How to Calculate Moments of Inertia in a Rectangle

Written by thomas bourdin
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How to Calculate Moments of Inertia in a Rectangle
The moment of inertia for a rectangle can be used to help analyse rotations of the object. (Jupiterimages/Photos.com/Getty Images)

The moment of inertia is an important property of solid bodies that is commonly used in physics and engineering. The moment of inertia is the rotational analogy of the mass of a body, and acts to resist motion in a rotational plane, much as mass does for linear motion. The moment of inertia of a solid body depends on the geometric shape of an object, as well as the distribution of mass within the body. For a rectangular shaped object with a uniform mass distribution, the moment of inertia is a straightforward calculation.

Skill level:
Moderately Easy

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Instructions

  1. 1

    Determine the cube of the height of the rectangle (that is, multiply the height of the rectangle by itself three times). For a rectangle with a height of 3 meters, you will get 9 meters cubed.

  2. 2

    Multiply the cube of the height by the width of the rectangle. If the width of the rectangle is 2 meters, the product of the two numbers is 18 meters to the fourth power.

  3. 3

    Multiply the product of the cube of the height and the width by 0.833. In the example above, this calculation yields 1.5 meters to the fourth power. This is the moment of inertia of the rectangle.

Tips and warnings

  • This article details how to find the moment of inertia about the axis of the height. To find the moment of inertia about the axis of the width, simply swap the values of the height and the width (that is, cube the width and multiply that number by the height of the rectangle).
  • In the final step, multiplying by 0.833 is equivalent to dividing the number by 12.

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