Tension can apply torque on a pulley only if there is friction between the rope and the pulley; without friction, the pulley cannot rotate. In the discussed scenario, if the pulley is considered frictionless, the torque is effectively zero, leading to confusion in understanding the mechanics involved. The distinction between axle friction and friction at the rope's contact point is crucial, as the latter is necessary for torque generation. Real-life applications often involve friction that allows the pulley to rotate in sync with the rope. Understanding these concepts is essential for solving physics problems accurately, rather than relying solely on memorization.