Supposed that a man is standing on the edge of a spinning merry-go-round which rotates at an constant angular speed with respect to a stationary fame of reference(the ground), there will be a centripetal force pulling him toward the centre of the marry-go-round and prevents him from sliding off it. Then comes the question, what happens if you take the rotating fame of reference of the marry-go-round as stationary, and it is the earth rotating in the opposite direction at the same angular speed, will there still be any force pulling you toward the centre of the 'stationary' merry-go-round? If we consider the earth as stationary and it is the universe rotating around it, how can we define the centripetal force? As the earth is not spinning, the gravitational pull of the poles will be identical to that of the equator if we consider the earth as an uniform sphere, which contradicts with the reality that in the poles there will be a theoretically greater gravitatinal pull since there is no centripetal force acting. Could anyone explain it?
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