Question

An ice skater is spinning in a circle with a constant angular speed ( ω0 ) with her arms extended out. She brings her arms in.

i. After she brings her arms in, for the system of just the skater, her angular momentum is:
1. the same as when her arms were extended out.
2. smaller than when her arms were extended out.
3. larger than when her arms were extended out.
4. not possible to determine without more information.
ii. After she brings her arms in, her angular speed is:
1.the same as ω0
2. larger than ω0
3. smaller than ω0
4. not possible to determine without more information.
iii. After she brings her arms in, for the system of just the skater, how do the following quantities change? (choose all)
. Her moment of inertia remains the same.
Her moment of inertia decreases.
Her moment of inertia increases.
Her rotational kinetic energy increases.
Her rotational kinetic energy decreases.
Her rotational kinetic energy remains the same.

Answer 1

Upon bringing her arms in, an ice skater's angular momentum remains the same, her angular speed increases, and her moment of inertia decreases while her rotational kinetic energy increases.

Step-by-step explanation:

Understanding the Conservation of Angular Momentum in Ice Skaters

When an ice skater is spinning with arms extended and pulls them in, several things occur related to the principles of physics, specifically conservation of angular momentum and changes in moment of inertia:

1. Angular momentum is conserved because the net torque on the skater is negligibly small. Hence, once the skater brings her arms in, her angular momentum remains the same as when her arms were extended out.
2. The angular speed will increase (larger than ω0) after the skater brings her arms in, since bringing arms closer to the axis of rotation reduces the moment of inertia and to conserve angular momentum, the skater spins faster.
3. As the skater's moment of inertia decreases, her rotational kinetic energy increases due to the work done to pull the arms inward. Thus, her moment of inertia decreases and her rotational kinetic energy increases.