I feel like I’ve thought about this my entire life and can never wrap my head around it.
****On a merry go round the further you get from center the more centrifugal force you feel and consequently the more centripetal force (they are equal and opposite if you are at equilibrium). But at the center they are both net zero.
****On earth, presumably the equator would exert the maximum centripetal force due to it being the furthest away from the axis. The centripetal force keeping you on the ground is gravity and that equals your centrifugal force trying to fling you off earth.
****But at the poles, how….. and why….. where tf did gravity go? There’s no centrifugal force which means there’s no equal and opposite centripetal force (gravity).
...your second bullet point is wrong, or at least the 2nd sentence therein is wrong. Gravity (GMm/r^2) is much stronger than the 'centripetal' force required to maintain you in circular motion.
...your third point... well,gravity is still there, binding you to earth. It's just that it no longer needs to counteract your inertia (inertia is what you're calling 'centrifugal force')
To be honest, this is actually pretty difficult to understand because of how they teach 'centripetal' and 'centrifugal' acceleration.
Well…. I’m sorry but this comment is wrong lol. The wrong part in bullet two is assuming centrifugal force increases with radius vs the inverse. Gravity is absolutely working as a centripetal force just by the very definition of centripetal force.
Centrifugal force increases with decreasing radius therefore at the poles or near them centrifugal force is greatest. But here’s the catch, the vector of centrifugal force becomes more perpendicular to the gravitational force and that’s actually the answer to bullet 3. Now the question becomes…. What counteracts the near perpendicular centrifugal force at the poles? That’s angular momentum driven and is so low that it’s not worth asking the question.
(sigh)... I know why you're saying this, but it's wrong! Since the earth is a sphere, every point on earth has the exact same angular velocity. This means that people near the poles have effectively zero inertia (which, again, is what you're calling centrifugal force) So near the poles, effectively zero force is required to counteract the inertia.
Again, this is a difficult topic, and I doubt that many physics PhDs understand it.