Perpendicular axis theorem

For calculating the moment of inertia of a lamina about an axis perpendicular to the lamina we use the perpendicular axis theorem which states that"The moment of inertia of a plane lamina about an axis perpendicular to the plane of the lamina and passing to its centroid is equal to the sum of the moment of inerta about two mutually perpendicular axis passing through the centroid and in the plane of the lamina"
Does this moment of inertia of the lamina about an axis perpendicular to the plane of the lamina have a physical significance by itself or is use only as an aid in calculating the moment of inertia of the lamina about axis which lie in the plane of the lamina??

 

[vonlueke]

Yes, it also has a physical significance by itself; it represents resistance to rotation of the lamina about an axis perpendicular to the lamina plane, and is called polar moment of inertia, whereas the other two moments of inertia you mentioned are called rectangular moments of inertia.

 

Suppose we have a rectangulsr cross section of dimensions "b" x "d" ("b" corresponds to the width and "d" to the depth of the section).Suppose i need to calculate the polar moment of inertia of this section it means the moment of inertia of the rectangular lamina about an axis perpendicular to the plane of the lamina.Will this polar moment of inertia for this section denote the resistance to torsion?

 

[prex]

Well, not the resistance to torsion (stress), but the torsional deformation (strain). However unfortunately this is only true for circular sections. For all other sections the polar moment of inertia must be replaced by a torsional stiffness constant, that is a fraction of the moment of inertia, and may be much smaller.
In the site below under Beams -> Cross sections you may find some values and formulae for stiffness constants. prex
motori@xcalcsREMOVE.com

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