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For a solid disk of mass M and radius R, what is the moment of inertia about an

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Question: For a solid disk of mass M and radius R, what is the moment of inertia about an axis perpendicular to the disk and passing through its center?

Options:

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

Correct Answer: 1/2 MR^2

Solution: 

The moment of inertia of a solid disk about an axis through its center is I = 1/2 MR^2.

For a solid disk of mass M and radius R, what is the moment of inertia about an

Practice Questions

Q1
For a solid disk of mass M and radius R, what is the moment of inertia about an axis perpendicular to the disk and passing through its center?
  1. 1/2 MR^2
  2. 1/4 MR^2
  3. MR^2
  4. 3/4 MR^2

Questions & Step-by-Step Solutions

For a solid disk of mass M and radius R, what is the moment of inertia about an axis perpendicular to the disk and passing through its center?
  • Step 1: Understand what moment of inertia is. It is a measure of how difficult it is to change the rotation of an object.
  • Step 2: Identify the shape of the object. In this case, it is a solid disk.
  • Step 3: Know the parameters involved. The mass of the disk is M and the radius is R.
  • Step 4: Recall the formula for the moment of inertia of a solid disk about an axis through its center. The formula is I = 1/2 MR^2.
  • Step 5: Substitute the values of M and R into the formula if needed, but the formula itself gives you the moment of inertia directly.
  • Moment of Inertia – The moment of inertia is a measure of an object's resistance to rotational motion about a given axis.
  • Solid Disk Properties – Understanding the geometric and mass distribution properties of a solid disk is essential for calculating its moment of inertia.
  • Axis of Rotation – The axis about which the moment of inertia is calculated significantly affects the value, as it depends on the distribution of mass relative to that axis.
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