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For a rectangular plate of mass M and dimensions a x b, what is the moment of in

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Question: For a rectangular plate of mass M and dimensions a x b, what is the moment of inertia about an axis through its center and parallel to side a?

Options:

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

Correct Answer: 1/12 Mb^2

Solution: 

The moment of inertia of a rectangular plate about an axis through its center parallel to side a is I = 1/12 Mb^2.

For a rectangular plate of mass M and dimensions a x b, what is the moment of in

Practice Questions

Q1
For a rectangular plate of mass M and dimensions a x b, what is the moment of inertia about an axis through its center and parallel to side a?
  1. 1/12 Mb^2
  2. 1/3 Mb^2
  3. 1/4 Mb^2
  4. 1/6 Mb^2

Questions & Step-by-Step Solutions

For a rectangular plate of mass M and dimensions a x b, what is the moment of inertia about an axis through its center and parallel to side a?
  • 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 rectangular plate with dimensions a (length) and b (width).
  • Step 3: Recognize the axis of rotation. The axis is through the center of the plate and is parallel to side a.
  • Step 4: Recall the formula for the moment of inertia of a rectangular plate about an axis through its center parallel to one of its sides.
  • Step 5: The formula for the moment of inertia (I) about the specified axis is I = 1/12 * M * b^2, where M is the mass of the plate and b is the width.
  • Step 6: Substitute the values into the formula if needed, but the general result is I = 1/12 * M * b^2.
  • Moment of Inertia – The moment of inertia is a measure of an object's resistance to rotational motion about a given axis.
  • Rectangular Plate – A rectangular plate is a flat, two-dimensional shape defined by its length and width, which affects its moment of inertia.
  • Axis of Rotation – The axis about which the moment of inertia is calculated is crucial, as it determines how mass is distributed relative to that axis.
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