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In a rotating system, if the angular momentum is doubled while the moment of ine

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Question: In a rotating system, if the angular momentum is doubled while the moment of inertia remains constant, what happens to the angular velocity?

Options:

  1. It doubles
  2. It halves
  3. It remains the same
  4. It quadruples

Correct Answer: It doubles

Solution: 

Since L = Iω, if L is doubled and I remains constant, then ω must also double.

In a rotating system, if the angular momentum is doubled while the moment of ine

Practice Questions

Q1
In a rotating system, if the angular momentum is doubled while the moment of inertia remains constant, what happens to the angular velocity?
  1. It doubles
  2. It halves
  3. It remains the same
  4. It quadruples

Questions & Step-by-Step Solutions

In a rotating system, if the angular momentum is doubled while the moment of inertia remains constant, what happens to the 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 problem, the moment of inertia (I) remains constant.
  • Step 3: Recognize that if the angular momentum (L) is doubled, we can express this as 2L.
  • Step 4: Set up the equation with the new angular momentum: 2L = Iω'. Here, ω' is the new angular velocity we want to find.
  • Step 5: Since L = Iω, we can replace L in the equation: 2(Iω) = Iω'.
  • Step 6: Simplify the equation: 2Iω = Iω'.
  • Step 7: Since I is constant and not zero, we can divide both sides by I: 2ω = ω'.
  • Step 8: This shows that the new angular velocity (ω') is double the original angular velocity (ω).
  • Angular Momentum – Angular momentum (L) is the product of moment of inertia (I) and angular velocity (ω), represented by the equation 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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