Juan Houston of North Wales poses a relativity paradox and asks :-
According to Einstein the speed of light is constant for all observers irrespective of their speed and location. Thus whether or not an object is said to be rotating will depend upon the observer. However, rotating objects distort. Our Earth is slightly flattened at the poles for this reason. Does this not imply that the rotation is intrinsic to the object itself and is not related to the measurements of independent observers?
Blair Blakie, a physicist at the University of Otago, responded.
To investigate this question we can go back to the Galilean Relativity Principle. This states that Newton's laws of mechanics only hold in inertial reference frames, or more simply, Newton's laws are only true for observers moving at constant velocity. For accelerating observers the real forces acting are often disguised by their motion. Most people realize that acceleration occurs when the speed of something changes, however acceleration also occurs for motion with constant speed but with changing direction, as in circular motion. The resolution of the paradox is that the laws of mechanics are not the same for rotating observers because they are accelerating.
Now let's consider Earth's bulge. The gravitational force is responsible for the formation of the planets and stars in our universe, and the most stable form for these objects is spherical. If a planet is rotating then different points of the surface of the planet will rotate at different speeds. On earth the effects of rotation are most pronounced at the equator. The acceleration associated with the Earth's rotation is small; however it partially cancels the gravitational force and causes the equatorial radius to be about 21km larger than the polar radius.
The Galilean Relativity Principle was later advanced by Einstein in a way that has had profound implications for our understanding of space and time. In his Special Theory of Relativity, Einstein postulated that all the laws of physics should be the same in all inertial reference frames.