Question

why do stars appear to move east to west whereas the pole star appears stationary

Answer 1

Polaris, the North Star, appears stationary in the sky because it is positioned close to the line of Earth's axis projected into space. As such, it is the only bright star whose position relative to a rotating Earth does not change. All other stars appear to moveopposite to the Earth's rotation beneath them.

Answer 2

The pole star appears to be stationary as it is at the top of the north pole of the earth. Stars do not move or rotate, they remain stationary in their positions ( like the sun ). stars appear to move because of the earth's rotation and revolution. When the Polestar is situated above the axis of the earth it appears to be stationary unlike other stars.