Question: Even though the Earth is spinning and we all experience a centrifugal acceleration, we are not flung off the Earth due to the gravitational force.

Even though the Earth is spinning and we all experience a centrifugal acceleration, we are not flung off the Earth due to the gravitational force. In order for us to be flung off, the Earth would have to be spinning a lot faster.
A) Derive a formula for the new rotational time of the Earth, such that a person on the equator would be flung off into space. (Take the radius of Earth to be R).
B) Using R = 6:4 million km, calculate a numerical answer to part A) and compare it to the actual rotation time of the Earth today.

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