Final answer:
After an ice skater brings her arms in while spinning, her angular speed becomes larger than the initial speed (ω0) due to the conservation of angular momentum. The decrease in moment of inertia results in an increase in angular velocity option 2 is correct.
Step-by-step explanation:
The question asks about the change in angular speed of an ice skater who brings her arms in while spinning with an initial constant angular speed ω0. According to the conservation of angular momentum, if the net external torque acting on a spinning object is negligible, the object's angular momentum remains constant. The ice skater's angular momentum, which is the product of her moment of inertia and angular velocity (L = Iω), is conserved.
When the skater pulls her arms in, her moment of inertia decreases. Because angular momentum must be conserved, and the moment of inertia is now smaller, the skater's angular velocity must increase to keep the product of the moment of inertia and angular velocity constant. Therefore, after she brings her arms in, her angular speed is larger than ω0.
In summary, the conservation of angular momentum leads to an increase in the skater's rotational speed when she decreases her moment of inertia by pulling her arms closer to her body. This is a manifestation of the conservation of angular momentum and is well-demonstrated in examples involving ice skaters performing spins.