If the Earth stops rotation on its axis , then what would be the change in the value of gravitational acceleration at equator and poles ?
The value of gravitational acceleration (in latitude)
$$ g' = g - \omega^2R cos^2 \lambda $$
(i) For poles , $$ \lambda = 90^{\circ} , \therefore \, cos^2 \lambda = 0 $$
Therefore $$ g' = g $$
Therefore, even the Earth stops its rotation , i.e., $$ \omega = 0 $$, there will be no change in gravitational acceleration.
(ii) For equator , $$ \lambda = 0 , \therefore \, cos \lambda = 1 $$
If $$ \omega = 0 $$ i.e., Earth stops rotation , then
$$ g' = g $$
Thus the value of gravitational acceleration increase on the equator when Earth stops it's rotation.