Elevator on rotating wheel space station

Is there any reason an elevator, moving from the central hub to the outer ring, would not function on a rotating wheel space station with artificial gravity?

Any parameter of the radius or rotation rate of the station is fine. I don't have any particular G force in the outer ring in mind. Any level of G's that would be logical for "normal" human habitation on such a station would be fine.

This was depicted in 2001: A Space Odyssey.

Is there anything wrong with this configuration, if the people on the elevator are sitting whether they start at the central hub or outer rim?

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Elevator on rotating wheel space station

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