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If the angular momentum of a rotating body is doubled while its moment of inerti

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Question: If the angular momentum of a rotating body 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. Quadruples

Correct Answer: Doubles

Solution: 

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

If the angular momentum of a rotating body is doubled while its moment of inerti

Practice Questions

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

Questions & Step-by-Step Solutions

If the angular momentum of a rotating body 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 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 substitute L in the equation: 2(Iω) = Iω'.
  • Step 6: Simplify the equation by dividing both sides by I (since I is constant and not zero): 2ω = ω'.
  • Step 7: Conclude that if angular momentum is doubled while moment of inertia is constant, the angular velocity must also double.
  • Angular Momentum – Angular momentum (L) is the product of a body'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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