Final answer:
Yes, a roller skater experiences work when pushing off a wall, as force is applied over a distance. A spinning skater also performs work when pulling her arms in, leading to an increase in rotational kinetic energy while maintaining constant angular momentum.
Step-by-step explanation:
When a roller skater straightens her arms and pushes off the wall, she does experience work. Work in physics is defined as a force applied over a distance where the force and distance are in the same direction. If the skater applies a force to the wall and moves in the opposite direction (as a reaction), then work is done by the wall on the skater.
In the case of a spinning skater who pulls in her arms, the force exerted on each arm is directed inward and the arms move over a distance, even spiraling to a certain extent as they are brought closer to the body. This action requires work because it involves a component of force in the direction of the movement. The angular momentum remains constant because it is a conserved quantity in the absence of external torques. Meanwhile, the skater's moment of inertia decreases, and as a result, the rotational kinetic energy increases. This increase in rotational kinetic energy is the outcome of the work done by the skater when pulling her arms inward.