Note the terms in the quote below, i.e. "interpreted as a force (an apparent force)" and the 'special case'. Since we reside and observe within the rotating frame of reference, it is basically a useful simplification for educational purposes that enables access for an audience that may not have an extensive math / physics background for the strict definition.

From "A Coriolis Tutorial", James F. Price, Woods Hole Oceanographic Institution at https://www2.whoi.edu/staff/jprice/wp-content/uploads/sites/199/2019/01/aCt_2003.pdf

"... An Earth-attached and thus rotating reference frame is almost always used for the analysis of the atmosphere and ocean. The equation of motion transformed into a general rotating frame includes two terms that involve the rotation rate — a centrifugal term and a Coriolis term. In the special case of an Earth-attached frame the centrifugal term is exactly balanced by a small tangential component of gravitational mass attraction and so drops out of the dynamical equations. The Coriolis term that remains is a part of the acceleration seen from an inertial frame, but is interpreted as a force (an

apparent force) when we solve for the acceleration seen from the rotating frame. The rotating frame perspective gives up the properties of global momentum conservation and invariance to Galilean transformations, but leads to a greatly simplified analysis of geophysical flows."

Yes, affected the currents on the ocean on the direction and the winds also. Thosr effects are important on yhe heat bufget balsnce on thebearth

To supplement Michael John Patrick's answer, the centrifugal force has no direct meteorological effects because (a) it is a property of an object at rest in a rotating frame (as distinct from Coriolis force, which only affects objects that are moving in a rotating frame), and (b) because the centrifugal force is balanced by the component of gravity that is also ground-parallel. That gravity component in turn arises because the earth is not a perfect sphere but is shaped more like an orange, with radius from earth center to equator a few km. longer than the radius from earth center to the poles.

If the earth was a perfect sphere, the centrifugal force would cause all the fluids on its surface to pile up at the equator. Something like that probably happened as the earth was being formed however many billion years ago - but as it solidified, the shape of the earth equilibrated with the centrifugal force to take on the (non-spherical) shape that it has now.

Atmospheric or oceanic fluid particles sitting at mid-latitudes feel gravity directed towards the earth center, but since the earth is "flattened" a bit, that gravity vector is not perpendicular to the surface, but has a component parallel to the surface directed towards the nearest pole. That's the component that balances the centrifugal force.

Because of that balance, true gravity can be modified for meteorological purposes to be simply the component perpendicular to the surface, while the centrifugal force and gravity components parallel to the surface can be neglected since they cancel each other out.

BTW, this modification actually is treated in many standard meteorological textbooks. Certainly, my copy of Holton's "Introduction to Dynamic Meteorology" deals with it in section 1.5.2, and Fig. 1.6. See too this article by Norman Phillips, which explains the effect in Fig. 1: https://journals.ametsoc.org/view/journals/bams/81/2/1520-0477_2000_081_0299_aeotce_2_3_co_2.xml .

As a first approximation and on average we can consider the troposphere stationary with respect to the Earth’s surface. Otherwise, the winds would be in the order of 400-500 m/s and it is clear that this is not the case.

The idea that the Earth's surface is equipotential and that this translates into a component of the gravitational force parallel to the Earth's surface as opposed to the same component of the centrifugal force is a reasonable and simplifying hypothesis. But it would seem strange to me that the convective motions of the entire planet during its formation maintained an equipotential state.

However, the Gravity Recovery And Climate Experiment (GRACE) has shown that gravitational anomalies are significant and extensive.

Over the last year I have observed cyclonic circulations in the two hemispheres, the data is available to everyone on the internet, and I have noticed a greater frequency of strong winds on the northward side of the circulation in the southern hemisphere and on the southward side in the northern hemisphere. I would like to say that this is not scientific data, which would require in-depth statistical analysis, but it could become proof of the influence of (apparent) centrifugal force.