 Feb 19 '13 at 10:48

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