Question
Download Solution PDFA dancer standing on the rotating table with his hands lowered. When he outstretches his hands, the angular momentum of the dancer:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
Angular momentum:
- Angular momentum is the property of any rotating object given by moment of inertia times angular velocity.
- It is a vector quantity.
- Its SI unit is kg-m2/sec.
- If I and ω are the moment of inertia and the angular velocity respectively, then the angular momentum is given as,
⇒ L = Iω
⇒ L = rP
Where r = radius of rotation and P = linear momentum
Conservation of angular momentum:
- According to the conservation of angular momentum, if the total external torque on the system of particles is zero, then the total angular momentum of the system remains conserved.
EXPLANATION:
- Sit on a swivel chair with arms folded and feet not resting on, i.e., away from, the ground.
- Rotate the chair rapidly.
- While the chair is rotating with considerable angular speed stretch your arms horizontally.
- Your angular speed is reduced. If you bring back your arms closer to your body, the angular speed increases again.
- This is a situation where the principle of conservation of angular momentum is applicable.
- If friction in the rotational mechanism is neglected, there is no external torque about the axis of rotation of the chair and hence Iω is constant.
- Stretching the arms increases I about the axis of rotation, resulting in decreasing the angular speed ω.
- Bringing the arms closer to the body has the opposite effect.
- Since no external force is acting on the dancer when the dancer is standing on the rotating table, so the torque on the dancer will also be zero.
- Therefore by the conservation of angular momentum, the angular momentum of the dancer will remain to conserve when the dancer outstretches his hands. Hence, option 3 is correct.
Last updated on Jul 4, 2025
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