Calculate how long would a day be if the Earth were rotating so fast that objects at the equator were apparently weightless?

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Hint: in order to be weightless, acceleration must be equal to g.

Now, We know that acceleration due to gravity varies with the angle such as, \[g'=g-w ^{2}r \cos \Theta\] At, Equator \[\Theta=0^{0}\] Therefore g'=0 to solve this problem !

\[w ^{2} = a/R\] \[w=v/r = 2\pi/t\] \[t =\sqrt(4\pi ^{2} R/a) \] \[t \approx 161 \sec \approx 2.6 \min\] that is awesome result we will no longer inertial frame.

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