Before the space station spins, everything not attached should be "floating" inside it.
When the space station is made to spin, to experience "artificial gravity", everything must spin with the space station.
If the ball is not attached somehow to the space station, and does not spin with it, it remains "floating" as the space station turns past it.
However, if the ball was "floating" in a e.g. room on the space station,
it will hit a wall when the station starts spinning. This will make it spin with the station, (perhaps after a few rebounds), and it will "fall down", towards the "floor" ( the" floor" will be the outer surface of the room)
The acceleration at the outer edge of a space station of radius "r" rotating at "n" rotations per second is:-
accn. = 4 * pi^2 * n^2 * r
With a suitable choice of "n" and "r", the acceleration can be made equal to 9.8 m/sec^2, as on the Earth's surface.
People standing at the outer edge of the space station as it turned would then "feel their normal weight".
However, should they somehow move nearer to the centre of the spinning station, they would feel "lighter and lighter", and float again if they reached the centre,
The space station in the film 2001 showed the effect.
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