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Circular motion?

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How should the period of earth be if it is rotating so fast that it feels apparent weightlessness?

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  1. Assume you are on the equator.

    Centripetal acceleration= -g = v^2/r

    v= sqrt (-g *r)

    period = r *2 pi/v

    period = r*2pi / sqrt (-g*r)

    period = 2 pi * sqrt (-r/g)

    g = - 9.8 m/s^2

    r = 6370 km

    period = 807 secs

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