Variation in $g$ due to rotation of earth
$g'=g-\omega^{2} R \cos ^{2} \lambda$
At poles, $\lambda=90^{\circ}$ in the above expression, we get
$g_{\text {pole }}=g-\omega^{2} R \cos ^{2} 90^{\circ}$
$\therefore g_{\text {pole }}=g$
i.e., there is no effect of rotational motion of the earth on the value of $g$ at poles.