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A rotating object has an angular momentum of L. If its moment of inertia is halv

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Question: A rotating object has an angular momentum of L. If its moment of inertia is halved and its angular velocity is doubled, what is the new angular momentum?

Options:

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

Correct Answer: 4L

Solution: 

New angular momentum L\' = I\'ω\' = (1/2I)(2ω) = L.

A rotating object has an angular momentum of L. If its moment of inertia is halv

Practice Questions

Q1
A rotating object has an angular momentum of L. If its moment of inertia is halved and its angular velocity is doubled, what is the new angular momentum?
  1. L
  2. 2L
  3. 4L
  4. L/2

Questions & Step-by-Step Solutions

A rotating object has an angular momentum of L. If its moment of inertia is halved and its angular velocity is doubled, what is the new angular momentum?
  • Step 1: Understand that angular momentum (L) is calculated using the formula L = I * ω, where I is the moment of inertia and ω is the angular velocity.
  • Step 2: Identify the initial moment of inertia (I) and angular velocity (ω) of the object, which gives us the initial angular momentum L.
  • Step 3: Note that the moment of inertia is halved, so the new moment of inertia (I') is I' = 1/2 * I.
  • Step 4: Note that the angular velocity is doubled, so the new angular velocity (ω') is ω' = 2 * ω.
  • Step 5: Substitute the new values into the angular momentum formula: L' = I' * ω' = (1/2 * I) * (2 * ω).
  • Step 6: Simplify the equation: L' = (1/2 * I) * (2 * ω) = I * ω = L.
  • Step 7: Conclude that the new angular momentum L' is equal to the original angular momentum L.
  • Angular Momentum – Angular momentum (L) is the product of an object's moment of inertia (I) and its 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.
  • Angular Velocity – Angular velocity (ω) is the rate of rotation of an object, typically measured in radians per second.
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