Final answer:
An ice skater's angular speed increases when they bring their arms inward due to the conservation of angular momentum and the decrease in moment of inertia, which results in higher rotational kinetic energy.
Step-by-step explanation:
When an ice skater spins with their arms extended, they have a certain angular speed wi. However, when the skater brings their arms inward, the distance from their spin center decreases, leading to a decrease in moment of inertia.
According to the conservation of angular momentum, this means the skater's angular speed must increase since angular momentum is the product of moment of inertia and angular velocity and is conserved in the absence of external torques. This effect is a demonstration of the conservation of angular momentum, where the skater's spinning rate, or angular velocity, increases when the moment of inertia decreases as the arms are pulled closer to the body.
Moreover, by pulling the arms inward, the ice skater does work, which contributes to an increase in their rotational kinetic energy. In a frictionless environment like ice skating, the total energy of the system remains constant, so this additional rotational kinetic energy is accounted for by the work done by the skater to pull their arms inward.
Therefore, by bringing the arms inwards, the skater's angular speed increases, while their angular momentum remains constant.