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This was in Berkeley Review Ch2 Passage 1, but an overview of the question with explanation can be found here as well. http://curious.astro.cornell.edu/question.php?number=310
Essentially the question posits if one weighs more at the equator vs north pole. The explanation is yes ie
North Pole: there is no centripetal acceleration so N- mg = m(0) ------> N=mg
Equator: there is centripetal acceleration so N - mg = -mv^2/r ----> N = mg - mv^2/r
My confusion: If gravity is not a "downward" force, but rather a force towards the center of the earth, then what makes the north pole fundamentally different from the equator?
Which of my understandings/assumptions is incorrect:
The radius to the center of the earth is the same in either location.
If the earth orbits the moon in uniform circular motion then wouldn't a centripetal force tangent to velocity always to be required to keep the orbit. I don't understand why there wouldn't be a centripetal force at the north pole if there is a uniform orbit (is there?)
Essentially the question posits if one weighs more at the equator vs north pole. The explanation is yes ie
North Pole: there is no centripetal acceleration so N- mg = m(0) ------> N=mg
Equator: there is centripetal acceleration so N - mg = -mv^2/r ----> N = mg - mv^2/r
My confusion: If gravity is not a "downward" force, but rather a force towards the center of the earth, then what makes the north pole fundamentally different from the equator?
Which of my understandings/assumptions is incorrect:
The radius to the center of the earth is the same in either location.
If the earth orbits the moon in uniform circular motion then wouldn't a centripetal force tangent to velocity always to be required to keep the orbit. I don't understand why there wouldn't be a centripetal force at the north pole if there is a uniform orbit (is there?)