The rolling assembly has a rotation axis and a rim having rim seats and flanges, an adapter and a tire having beads. The adapter provides the connection between one of the beads and the rim. The rim comprises a portion of a width W extending outwardly from the flange and a connecting introduction portion and a body. The body has a point A that is 10% of W axially inward from an axially outermost of the body or from an axially outermost of the adapter. The portion creates a virtual straight line GD between an innermost of the connecting introduction portion and the point A. The portion and the adapter has a radial distance d at the point A. The body has a maximum radial distance e from the virtual straight line GD at axially inward from the point A, and the body has no contact with the adapter.