If I take a rock attached to a mass-less rope and start spinning it over my head (or on a friction-less surface, I don't think it matters) I can accelerate the linear speed of the rock (I can spin it faster).
That means there is some form of angular acceleration, which implies a torque acting on the rock. But because there only force acting on the rock is through the tension in the rope, which is always perpendicular to it's direction of travel, where does the torque come from?
My best guess is that in a perfect world you wouldn't actually be able to accelerate the rock, but because you can sort of move your hand a little outside of the centre of the rock's orbit that you can pull it along a little bit. If this is the case, is it possible to accelerate a rock on a string using a stationary machine that spins the rope around, always pulling from the centre of the orbit?