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A rotating object has an angular momentum of L. If its angular velocity is doubl

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

Options:

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

Correct Answer: 4L

Solution: 

Angular momentum L = Iω, if ω is doubled, L becomes 2I(2ω) = 4L.

A rotating object has an angular momentum of L. If its angular velocity is doubl

Practice Questions

Q1
A rotating object has an angular momentum of L. If its angular velocity is doubled and its moment of inertia remains constant, what will be 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 angular velocity is doubled and its moment of inertia remains constant, what will be the new angular momentum?
  • 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 problem, the moment of inertia (I) remains constant.
  • Step 3: Recognize that if the angular velocity (ω) is doubled, it becomes 2ω.
  • Step 4: Substitute the new angular velocity into the angular momentum formula: L = I(2ω).
  • Step 5: Simplify the equation: L = 2Iω.
  • Step 6: Since the original angular momentum is L = Iω, we can express the new angular momentum as L' = 2L.
  • Step 7: Therefore, if we double the angular velocity, the new angular momentum becomes 4L.
  • Angular Momentum – Angular momentum (L) is the product of an object's moment of inertia (I) and its angular velocity (ω).
  • Moment of Inertia – Moment of inertia (I) is a measure of an object's resistance to changes in its rotation.
  • Angular Velocity – Angular velocity (ω) is the rate of rotation of an object, typically measured in radians per second.
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