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I imagine if there is any amount of angular momentum imparted to the water in our cells, the reversal of the force propelling it would create a turbulent episode of transition.


The differences in force are way too miniscule on that scale. If you're looking for a measurable force differential across the extent of your own body, look at gravity instead. When standing up, the gravity at your feet is about 0.5 ppm smaller than at your head (for a body height of 1.75 meters). You don't feel that either; there is just no evolutionary advantage to being able to measure such tiny differences in local gravity, especially since we have acceleration sensors in our ears that are way more efficient at telling up from down.

The coriolis force differential, besides being rather small to begin with, has the additional problem that the coriolis force is proportional to the speed at which you're moving over the earth. If you were to accelerate to a speed where the coriolis force differential might be appreciable (e.g. by sitting in a bullet train or in a plane), it will be completely drowned out by any other momentary forces imparted upon you by the vehicle (trains or planes can move mostly straight, but not in a mathematical-grade straight line).




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