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In a system of two rotating bodies, if one body has twice the moment of inertia

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Question: In a system of two rotating bodies, if one body has twice the moment of inertia of the other, how does their angular momentum compare if they rotate with the same angular velocity?

Options:

  1. The same
  2. Twice as much
  3. Half as much
  4. Four times as much

Correct Answer: Twice as much

Solution: 

Angular momentum L = Iω; if one has twice the moment of inertia, it will have twice the angular momentum at the same angular velocity.

In a system of two rotating bodies, if one body has twice the moment of inertia

Practice Questions

Q1
In a system of two rotating bodies, if one body has twice the moment of inertia of the other, how does their angular momentum compare if they rotate with the same angular velocity?
  1. The same
  2. Twice as much
  3. Half as much
  4. Four times as much

Questions & Step-by-Step Solutions

In a system of two rotating bodies, if one body has twice the moment of inertia of the other, how does their angular momentum compare if they rotate with the same angular velocity?
  • Step 1: Understand what moment of inertia (I) means. It is a measure of how difficult it is to change the rotation of an object.
  • Step 2: Know that angular velocity (ω) is how fast something is rotating.
  • Step 3: Recall the formula for angular momentum (L): L = I * ω.
  • Step 4: Identify the two bodies. Let's call the first body Body A and the second body Body B.
  • Step 5: Assume Body A has a moment of inertia I and Body B has a moment of inertia 2I (twice that of Body A).
  • Step 6: Both bodies are rotating at the same angular velocity (ω).
  • Step 7: Calculate the angular momentum for Body A: L_A = I * ω.
  • Step 8: Calculate the angular momentum for Body B: L_B = 2I * ω.
  • Step 9: Compare the angular momentum: Since L_B = 2 * L_A, Body B has twice the angular momentum of Body A.
  • 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 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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