I know friction doesn't depend on surface area and the professor has been demonstrating the same in all the previous lectures. But in this lecture he shows an application where the friction helps in balancing a large weight (T2) with a much smaller weight (T1).
He further says increasing the angle the rope is in contact with the cylinder increases the frictional force and helps in balancing a much larger weight $T_2$. Doesn't this contradict the fact that friction doesn't depend on surface area?
Hope I gave all the details so seeing the video is not required but here it is.