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How is gravity on the earth surface related to the circular motion of the earth about its axis?

If i'm not wrong, my lecturer once taught me that i can actually equate both gravitational force and centripetal force together since they are both the same. (Gravitational force holds all objects on earth together and move them in a circular orbit which is also what centripetal force does on the objects moving in circular motion.) which i think by further simplifying the equation GM/r^2 = rw^2 gives kepler's law, T^2 is directly proportionate to r^3.

Alright, now here's the problem. If both GM/r^2 and rw^2 can be equated like what my lecturer said, then both of the equation should give the value of gravitational field strength of the Earth on its surface which is (9.81ms^-2) However, by workin out rw^2, i'm unable to get the value 9.81ms^-2, what i get was only 0.03ms^-2. Is there a problem with my calculations or had i miss out certain things. I'm really quite confused over this.

Any help given will be greatly appreciated. Thanks!

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# Gravitation and Circular motion.

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