I am not sure that's true. At least in Newtonian mechanics, there is a notion of an inertial frame of reference, and rotations are the same under all inertial frames of reference.
Mhh. You may be right. My intuition was that if you are rotating in empty space with no point of reference, you cannot know you are rotating, whereas if you have a point of reference which is not stationary under your own frame of reference (isn't orbiting around you at the same rate you are rotating) then you can be aware of your rotational motion, so rotation is also a relative quantity, but I am probably wrong - I was never that good at rotational mechanics.
You can tell that the Earth is rotating in several ways. Of the top of my head:
* The Coriolis effect.
* You can see stars and distant galaxies apparently rotating around you (and they would be traveling at superluminar speeds).
* Foucault's pendulum works.
* The Earth is wider around the equator because of the centrifugal force created by its rotation.