A cylindrical pole is inserted into a frozen lake so the pole stands vertically. One end of a rope is attached to a point on the surface of the pole near where it enters the ice, and the rope is then laid out in a straight line on the surface. An ice skater with initial velocity \(\mathbf{v}_{\mathbf{0}}\) approaches the opposite end of the rope, moving perpendicular to the rope. As she reaches the rope she grabs it and holds on, so the rope winds up around the pole.

(a) When the rope is half wound up, what is her speed, assuming there is no friction between the rope or herself and the ice?

(b) Has there been any change in her kinetic energy ? If so, identify what positive or negative work has been done on her, and by what source.

(c) Has there been any change in her angular momentum? If so, identify the source of the torque done upon her.