While tackling an Olympiad question, it came to my mind that friction need not act in the same direction at all points on a body. I thought of using integration to evaluate the net frictional force, but was stopped by this statement.
Frictional force between 2 bodies, doesn't depend on the surface area in contact.
If that is the case, then how does the force act on a body like the following, where only the narrow strip marked is rough and hence friction can act only there? What are the individual frictional forces at the points A and B?
The image shows a hollow cylinder, mass $M$ and radius $R$ from top view. The cylinder is placed with its flat end in contact with the ground. Only the gray shaded line is rough, id est, friciton acts only there. The cylinder is rotating about the topmost point. Ignore the $v$ in the diagram.