Calculating Inertia in 3D: What You Need to Know

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Calculating inertia in 3D involves understanding both the second moment of area and the mass moment of inertia, which are distinct concepts. The second moment of area applies to plane figures and is sometimes referred to as moment of inertia, while the mass moment of inertia pertains to 3D bodies and measures resistance to rotational acceleration. The units for these properties differ, with the second moment of area having units of L^4 and mass moment of inertia having units of ML^2. Clarification is needed on whether the focus is on the second moment of inertia for various shapes in 3D or the mass moment of inertia. Understanding these differences is crucial for accurate calculations in 3D inertia.
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Isawyou0 said:
Hi!
is there anyway to calculate inertia in 3d?
for all forms, like we do in 2d, is it the same?

https://upload.wikimedia.org/math/d/d/3/dd3b5877d05c86142f03703ac1c6562b.png
The formula you attached appears to calculate the second moment of area of a general polygon, using the (x,y) coordinates of the vertices.

You'll have to be more specific about what you mean by "calculat(ing) inertia in 3d".
 
the moment of inertia in 3d is it the same for 2d?
 
Isawyou0 said:
the moment of inertia in 3d is it the same for 2d?
It depends.

The second moment of area is sometimes referred to as the moment of inertia. This is a property of plane figures.

The mass moment of inertia for 3-D bodies determines how easy or how difficult it is to accelerate a body in rotation.

As I asked before, which of these two properties do you wish to calculate in 3-D?
 
so there is second moment of inertia and moment of inertia I didn't knew that :/
of course I'm talking about second moment of inertia in 3d, for different shapes...
 
Last edited:
Isawyou0 said:
so there is second moment of inertia and moment of inertia I didn't knew that :/
of course I'm talking about second moment of inertia in 3d, for different shapes...
No, you have confused things.

1. There is a second moment of area for plane shapes, which is also referred to as a moment of inertia. The second moment of area has units of L4.

https://en.wikipedia.org/wiki/List_of_area_moments_of_inertia

2. There is a mass moment of inertia for 3-D bodies, which has units of ML2:

https://en.wikipedia.org/wiki/List_of_moments_of_inertia
 

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