If we imagine an object falling from a height h above the surface of the earth. We can go into a rotating frame and therefore introduce Coriolis and centrifugal forces.
Using the Coriolis force the deflection in the East-West Plane can be calculated. However, I am wondering does the centrifugal force influence the trajectory of the particle? Therefore, introducing some displacement in the North-South Plane.
To summarise my question is:
Does the centrifugal force cause objects to deflect when they fall , when considered in the rotating frame?
I have never seen it introduced into this type of question and therefore I am tempted to say it doesn't. However, I can not think of why this would be true.