And this is a 'special' situation? I think.In general, an object moving uniformly in an inertial frame, moves on a spiral in the rotating frame. The circle is a special case.
No, the special case where the trajectory in the rotating frame is a circle, is when the object is at rest in the inertial rest frame of the rotation axis. When you jump radially of the wall of a rotating station, you move linearly in the inertial frame, so your path in the rotating frame is not a circle.And this is a 'special' situation?
Yes, because the higher your jump and the longer you spend in the air traveling a straight line while your jumping-off point is following the curved path, the less accurate the small-angle approximation becomes.So if one were to jump "really hard", would that enable one to land on a different spot than the one you jumped off from?
However high you jump there is a difference between your travelled distance and how far the floor has travelled by the time you land. The difference is increasingly relevant, the higher you jump.So if one were to jump "really hard", would that enable one to land on a different spot than the one you jumped off from?