## Moment of inertia of system in 3D

Hey i am working on something and i need to know how to calculate moment of inertia of a 3D system of objects.

I know these variables:
Mass of whole system
Center of mass of whole system

Center of mass of each object
Offset of each object
Mass of each object
Moment of Inertia of each individual object(its precalculated)

I think i need to use parallel axis theorem but i am not sure how to actually calculate the "sum".

Is this right:

$\vec{I_i}= \vec{I_{com_i}} + mass_i * (\vec{com_{system}}-\vec{offset_i} + \vec{com_i})^2$
$\vec{I_{system}} = \sum^{N}_{i=1}{\vec{I_i}}$

?
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 Quote by PJani Hey i am working on something and i need to know how to calculate moment of inertia of a 3D system of objects. I know these variables: Mass of whole system Center of mass of whole system Center of mass of each object Offset of each object Mass of each object Moment of Inertia of each individual object(its precalculated) I think i need to use parallel axis theorem but i am not sure how to actually calculate the "sum". Is this right: $\vec{I_i}= \vec{I_{com_i}} + mass_i * (\vec{com_{system}}-\vec{offset_i} + \vec{com_i})^2$ $\vec{I_{system}} = \sum^{N}_{i=1}{\vec{I_i}}$ ?
How are you defining an object's "offset"? I expected it to mean offset of object's c.o.m. from system's c.o.m., which would be $\vec{com_i}-\vec{com_{system}}$.
Anyway, assuming you want the MI about the system's c.o.m, I make the answer
$\vec{I_i}= \vec{I_{com_i}} + mass_i * |\vec{com_i}-\vec{com_{system}}|^2$

 Quote by haruspex How are you defining an object's "offset"? I expected it to mean offset of object's c.o.m. from system's c.o.m., which would be $\vec{com_i}-\vec{com_{system}}$. Anyway, assuming you want the MI about the system's c.o.m, I make the answer $\vec{I_i}= \vec{I_{com_i}} + mass_i * |\vec{com_i}-\vec{com_{system}}|^2$
offset is position of object from center of system(not the $com_{system}$) the $com_i$ is "local" center of mass.

Recognitions:
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 Quote by PJani offset is position of object from center of system(not the $com_{system}$) the $com_i$ is "local" center of mass.