A rotating frame equation for the "carousel experiment"

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TL;DR
The "carousel experiment" is the worst case to show the Coriolis force despite claims it show the "Coriolis effect".
As was repeatedly shown by Anders Persson,

https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.2477
<link removed>

the "carousel experiment" is a poor case to show the Coriolis force despite claims it show the "Coriolis effect". Indeed, the Coriolis force, if it was alone (which is true for an elastoid), would should a narrow circle that oceanographers know well under the misleading term "inertia circle", quite different from the wide deflection occuring in the "carousel experiment".

This led me to a very short exercise:

An alternative rotating frame equation, without the Coriolis force, is simply as follows:
a_r = a_a - 2 Ω x v_a + a_cp
with a_cp a centripetal term

In the "carousel experiment", a_a=0 and v_a=cst => a_r = cst + a_cp .

The Coriolis equation was implicitly a choice made by G.Coriolis because he has chosen not to try another decomposition whereas geometry allows an infinite choice and in some cases there are better choices than his. Geophysicists understood afterwards that his decomposition is exactly the right one to show the fundamental "elastoid-inertial" planetary mode, but this is another story, very different from the "carousel experiment" (which does not include any elastoid).
 
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