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What is the moment of inertia of a uniform thin square plate of mass M and side

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Question: What is the moment of inertia of a uniform thin square plate of mass M and side length a about an axis through its center and parallel to one of its sides?

Options:

  1. 1/6 Ma²
  2. 1/12 Ma²
  3. 1/4 Ma²
  4. 1/3 Ma²

Correct Answer: 1/12 Ma²

Solution: 

The moment of inertia of a square plate about an axis through its center and parallel to one side is I = 1/12 Ma².

What is the moment of inertia of a uniform thin square plate of mass M and side

Practice Questions

Q1
What is the moment of inertia of a uniform thin square plate of mass M and side length a about an axis through its center and parallel to one of its sides?
  1. 1/6 Ma²
  2. 1/12 Ma²
  3. 1/4 Ma²
  4. 1/3 Ma²

Questions & Step-by-Step Solutions

What is the moment of inertia of a uniform thin square plate of mass M and side length a about an axis through its center and parallel to one of its sides?
  • 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 uniform thin square plate.
  • Step 3: Note the mass (M) of the plate and the length of one side (a).
  • Step 4: Recognize that we need to find the moment of inertia about an axis that goes through the center of the plate and is parallel to one of its sides.
  • Step 5: Use the formula for the moment of inertia of a square plate about the specified axis, which is I = 1/12 Ma².
  • Step 6: Substitute the values of M and a into the formula if needed, but the formula itself gives the answer directly.
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