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A man standing on a table rotating about the central axis pulls his hands holding the dumb bells towards chest. How the angular velocity will change?
- a)increase
- b)remains same
- c)increase or decrease depending on the magnitude of angular velocity of the wheel
- d)decrease
Correct answer is option 'A'. Can you explain this answer?
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A man standing on a table rotating about the central axis pulls his ha...
When the man pulls his hands towards chest, the moment of inertia will decrease and due to conservation of angular momentum, angular velocity will increase.
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A man standing on a table rotating about the central axis pulls his ha...
To understand how the angular velocity will change when a man standing on a rotating table pulls his hands holding dumbbells towards his chest, we need to consider the principle of conservation of angular momentum.
**Conservation of Angular Momentum:**
Angular momentum is the rotational equivalent of linear momentum. According to the law of conservation of angular momentum, the total angular momentum of a system remains constant unless an external torque acts on it.
**Initial Situation:**
In the initial situation, the man is standing on a rotating table and holding dumbbells. The system consists of the man, the dumbbells, and the table. The angular momentum of the system is given by the product of the moment of inertia and the angular velocity.
**Change in Angular Velocity:**
When the man pulls his hands holding the dumbbells towards his chest, the moment of inertia of the system decreases. This is because the moment of inertia depends on the distribution of mass and its distance from the axis of rotation. By pulling the dumbbells closer to his chest, the man reduces the moment of inertia of the system.
Since the angular momentum of the system is conserved, according to the equation L = Iω (where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity), a decrease in the moment of inertia (I) will result in an increase in the angular velocity (ω). Therefore, the angular velocity of the rotating table will increase when the man pulls his hands towards his chest.
**Explanation of the Correct Answer:**
The correct answer is option 'A' - increase. As explained above, when the man pulls his hands holding the dumbbells towards his chest, the moment of inertia decreases, leading to an increase in the angular velocity. Therefore, the angular velocity will change and increase in this scenario.
**Conservation of Angular Momentum:**
Angular momentum is the rotational equivalent of linear momentum. According to the law of conservation of angular momentum, the total angular momentum of a system remains constant unless an external torque acts on it.
**Initial Situation:**
In the initial situation, the man is standing on a rotating table and holding dumbbells. The system consists of the man, the dumbbells, and the table. The angular momentum of the system is given by the product of the moment of inertia and the angular velocity.
**Change in Angular Velocity:**
When the man pulls his hands holding the dumbbells towards his chest, the moment of inertia of the system decreases. This is because the moment of inertia depends on the distribution of mass and its distance from the axis of rotation. By pulling the dumbbells closer to his chest, the man reduces the moment of inertia of the system.
Since the angular momentum of the system is conserved, according to the equation L = Iω (where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity), a decrease in the moment of inertia (I) will result in an increase in the angular velocity (ω). Therefore, the angular velocity of the rotating table will increase when the man pulls his hands towards his chest.
**Explanation of the Correct Answer:**
The correct answer is option 'A' - increase. As explained above, when the man pulls his hands holding the dumbbells towards his chest, the moment of inertia decreases, leading to an increase in the angular velocity. Therefore, the angular velocity will change and increase in this scenario.
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A man standing on a table rotating about the central axis pulls his hands holding the dumb bells towards chest. How the angular velocity will change?a)increaseb)remains samec)increase or decrease depending on the magnitude of angular velocity of the wheeld)decreaseCorrect answer is option 'A'. Can you explain this answer?
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