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From the start I stated that I would not confuse the students by taking into account the rotation of the Earth; I never have done that in my Freshman level physics class. The rotation does require that "part" of the Earth's pull be "used" to produce the centripetal (not centrifugal) acceleration to produce circular motion. This effect would slightly change the value of g versus a still Earth. But, at the Equator, it would still not change the value of g when carried out to 2 significant figures, which is all I do in class.