where the element of area is taken parallel to the x-axis.
| ES-210 Moment of Inertia by Integration |
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The moment of inertia of a body about the x-axis is defined by where the element of area is taken parallel to the x-axis. |
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The moment of inertia about the y-axis is defined by
where the element of area is taken parallel to the y-axis.
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The moment of inertia of a rectangle about its edge is given by   
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The moments of inertia Ixx and Iyy may be calculated from the same element by  where dIxx is the moment of inertia of a rectangle of infinitesimal base b=dx and height h=y, and dIyy is the moment of inertia of a thin rectangle about the y axis. |
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The polar moment of inertia of an object is defined by where the geometric configuration is as shown... |
  
| The polar moment of inertia may be expressed in terms of the rectangular moments of inertia as... |
  
| The radius of gyration (k) is defined as the location where a concentrated area should be placed so as to have the same moment of inertia and area as the original body |