Say you have a mass on a string being twirled around in a circle by your fingers at a constant angular velocity , and then you increase its angular velocity . What are the forces involved that increase the angular velocity of the mass? I first thought that one needed a torque to increase the angular velocity but can one really apply a torque on a piece of string?
There are two options: either your fingers move, or the string bends (or both).
When you use your fingers to make something spin, you actually have to move your fingers in a circle to make it accelerate; you can't do it while leaving the fingers in place. The tension of the string no longer points towards a center: it has a tangential component, which provides the torque.
If instead the string is attached to the shaft of a motor and you increase the speed, the part of the string closer to the center will start to move faster, which will make it bend and have a bit of a curve. This will again provide a tangential force, and the mass will accelerate until it catches up and the string is straight again.