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The question is based on, for example, 2001: A space Odyssey with the running, or astronauts running around Skylab. It sparked a comment on Reddit where someone was saying that the longer they run, the faster the station would rotate, which of course would be a problem for reaction wheels or thruster fuel.

Conservation of angular momentum was quickly brought up, but that was "refuted" with hand wavy sounding things about energy being expended by the runner and therefore not violating anything.

I just want to make sure I'm not missing something. It seems like the spinning would stop as soon as the runner stopped.

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    $\begingroup$ Momentum and angular momentum in a closed system are always conserved. The refutation is bogus. $\endgroup$
    – PM 2Ring
    Jun 13, 2018 at 3:15

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Angular momentum is always conserved. To add angular momentum to a satellite a propulsion engine has to give an impulse , the gasses leaving conserve the angular momentum gained by the satellite.( that is why propulsion engines are balanced around the center of mass)

This video of an astronaut spinning ( towards the end) shows how conservation of angular momentum works on closed systems. The dominant effect of the change in rotational velocity of the satellite when the astronaut runs around in the inside perimeter is similar to the increase and decrease of rotation of Mike Fossum when extending and closing his arms , as the whole system is closed. ( this is the same with ice skating figures). When the motion stops the satellite will return to its previous rotational velocity. The total angular momentum does not change.

A small caveat: The only way energy and momentum can leave the closed satellite system due to a person running is by radiation. Part of the frictional energy of the feet, and of the person's muscles' energy expenditure will radiate away, and some of it will be directional as the person is not in the center of mass, and the momentum gained by the feet is directional. This should give a tiny addition ( or subtraction if the running was against the rotation direction) to the original total angular momentum.

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    $\begingroup$ This answer covers it pretty well. I guess with further probing, it seems the real problem is the person doesn't understand what's meant by "closed system" and they think the astronaut on the inside counts as outside influence. Somehow. Or that thrusters on the outside aren't somehow different. $\endgroup$
    – Vectorjohn
    Jun 13, 2018 at 22:11

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