Cases where centrifugal and coriolis forces are applicable

Question

I'd like to ask my query through 2 case examples:

Case 1) Suppose a person whirls a stone tied to a string in a horizontal circle around him such that he/she is always pointing and looking towards the stone such that the stone appears stationary.
Case 2) Suppose a person stands at the edge of a rotating disc and throws a ball towards the center.

In which cases are the centrifugal, and in which cases are the Coriolis forces applicable?

Under no inertial reference frame are they applicable, but if you consider rotating frames, then they are applicable at the same time. There is no possibility of them appearing separately. But they are different things and so they must not be confused with each other. — naturallyInconsistent, Apr 24 '23 at 14:21
One of these posts may help you understand these forces - Coriolis Force: Direction Perpendicular to Rotation Axis Visualization, Trying to gain better intuition about fictitious forces — mmesser314, Apr 24 '23 at 14:42
@naturallyInconsistent Usually the two go hand in hand, but on the equator there may be a centrifugal force but no Coriolis force, while at the poles there may be a Coriolis force but no centrifugal force. — Nuclear Hoagie, Apr 24 '23 at 15:01
@NuclearHoagie I would rather say that they both exist, just that in some special limits, the formulæ may evaluate to zero. Also, I do not think what you say is true. Centrifugal effect may uniformly vanish at the poles but Coriolis will be detectable at any place by sampling different velocity directions. — naturallyInconsistent, Apr 24 '23 at 15:13

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