A family of rotating cutting tools includes at least two toolholders having different diameters, each toolholder including a first side and a second side, the first side and the second side being substantially perpendicular to an axis of rotation of the toolholder, and at least one insert abutment surface on each of the first side and the second side, the insert abutment surfaces on the first side and the second side of each toolholder being substantially mirror images of each other, and the insert abutment surfaces on each of the first side and the second side of each toolholder being substantially identical to the insert abutment surfaces on each other one of the at least two toolholders, and a plurality of identical inserts mounted on each of the at least two toolholders, each insert having a first side surface, a second side surface, and a plurality of edge surfaces between the first and second side surfaces, each edge surface intersecting with another edge surface at a corner and forming a cutting edge, wherein the first and second side surfaces each have a side insert supporting surface for abutting against one of the abutment surfaces. For each toolholder, the insert abutment surfaces on the first and second sides define an angle with a plane perpendicular to the axis of rotation of the toolholder, and the angle defined by the insert abutment surfaces and the plane perpendicular to the axis of rotation of the toolholder is different for the at least two toolholders having different diameters.