Answer
The linear speed at the North Pole or the South Pole is zero.
Work Step by Step
The earth rotates through an angle of $2\pi$ radians in 24 hours. We can find the angular speed:
$\omega = \frac{2\pi~rad}{24~hrs}$
$\omega = \frac{\pi~rad}{12~hrs}$
$\omega = 0.2618~rad/hr$
The angular speed is $0.2618~rad/hr$
At the North Pole or the South Pole, the radius of rotation is zero. We can find the linear speed:
$v = \omega ~r$
$v = (0.2618~rad/hr)(0)$
$v = 0$