Final answer:
Work is done by the skater when she pulls in her arms during a spin, but this action does not increase angular momentum. The skater exerts a force on each arm to pull them inward, reducing the distance moved and increasing the angular velocity to keep angular momentum constant.
Step-by-step explanation:
When a skater pulls in her arms during a spin, work is done by the skater on her own body. This is because the skater exerts a force on each arm to pull them inward, and since the distance the arms move is reduced, the work done is equal to the force magnitude multiplied by the reduced distance. However, pulling in her arms does not increase angular momentum. Angular momentum is conserved in the absence of external torques, so even though the moment of inertia of the skater decreases when she pulls in her arms, her angular velocity (rate of spin) increases to compensate and keep the angular momentum constant. This can be understood by considering Newton's second law for rotation, which states that the torque applied to an object is equal to the moment of inertia multiplied by the angular acceleration. Thus, when the moment of inertia decreases, the angular acceleration increases, resulting in a higher angular velocity.