Will a wheel keep rolling in perfect vacuum? I have a query which I cannot resolve by finding enough arguments.
A perfectly round wheel that also doesn't have any contractions due to gravity is placed in a perfect vacuum, so no drag is present. Will it stop due to friction force or will it roll forever? 
 A: Any real-world wheel will eventually come to rest due to rolling resistance. All materials will have some slight deformation at the contact patch between the wheel and the surface it's rolling on. As long as there is contact between the two (i.e. the wheel is in fact rolling), there will be a force and deformation, and that is true regardless of gravity or air resistance. In a perfectly idealized scenario with a completely rigid wheel and rolling surface, the wheel would roll forever in the absence of air resistance, but the stipulation of a wheel with no rolling resistance doesn't seem to be part of your question.
A: According to classical physics, the wheel can roll forever provided there is no friction and the motion of the wheel is perfectly symmetrical so that no energy can escape in the form of radiation. E.g. a quadrupole moment would cause gravitational radiation to be emitted which will slow down the wheel.
However, due to quantum mechanical effects, the wheel will slow down even under ideal conditions. A rotating wheel will exhibit rotational superradiance, it will emit electromagnetic radiation even in a perfect vacuum when no radiation is incident on the rotating wheel. 
