A problem I encountered is as follows: A pulley consists of a circle of radius $R$ is pivoted about a point a distance $R/2$ from the circle’s center. A string attaches to a block hanging from the pulley as shown. The coefficient of friction between the string and pulley is infinite. Find the tension in the horizontal part of the string if the system is at rest.
The solution is simple at first glance: the vertical part of the string must have a tension of $mg$ to hold the weight, so to balance the torque on the pulley about its pivot, the horizontal part of the string must have a tension of $2mg$.
However, how can the torque from the string be reduced to the torque of the two forces of tension at the top and on the side of the pulley? From my understanding, it's not really "tension" that is pulling on the sides of the pulley; rather, it is friction and normal force from each segment of the string that are truly acting on the pulley. It's not obvious to me how summing the torques from each of the segments' friction and normal forces add up to the torque of the two forces I described earlier, especially when taken about a pivot that is not the center of the pulley.