|ES-210 Moment of Inertia by Integration|
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.
|The moment of inertia about the y-axis is defined by where the element of area is taken parallel to the y-axis.|
The moment of inertia of a rectangle about its edge|
is given by
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.
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|