Final answer:
The ice skater extending her arms during a spin increases her moment of inertia, decreases her angular speed, but does not decrease her total angular momentum, which remains constant due to the conservation of angular momentum. Therefore, the correct answer is A.
Step-by-step explanation:
When an ice skater is spinning with her arms held tightly to her body, she has a certain moment of inertia and angular speed. According to the conservation of angular momentum, her total angular momentum remains constant when no external torques are acting on her. If she extends her arms, she increases her moment of inertia; however, to conserve angular momentum, her angular speed must decrease.
- A. Her total angular momentum has decreased: This statement is not true. The total angular momentum remains constant due to the conservation of angular momentum.
- B. She increases her moment of inertia: This is true because her arms are further from the axis of rotation.
- C. She decreases her angular speed: This is true because to conserve angular momentum, as the moment of inertia increases, angular speed must decrease.
- D. Her moment of inertia changes: This is true because extending her arms changes her distribution of mass relative to the axis of rotation.
The correct statement is A, which is not true in the context of an ice skater extending her arms.