how do we know that the earth is rotating?

(1) All the stars appear to go around the Earth together at the same time. If the Earth wasn't rotating, there would have to be some magical connection between all the stars.

(2) Foucault pendulum appears to go around, with no force to make it do so. Again, either the Earth is rotating underneath the pendulum, or some magic is making the pendulum go around.

(3) The Earth bulges out a bit at the equator, just like it should if it were rotating.

Because the stars appear to circle the Earth. But because they have been measured to be so far away that it would be impossible for them the revolve around the Earth every 24 hours, it is deemed that it must be the Earth that is rotating.

It's called night and day. But if you stand on the north pole or the south pole, you will find that you don't have night and day during some parts of the year.

Foucault's Pendulum

The stars appear once a day, as the Earth rotates.

Every time the big hand goes around twelve times the little hand goes around one time. So something gotta be moving.