Is the Moon Supposed to "Cartwheel"?

By cartwheel, I mean appear to rotate clockwise or counterclockwise
throughout the course of the night? Or, is is supposed to appear
stationary from a fixed point on earth?

A fair question is "Why don't you go outside and look?" My answer is
that I have and while the first few times the moon seemed to stay in
place, the last few times I have looked it had, indeed, appeared to have
rotated 45 degrees or so clockwise over the course of several hours.