Final answer:
The angular velocity of a skater increases when she pulls her arms in because her moment of inertia decreases while the angular momentum remains constant. This is due to the conservation of angular momentum and the relationship between moment of inertia and angular velocity.
Step-by-step explanation:
Changes in Angular Velocity
When a skater pulls her arms and legs in towards her trunk, her angular velocity increases. This phenomenon is due to the conservation of angular momentum, which is the product of moment of inertia and angular velocity (L = Iw). As she pulls in her arms, her moment of inertia (I) decreases, and to keep the angular momentum (L) constant, the angular velocity (w) must increase. This is expressed as L = Iw = I'w', where primed quantities represent values after the skater has pulled in her arms. Since I' is smaller, w' must be larger to ensure that the product I'w' remains equal to the original angular momentum.
This principle also explains the work-energy relationship involved. As the skater pulls her arms inward, work is done to decrease the moment of inertia, which in turn increases the rotational kinetic energy since the energy needs to be conserved in a frictionless environment. If the skater were to extend her arms again, her angular velocity would return to the original value, assuming no external torques act on the system.
Therefore, when a skater pulls in her arms while spinning, her angular velocity in rpm (revolutions per minute) will increase, which matches option (a) Increased.