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If two identical disks are stacked on top of each other, what is the moment of i

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Question: If two identical disks are stacked on top of each other, what is the moment of inertia about the axis of the bottom disk?

Options:

  1. MR^2
  2. 2MR^2
  3. 1/2 MR^2
  4. 4MR^2

Correct Answer: 2MR^2

Solution: 

The moment of inertia of the bottom disk is MR^2, and the top disk contributes an additional MR^2 due to the parallel axis theorem, giving a total of 2MR^2.

If two identical disks are stacked on top of each other, what is the moment of i

Practice Questions

Q1
If two identical disks are stacked on top of each other, what is the moment of inertia about the axis of the bottom disk?
  1. MR^2
  2. 2MR^2
  3. 1/2 MR^2
  4. 4MR^2

Questions & Step-by-Step Solutions

If two identical disks are stacked on top of each other, what is the moment of inertia about the axis of the bottom disk?
Correct Answer: 2MR^2
  • Step 1: Understand that the moment of inertia (I) is a measure of how difficult it is to rotate an object around an axis.
  • Step 2: Identify that we have two identical disks, each with mass (M) and radius (R).
  • Step 3: Calculate the moment of inertia of the bottom disk about its own axis, which is given by the formula I = MR^2.
  • Step 4: Recognize that the top disk is also identical and has the same mass (M) and radius (R).
  • Step 5: Use the parallel axis theorem to find the moment of inertia of the top disk about the axis of the bottom disk. The parallel axis theorem states that I = I_cm + Md^2, where I_cm is the moment of inertia about its own center and d is the distance between the two axes.
  • Step 6: For the top disk, I_cm is also MR^2, and the distance (d) from the bottom disk's axis to the top disk's axis is equal to the diameter of the disk, which is 2R.
  • Step 7: Calculate the additional moment of inertia for the top disk: I_top = MR^2 + M(2R)^2 = MR^2 + 4MR^2 = 5MR^2.
  • Step 8: Add the moment of inertia of the bottom disk and the top disk: Total I = MR^2 (bottom disk) + 5MR^2 (top disk) = 6MR^2.
  • Step 9: However, we only need the contribution of the top disk to the bottom disk's moment of inertia, which is 4MR^2.
  • Step 10: Therefore, the total moment of inertia about the axis of the bottom disk is 2MR^2.
  • Moment of Inertia – The moment of inertia quantifies an object's resistance to rotational motion about a given axis.
  • Parallel Axis Theorem – This theorem allows the calculation of the moment of inertia of a body about any axis parallel to an axis through its center of mass.
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