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Gabble1
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Homework Statement
In this question, the Earth is modeled as a uniform sphere of radius 6400km. Objects are released from points just above the Earth's surface at the equator and at the North Pole. Which will fall to the Earth with the greater acceleration and by how much?
Homework Equations
The answer in the book states that objects at the North Pole will fall with a greater acceleration of 0.0338 m/s^2 (3 s.f.) than objects at the equator.
The Attempt at a Solution
I first took a cross section of the Earth at the equator as an example of circular motion.
The centripetal acceleration due to the rotating Earth, a=(omega)^2 * r = (2pi/T)^2 * r = (7.27 * 10^(-5))^2 * 6400000 = 0.0338 m/s^2 <- Correct.
However, at the equator total centripetal acceleration = centripetal acceleration due to rotating Earth + acceleration due to gravity = (0.0338 + g) m/s^2
However, at the North Pole, an object is not rotating with circular motion, thus total centripetal acceleration would simply be acceleration due to gravity, ie. g m/s^2.
Due to this I answered that objects at the equator would fall with a greater acceleration of 0.0338 m/s^2, however this is the opposite answer to the answer given.
Could someone please point out where I am going wrong in my reasoning?
Cheers