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What is the moment of inertia of a thin circular plate of mass M and radius R ab

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Question: What is the moment of inertia of a thin circular plate of mass M and radius R about an axis through its center and perpendicular to its plane?

Options:

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

Correct Answer: 1/2 MR^2

Solution: 

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

What is the moment of inertia of a thin circular plate of mass M and radius R ab

Practice Questions

Q1
What is the moment of inertia of a thin circular plate of mass M and radius R about an axis through its center and perpendicular to its plane?
  1. 1/2 MR^2
  2. MR^2
  3. 1/4 MR^2
  4. 1/3 MR^2

Questions & Step-by-Step Solutions

What is the moment of inertia of a thin circular plate of mass M and radius R about an axis through its center and perpendicular to its plane?
  • Step 1: Understand what moment of inertia means. 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 thin circular plate.
  • Step 3: Recognize the key parameters: mass (M) and radius (R) of the plate.
  • Step 4: Know that the formula for the moment of inertia (I) of a thin circular plate about an axis through its center is derived from integration over its area.
  • Step 5: The formula for the moment of inertia of a thin circular plate is I = 1/2 MR^2.
  • Step 6: Conclude that for a thin circular plate with mass M and radius R, the moment of inertia is I = 1/2 MR^2.
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