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If a body is rotating with an angular momentum L and its moment of inertia is ha

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Question: If a body is rotating with an angular momentum L and its moment of inertia is halved, what will be the new angular momentum if the angular velocity remains constant?

Options:

  1. L
  2. 2L
  3. L/2
  4. 4L

Correct Answer: L

Solution: 

Angular momentum L = Iω; if I is halved and ω remains constant, L remains L.

If a body is rotating with an angular momentum L and its moment of inertia is ha

Practice Questions

Q1
If a body is rotating with an angular momentum L and its moment of inertia is halved, what will be the new angular momentum if the angular velocity remains constant?
  1. L
  2. 2L
  3. L/2
  4. 4L

Questions & Step-by-Step Solutions

If a body is rotating with an angular momentum L and its moment of inertia is halved, what will be the new angular momentum if the angular velocity remains constant?
  • Step 1: Understand that angular momentum (L) is calculated using the formula L = Iω, where I is the moment of inertia and ω is the angular velocity.
  • Step 2: Note that in this scenario, the moment of inertia (I) is halved, meaning it becomes I/2.
  • Step 3: Recognize that the angular velocity (ω) remains constant, so it does not change.
  • Step 4: Substitute the new moment of inertia into the angular momentum formula: L = (I/2)ω.
  • Step 5: Since ω is constant, the new angular momentum becomes L/2, which means it is halved.
  • Angular Momentum – Angular momentum (L) is the product of the moment of inertia (I) and angular velocity (ω), expressed as L = Iω.
  • Moment of Inertia – Moment of inertia (I) is a measure of an object's resistance to changes in its rotation, depending on the mass distribution relative to the axis of rotation.
  • Conservation of Angular Momentum – If no external torque acts on a system, the total angular momentum remains constant.
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