>But they are turns of a circle of a given radius. No, a revolution is a revolution. If you turn a 1 m wheel by one revolution and a 2 m wheel also by one revo

>But they are turns of a circle of a given radius. No, a revolution is a revolution. If you turn a 1 m wheel by one revolution and a 2 m wheel also by one revolution, both will have turned one revolution, or 2 pi radians. If you roll both of them 2 pi m forward on the ground, one will have turned one revolution, or 2 pi radians, and the other will have turned half a revolution, or pi radians.