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 I_{xx} and I_{yy} may be calculated from the same element by where dI_{xx} is the moment of inertia of a rectangle of infinitesimal base b=dx and height h=y, and dI_{yy} 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 |