I'm reading Halliday's chapter or rigid body rotation. In the derivation of Newton's second law for rotation, it is assumed that the object is hinged about some axis ( the connection would be a frictionless pin). The law is derived for such a connection, but is later applied to objects that aren't hinged. How is this? To give an example, assume we have a uniform solid cylinder rolling on a horizontal surface. The normal force from the ground and the weight of cylinder both pass vertically through its center of mass. Friction is the only horizontal force, and there is no opposing horizontal "reaction" occurring at the center of mass of the disk. How can we apply the second law for rotation? There is no reaction at the axis of rotation. How can a single force of friction cause rotation, without there being a couple? Without the reaction, won't friction just cause translation instead of rotation?