This is actually a matter for general relativity.
The basic problem is that acceleration is equivalent to gravity and therefore to a curved spacetime. So, it *is* possible to find a frame that works for a rotating object. But that locally inertial frame simply doesn't work globally. The Coriolis forces are seen as gravitational in that frame.
Technically, the metric tensor is diagonal in 'nice' reference frames. In rotating ones (like in rotating black holes), there are off-diagonal components that represent frame dragging.
One way of thinking about this is with latitude and longitude on the Earth. Close to any point (other than the poles), they give a nearly Euclidean description of the local geometry. That corresponds to a locally inertial frame. Geodesics locally look flat.
But, if there are mountains and valleys, small distances on the coordinate grid can correspond to large distances in the actual geometry. And if the mountains and valleys have some 'texture' to them, the locally Euclidean aspect is destroyed. That is (sort of) what happens in rotating frames.
That said, we generally look for frames that are close to inertial on large segments of spacetime. The 'rotating' ones simply cannot be extended to large regions.
Think of it like this. Suppose you take a frame in which the Earth is not rotating. A geosynchronous satellite then hovers above a single point while satellites above and below will move. THAT shows you have a frame that is not inertial when extended to those sattelites.
The basic problem is that acceleration is equivalent to gravity and therefore to a curved spacetime. So, it *is* possible to find a frame that works for a rotating object. But that locally inertial frame simply doesn't work globally. The Coriolis forces are seen as gravitational in that frame.
Technically, the metric tensor is diagonal in 'nice' reference frames. In rotating ones (like in rotating black holes), there are off-diagonal components that represent frame dragging.
One way of thinking about this is with latitude and longitude on the Earth. Close to any point (other than the poles), they give a nearly Euclidean description of the local geometry. That corresponds to a locally inertial frame. Geodesics locally look flat.
But, if there are mountains and valleys, small distances on the coordinate grid can correspond to large distances in the actual geometry. And if the mountains and valleys have some 'texture' to them, the locally Euclidean aspect is destroyed. That is (sort of) what happens in rotating frames.
That said, we generally look for frames that are close to inertial on large segments of spacetime. The 'rotating' ones simply cannot be extended to large regions.
Think of it like this. Suppose you take a frame in which the Earth is not rotating. A geosynchronous satellite then hovers above a single point while satellites above and below will move. THAT shows you have a frame that is not inertial when extended to those sattelites.
