Relation between g and angular velocity omega.
g- R omega^2 cos^2 alpha.
Plz explain this.

Dear student

We have the given relation from Rotation of the earth about its own axis.

The value of g varies from place to place due to following factors:

(i) Shape of earth :

The earth is not perfectly spherical but is slightly ellipsoidal. It is bulging at the equator and flattened at the poles. Its equatorial radius is about 21 km more than the polar radius.

As $g \alpha \frac{1}{R^2}$ the value of g increases from equator to poles i.e. it is maximum at the poles and minimum at the equator.

(ii) Effect of earth’s rotation :

The earth rotates about its axis with angular velocity $\omega$

If $\omega$ is the angular velocity of rotation of earth about its own axis then acceleration due to gravity at a place having latitude $\alpha$ is given by

We will not derive it here, since it is not important here.

Refer the figure below for above discussion.



I hope it will help you!
Regards