Calculating Inertia in 3D: What You Need to Know

[Isawyou0]

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

 

[SteamKing]

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".

 

[Isawyou0]

the moment of inertia in 3d is it the same for 2d?

 

[SteamKing]

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?

 

[Isawyou0]

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...

 

[SteamKing]

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