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Let's imagine a grand hamster wheel in space. The wheel is very large and is constructed of the same reasonably inelastic material. It has three main features: The first is a solid disk rotating at the speed required to create 9.8 m/s of centripetal force at its outer edge. The second feature is the "floor" of the structure, a wide rim around the circumference of the disk which one could stand on and feel the full 9.8m/s "artificial gravity". And the third feature is a poll attached to the disk at the axis of rotation, which, being attached, rotates at the same speed as the disk and the rim.

A space traveler is able to "land" at the center of this great wheel with little to no issue, the rotation at the center is slow and the centrifugal force (illusory sensation of being pulled to the edge of the station) is nearly imperceptible. With no other gravitational forces pulling on the traveler however, if they hang onto the poll with a firm grip they should find that their legs slowly "fall" off the wall to point to the "floor" (the outer rim of the structure). Once the traveler is balanced in this position, presumably perpendicular to the "floor", the traveler lets go of the central poll and "falls" to the "floor".

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What does their trip to the edge, and more importantly the transition to the simulated gravity of the floor's centripetal force, look and feel like?

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I am having a very hard time imagining this. The two competing images I come up with are:

A) the traveler drifts to the floor as if they were light as a feather and then feels the "floor" suddenly accelerate up against their legs.

BUT, that would seem to indicate that the traveler was simply traveling at that speed, and so should have felt the full 9.8m/s while hanging. But if that were true then the "centrifugal force" at the center of a merry-go-round should feel equal to any other point on the platform, no matter how far out you go... which is wrong... right?

B) The traveler drifts down to the floor at the snails pace imparted by simply letting go of a rotating bar. But when the traveler reaches the rim, it is moving at a much higher speed relative to the center. The traveler's feet are swept out from under them. They tumble until they have, through impact and friction, accelerated their body to the speed the wall is traveling at.

BUT, that would seem to indicate that while the traveler has fallen, their trajectory has been bent away from perpendicular, so that they are effectively striking the floor at an angle. The angle is closer to parallel to the "floor" at first, and only becomes perpendicular again once the traveler has been accelerated to same speed as the rim. But what force would bend the traveler's path through empty space between releasing the poll and landing?

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    $\begingroup$ Interesting question. After he lets go of the bar, would he not continue to do backflips as he fell towards the floor. There would be nothing to stop him from doing those backflips. $\endgroup$
    – foolishmuse
    Commented Sep 9, 2022 at 4:06
  • $\begingroup$ Fair point, but if the rotational speed at the center is truly small the tumble could be avoided with the slightest flick of the wrist on release. The traveler is merely accounting for the difference in speed between their hands and their feet. However a flick of the wrist could not cause or negate the drastic differences between the the two scenarios I described. (Right?) $\endgroup$
    – Christo
    Commented Sep 9, 2022 at 17:49

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B is correct. Well, it would be a snail's pace radial speed, not a snail's pace relative tangential speed.

BUT, that would seem to indicate that while the traveler has fallen, their trajectory has been bent away from perpendicular, so that they are effectively striking the floor at an angle.

From the point of view of someone on the rim, yes. They would see someone floating down with significant horizontal speed.

But what force would bend the traveler's path through empty space between releasing the poll and landing?

In a non-inertial frame (such as that of a person on the rim), there are non-inertial forces (such as Coriolis) that appear to affect such trajectories. Video of ball on rotating table

Note that although the person is rotating with the speed of the station, the traveller does not have the horizontal/tangential speed that the rim does. They leave the pole with almost no tangential velocity. A person on the rim looking up would see the traveller leave the pole and immediately start drifting "backward" compared to the direction of rotation.

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    $\begingroup$ But if the ball starts out at the exact center, net force is zero and it will not move outwards $\endgroup$
    – Carl Witthoft
    Commented Sep 9, 2022 at 12:34
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An alternative situation: suppose we have a fully pliable "person" who ends up in the shape of a disk or cylinder equally spaced around the axis of rotation. if the person is holding on to the pole with his hands, the rotation will cause him to be wound around the pole. There is no centripetal or centrifugal force being applied. If he lets go of the pole, he will hang in space as the space station rotates around him. There is no force in a radial direction.

Perhaps you are assuming the person is a rigid rod, so that his attachment to the center pole causes him to rotate. Their asymmetric shape now allows for the existence of net centripetal force.

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