Spinning = dizzy. Not spinning = not dizzy. Therefore, we are not spinning. It's really much too simple to be undermined by apparently reasoned analysis that must have a mistake in it somewhere.
Ah, but how dizzy? Surely you agree that if you spin really fast, you get more dizzy than if you slowly spin around? So it must be more complicated than you assume.
As for my calculations:
acceleration(centripetal)=(tangential velocity)^2/(radius)
So, for a merry-go-round of 3m diameter (1.5m radius), going with a velocity of 2m/s, we have
a(c)=(2 x 2)/(1.5)=2.7m/s
But for the earth (where on the equator, one spins around the full 40,075,020m circumference in one day = 86400 seconds) the velocity is 462m/s and the radius, at the equator, is 6,377,563m. So we have
a(c)=(426 x 426)/(6377563) = 0.028m/s
So clearly, one will be dizzy to about 1% of the degree of dizziness experienced on a merry-go-round.
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