I have a doubt regarding the definition of rotational work, which is as follows [itex]W = \int \tau_z d \theta [/itex] Where [itex]\tau_z[/itex] is the component of the torque parallel to the axis of rotation [itex]z[/itex]. My doubt concerns the fact that, looking at this definition, it seems that any torque which has an axial component and causes a rotation, do rotational work. However, consider a problem of pure rotational motion (i.e. rolling with no slipping), for example a disk rolling down an inclined plane and take as pivot point for calculate torque the center of mass of the disk. The static friction force generates a torque which is totally axial and is the cause of the rotation of the disk (if there was no friction the disk would just slip). But the static friction is a classic example of a force that does not do work because it does not cause any displacement. A similar situation is the one with rigid bodies similar to yo-yos, i.e. falling pulleys that carry a wire (on which they roll without slipping). Again, the tension of the rope exerts an axial torque and causes the rotation of the yo-yo, but it seems very strange to me that tension can do work. Do these forces perform rotational work? I probably misunderstood the definition but I do not see what is wrong. Thanks in advance for your suggestions.