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If the angular momentum of a rotating object is doubled while its moment of iner

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Question: If the angular momentum of a rotating object is doubled while its moment of inertia remains constant, what happens to its angular velocity?

Options:

  1. Doubles
  2. Halves
  3. Remains the same
  4. Increases by a factor of 4

Correct Answer: Doubles

Solution: 

Angular momentum L = Iω; if L is doubled and I remains constant, ω must also double.

If the angular momentum of a rotating object is doubled while its moment of iner

Practice Questions

Q1
If the angular momentum of a rotating object is doubled while its moment of inertia remains constant, what happens to its angular velocity?
  1. Doubles
  2. Halves
  3. Remains the same
  4. Increases by a factor of 4

Questions & Step-by-Step Solutions

If the angular momentum of a rotating object is doubled while its moment of inertia remains constant, what happens to its angular velocity?
  • Step 1: Understand the formula for angular momentum, which is L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity.
  • Step 2: Identify that in this scenario, the moment of inertia (I) remains constant.
  • Step 3: Recognize that if the angular momentum (L) is doubled, we can express this as 2L = Iω'.
  • Step 4: Since I is constant, we can set up the equation: 2L = Iω' and L = Iω.
  • Step 5: Substitute L from the second equation into the first: 2(Iω) = Iω'.
  • Step 6: Simplify the equation: 2Iω = Iω'.
  • Step 7: Since I is constant and can be divided out, we get 2ω = ω'.
  • Step 8: This means that the new angular velocity (ω') is double the original angular velocity (ω).
  • 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 its mass distribution.
  • Angular Velocity – Angular velocity (ω) is the rate of rotation of an object, typically measured in radians per second.
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