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calculate moment of inertia using components on 3 axis

Engineering Asked by Abeer on July 16, 2021

I have some geometric shapes that modeled on Solidworks, and it shows me the moment of inertia taken at the center of the mass, my question is can I use these information (Px,Py,Pz) to calculate the total moment of inertia around some axis ?

Solidworks result like this

Center of mass: ( millimeters )
    X = -3.07
    Y = 2.41
    Z = 4.00

Principal axes of inertia and principal moments of inertia: ( grams *  square millimeters )
Taken at the center of mass.
     Ix = ( 1.00,  0.00,  0.00)     Px = 675.07
     Iy = ( 0.00,  1.00,  0.00)     Py = 2557.45
     Iz = ( 0.00,  0.00,  1.00)     Pz = 3111.07

Moments of inertia: ( grams *  square millimeters )
Taken at the center of mass and aligned with the output coordinate system.
    Lxx = 675.07    Lxy = 0.00  Lxz = 0.00
    Lyx = 0.00  Lyy = 2557.45   Lyz = 0.00
    Lzx = 0.00  Lzy = 0.00  Lzz = 3111.07

Moments of inertia: ( grams *  square millimeters )
Taken at the output coordinate system.
    Ixx = 923.41    Ixy = -84.13    Ixz = -139.59
    Iyx = -84.13    Iyy = 2846.59   Iyz = 109.79
    Izx = -139.59   Izy = 109.79    Izz = 3284.21

One Answer

You probably need the following two for the generic solution

Given the Moment of inertia with respect to the center of gravity you can calculate the moment of inertia with respect to a new axis.

you need to be careful about the order to rotation and parallel translation though.

Answered by NMech on July 16, 2021

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