Question
Part 1- A figure skater on ice spins on one foot. She pulls in her arms and her rotational speed increases. Choose the best statement below:
1. Her angular speed increases because her angular momentum is the same but her moment of inertia decreases.
2. Her angular speed increases because air friction is reduced as her arms come in.
3. Her angular speed increases because her angular momentum increases.
4. Her angular speed increases due to a net torque exerted by her surroundings.
5. Her angular speed increases because by pulling in her arms she creates a net torque in the direction of rotation.
6. Her angular speed increases because her potential energy increases as her arms come in.
Part 2- And again, choose the best statement below:
1. When she pulls in her arms, her rotational kinetic energy must decrease because of the decrease in her moment of inertia.
2. When she pulls in her arms, her angular momentum decreases so as to conserve energy.
3. When she pulls in her arms, the work she performs on them turns into increased rotational kinetic energy.
4. When she pulls in her arms, her rotational kinetic energy is conserved and therefore stays the same.
5. When she pulls in her arms, her moment of inertia is conserved.
6. When she pulls in her arms, her rotational potential energy increases as her arms approach the center.
1. Her angular speed increases because her angular momentum is the same but her moment of inertia decreases.
2. Her angular speed increases because air friction is reduced as her arms come in.
3. Her angular speed increases because her angular momentum increases.
4. Her angular speed increases due to a net torque exerted by her surroundings.
5. Her angular speed increases because by pulling in her arms she creates a net torque in the direction of rotation.
6. Her angular speed increases because her potential energy increases as her arms come in.
Part 2- And again, choose the best statement below:
1. When she pulls in her arms, her rotational kinetic energy must decrease because of the decrease in her moment of inertia.
2. When she pulls in her arms, her angular momentum decreases so as to conserve energy.
3. When she pulls in her arms, the work she performs on them turns into increased rotational kinetic energy.
4. When she pulls in her arms, her rotational kinetic energy is conserved and therefore stays the same.
5. When she pulls in her arms, her moment of inertia is conserved.
6. When she pulls in her arms, her rotational potential energy increases as her arms approach the center.
Answers
GPT-4o mini
**Part 1:** The best statement is:
1. **Her angular speed increases because her angular momentum is the same but her moment of inertia decreases.**
This aligns with the principle of conservation of angular momentum, which states that the angular momentum (L) of a rotating body is conserved in the absence of external torque. Angular momentum is given by the product of moment of inertia (I) and angular speed (ω): \( L = I \cdot ω \). When the skater pulls in her arms, her moment of inertia decreases, thus requiring her angular speed to increase to keep angular momentum constant.
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**Part 2:** The best statement is:
3. **When she pulls in her arms, the work she performs on them turns into increased rotational kinetic energy.**
When the skater pulls her arms in, she not only reduces her moment of inertia but also does work (muscular effort) on her body to achieve this configuration. This work results in an increase in her rotational kinetic energy as her rotational speed (angular velocity) increases. Thus, her rotational kinetic energy increases, even though total mechanical energy remains conserved barring losses due to friction or air resistance.
1. **Her angular speed increases because her angular momentum is the same but her moment of inertia decreases.**
This aligns with the principle of conservation of angular momentum, which states that the angular momentum (L) of a rotating body is conserved in the absence of external torque. Angular momentum is given by the product of moment of inertia (I) and angular speed (ω): \( L = I \cdot ω \). When the skater pulls in her arms, her moment of inertia decreases, thus requiring her angular speed to increase to keep angular momentum constant.
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**Part 2:** The best statement is:
3. **When she pulls in her arms, the work she performs on them turns into increased rotational kinetic energy.**
When the skater pulls her arms in, she not only reduces her moment of inertia but also does work (muscular effort) on her body to achieve this configuration. This work results in an increase in her rotational kinetic energy as her rotational speed (angular velocity) increases. Thus, her rotational kinetic energy increases, even though total mechanical energy remains conserved barring losses due to friction or air resistance.