Final answer:
A skater spins faster by pulling in her arms due to the conservation of angular momentum, which keeps the total momentum constant when the moment of inertia changes.
Step-by-step explanation:
A skater can spin faster by pulling her arms closer to her body or spin slower by spreading her arms out due to the conservation of angular momentum. The principle states that if the net external torque acting on a system is zero, the total angular momentum of the system remains constant. In the case of a skater, pulling arms in decreases the moment of inertia, which, in turn, increases the rotational speed to maintain the conservation of angular momentum. Conversely, extending the arms increases the moment of inertia, and the skater's spin rate decreases to conserve angular momentum.
An example of this is Figure 10.21 where an ice skater is spinning with arms extended and then pulls them in to spin faster. This action decreases the skater's moment of inertia, and since angular momentum is conserved, the rotational kinetic energy increases, resulting in a faster spin.