Q:

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

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 

A:

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.

