If I have a very long rigid rod which is of rectangular cross section and small mass. Let it's length be 1 light year and total mass be 1 kg now at one end if I rotate that rod, since the rod is rigid it should rotate as a body about the axis parallel to its length and normal to its cross sectional area. If this event happens instantaneously, does it mean that the information of rotating the rigid rod has been sent instantaneously (more than the speed of light)? If the assumption is false what actually happens there?
The solution to this "paradox" is that such a rod simply cannot exist. Relativity prohibits the existence of perfect rigidity.
If you rotated one end, that rotation would propagate from one end to the other at approximately the speed of sound in that rod. Since the speed of sound in any object is slower than the speed of light (c, that is in vacuum), your paradox is averted.