Relationship of Moments of Inertia

[minger]

Hey guys, I need some help. I have an old fortran program that needs axial moment of inertia as well as polar moment of inertia.

I have the part in Unigraphics NX5.0, where I can get the mass, volume, radius of gyration, and moment of inertias about each axis. However, I cannot find where to get polar moment of inertia.

So, I guess I either need someone who knows how to get J in NX, or some sort of relationship between the values I have and polar moment of inertia. I don't really think there is a direct relationship, but I'm struggling.

Thanks a lot guys,

 

[Topher925]

Every CAD program I have used will not give you the polar moment of inertia except for maybe solidworks, but they should all give you the inertial tensor which can be used to find the PMOI. There is a duality between conventional MOI and your PMOI. The PMOI is simply defined as:

J = $$\int$$r²dA

Of course wiki, has lots of info on it: http://en.wikipedia.org/wiki/Polar_moment_of_inertia

For relating the two to each other, look at radius of gyration: http://en.wikipedia.org/wiki/Radius_of_gyration

 

[FredGarvin]

You can take that relationship one step further and say that

$$J = I_x + I_y$$

Attached is a quick example

 

[minger]

Oh fantastic. So, if I need the Mass and Polar Moment of Inertia about an axis, the normal MMOI is I_x (assuming x in the axial direction) and J = I_y + I_z.

Great, appreciate the help guys.