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What is the moment of inertia of a uniform triangular lamina of mass M and base

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Question: What is the moment of inertia of a uniform triangular lamina of mass M and base b about an axis perpendicular to the base and passing through its centroid?

Options:

  1. 1/18 Mb^2
  2. 1/12 Mb^2
  3. 1/6 Mb^2
  4. 1/24 Mb^2

Correct Answer: 1/12 Mb^2

Solution: 

The moment of inertia of a triangular lamina about an axis through its centroid is I = 1/12 Mb^2.

What is the moment of inertia of a uniform triangular lamina of mass M and base

Practice Questions

Q1
What is the moment of inertia of a uniform triangular lamina of mass M and base b about an axis perpendicular to the base and passing through its centroid?
  1. 1/18 Mb^2
  2. 1/12 Mb^2
  3. 1/6 Mb^2
  4. 1/24 Mb^2

Questions & Step-by-Step Solutions

What is the moment of inertia of a uniform triangular lamina of mass M and base b about an axis perpendicular to the base and passing through its centroid?
  • Step 1: Understand what moment of inertia is. It measures how difficult it is to rotate an object around an axis.
  • Step 2: Identify the shape of the object. In this case, it is a uniform triangular lamina (a flat triangle).
  • Step 3: Know the parameters given: mass (M) and base (b) of the triangle.
  • Step 4: Recognize that we need to find the moment of inertia about an axis that is perpendicular to the base and goes through the centroid (the center of mass) of the triangle.
  • Step 5: Use the formula for the moment of inertia of a triangular lamina about this specific axis, which is I = 1/12 Mb^2.
  • Step 6: Substitute the values of M and b into the formula if needed, but the formula itself gives the answer directly.
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