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Steve Cox
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Homework Statement
I wanted a proof that an object's center of gravity is the same as the center of mass by breaking the object into tiny pieces and then integrating over them.
Homework Equations
Well, the gravitational equation g=Gm1m2/r^2
The Attempt at a Solution
I tried using some calc three to integrate a uniform sphere using spherical shells. However, my answer wasn't working out and I would like a much more general proof.
Well, I just learned that the center of mass is different from the center of gravity of Earth because the gravitational field isn't uniform. Assuming gravity is uniform, how can we prove that the sum of all of the gravities are as gravity as a whole were acting on its center of mass?
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