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In a system of two rotating disks, if disk A has twice the moment of inertia of

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Question: In a system of two rotating disks, if disk A has twice the moment of inertia of disk B and they are both rotating with the same angular velocity, what can be said about their angular momentum?

Options:

  1. LA = LB
  2. LA = 2LB
  3. LA = 4LB
  4. LA = 1/2 LB

Correct Answer: LA = 2LB

Solution: 

Angular momentum L = Iω; since IA = 2IB and ωA = ωB, LA = 2LB.

In a system of two rotating disks, if disk A has twice the moment of inertia of

Practice Questions

Q1
In a system of two rotating disks, if disk A has twice the moment of inertia of disk B and they are both rotating with the same angular velocity, what can be said about their angular momentum?
  1. LA = LB
  2. LA = 2LB
  3. LA = 4LB
  4. LA = 1/2 LB

Questions & Step-by-Step Solutions

In a system of two rotating disks, if disk A has twice the moment of inertia of disk B and they are both rotating with the same angular velocity, what can be said about their angular momentum?
  • Step 1: Understand the terms. Moment of inertia (I) is a measure of how difficult it is to change the rotation of an object. Angular velocity (ω) is how fast the object is rotating.
  • Step 2: Identify the moment of inertia for both disks. Disk A has twice the moment of inertia of disk B, so if IB is the moment of inertia of disk B, then IA = 2 * IB.
  • Step 3: Note that both disks are rotating at the same angular velocity. This means ωA = ωB.
  • Step 4: Use the formula for angular momentum (L). Angular momentum L is calculated as L = I * ω.
  • Step 5: Calculate the angular momentum for both disks. For disk A, LA = IA * ωA. For disk B, LB = IB * ωB.
  • Step 6: Substitute the known values into the equations. Since IA = 2 * IB and ωA = ωB, we can write LA = (2 * IB) * ωB.
  • Step 7: Simplify the equation for disk A's angular momentum. This gives LA = 2 * (IB * ωB) = 2 * LB.
  • Step 8: Conclusion: Since LA = 2 * LB, disk A has twice the angular momentum of disk B.
  • Angular Momentum – Angular momentum (L) is the product of the moment of inertia (I) and angular velocity (ω) of a rotating object.
  • Moment of Inertia – Moment of inertia (I) is a measure of an object's resistance to changes in its rotation, dependent on 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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