Gravitation Reasonings

If earth suddenly stops rotating about its axis, what would be the effect on ‘g’? Would this effect be the same at all places?

OR: What will happen to the value of acceleration due to gravity if the earth stops rotating about its axis?

The value of acceleration due to gravity considering the rotation of earth is,

\[g’=g-R\omega^2\cos^2\theta\] where $\theta$ is the latitude of the given place.

[Variation of g due to the rotation of the earth]

If the earth suddenly stops rotating, $\omega=0.$ So,


Thus, the value of g should be more after the earth stops rotating (since there is no minus term now). But this effect will not be seen on the poles of the earth as $\theta=90°$ at poles. So, even when the earth is rotating, \[g’=g-R\omega^2\cos^290°=g\]