Angular Momentum Conservation
An ice skater spinning with both arms outstretched suddenly pulls her arms close to her body, reducing her moment of inertia to one-third of its initial value. By what factor does her angular speed change?
Select the correct option:
Solution
Increases to 3 times
As stated in NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion), when no external torque acts on a system its total angular momentum L = Iω is conserved. This conservation law is one of the most powerful tools in rotational dynamics because it links the body's mass distribution to its spin rate. The skater pulling in her arms is purely an internal rearrangement of mass, so the external torque about the vertical spin axis is essentially zero and angular momentum stays constant throughout the manoeuvre. Therefore we may write I₁ω₁ = I₂ω₂. Given that the new moment of inertia is I₂ = I₁/3, we solve ω₂ = (I₁/I₂)ω₁ = (I₁ / (I₁/3))ω₁ = 3ω₁, so the angular speed triples. The option 'Decreases to one-third' is wrong because reducing inertia must increase, not decrease, the spin rate. The option 'Remains unchanged' violates conservation of angular momentum whenever the moment of inertia changes. The option 'Increases to 9 times' incorrectly squares the inertia ratio, which would apply to energy, not angular speed. A consistency check confirms that since L is fixed, lowering I by a factor of three must raise ω by the same factor of three, matching the everyday observation of spinning skaters visibly speeding up as they draw their arms inward.
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About This Question
- Subject
- physics
- Chapter
- rotational motion
- Topic
- angular momentum conservation
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
Increases to 3 times
As stated in NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion), when no external torque acts on a system its total angular momentum L = Iω is conserved. This conservation law is one of the most powerful tools in rotational dynamics because it links the body's mass distribution to its spin rate. The skater pulling in her arms is purely an internal rearrangement of mass, so the external torque about the vertical spin axis is essentially zero and angular momentum stays constant throughout the manoeuvre. Therefore we may write I₁ω₁ = I₂ω₂. Given that the new moment of inertia is I₂ = I₁/3, we solve ω₂ = (I₁/I₂)ω₁ = (I₁ / (I₁/3))ω₁ = 3ω₁, so the angular speed triples. The option 'Decreases to one-third' is wrong because reducing inertia must increase, not decrease, the spin rate. The option 'Remains unchanged' violates conservation of angular momentum whenever the moment of inertia changes. The option 'Increases to 9 times' incorrectly squares the inertia ratio, which would apply to energy, not angular speed. A consistency check confirms that since L is fixed, lowering I by a factor of three must raise ω by the same factor of three, matching the everyday observation of spinning skaters visibly speeding up as they draw their arms inward.
This medium difficulty physics question is from the chapter rotational motion, covering the topic of angular momentum conservation. It appeared in the 2025 exam.
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