Tension of a string on a rotating sphere and under the influence of gravity

Question

I was studying about circular motion and found a topic that is apparent weight and found an equation of apparent value of g.

But I can't understand why this is written

Answer 1

Check the force diagram at the equator from the inertial coordinate system:

$mg-N= m\omega^2R$.

So $mg>m\omega^2R$ or $g>\omega^2R$.

Obviously $2g>\omega^2R$.

This is a necessity to keep us from flying off the earth.