Consider a hollow cylinder rolling down an inclined plane, without slipping. I know that the rolling friction does no work on the point which is in contact with the cylinder, since that point must be at rest since we have rolling without slipping, but isn't the ENTIRE BODY still moving, so the friction force acts over this distance, so it must be doing work on the BODY. These seem to contradict. Furthermore, we know that forces acting anywhere on the body force the body to accelerate like a point mass at the center of mass, so in this case the friction force is acting opposite the acceleration of the center of mass, and hence doing work on the object. This seems to contradict the fact that rolling friction is supposed to do no work. So why does rolling friction do no work? What is wrong with the reasonings above?