Rotated Section - Moment of Inertia

[eriveraa80]

Hi everybody:

I can see that there are formulas to calculate the moment of inertia of a 2D Area (Second moment of area) here: http://en.wikipedia.org/wiki/Second_moment_of_area"

In the same link, there is a formula to calculate the Inertia moments about a ROTATED AXIS (Axis Rotation). But, is there a formula to calculate the Inertia moments of a ROTATED SECTION (rotated area) ??

Thanks in advance.
Eduardo

 

[SteamKing]

Not sure what you mean. Can you provide additional explanation by means of a diagram or other hand waving?

 

[eriveraa80]

Ok, i will explain a little bit:

1. You have a 2D Area in a XY axis. You can calculate the Moments of Inertia Ix, Iy, Pxy.
2. You rotate the 2D Area around the origin, with a tetha angle.
3. So, known Ix, Iy, Pxy and tetha: Is there a formula so i can calculate the new Ix, Iy, Pxy around the same axis?

In wikipedia, you can see that there is a way of calculating the Ix', Iy' and Pxy' around the rotated axis, but that is not what i want, because i am not rotating Axis. I am rotating only the 2D Area and i want calculate Ix, Iy, Pxy in the same axis based on the previously Ix, Iy, Pxy calculated.

Any ideas?

 

[Studiot]

Hello Eduardo, you should not create duplicate posts in different sections.

Can you see that rotating the area in one direction is the same thing as rotating the axes in the other direction?

So you should use the same formulae, but the rotation angle is negative.

 

[PJC01]

Hello Eduardo,

Yes, there is a formula to calculate the inertia moments of a rotated section. It is known as the parallel axis theorem, which states that the moment of inertia of a body about an axis is equal to the moment of inertia of the body about a parallel axis through its center of mass, plus the product of the mass of the body and the square of the distance between the two axes. This formula can be applied to calculate the moment of inertia of a rotated section by considering the original moment of inertia of the section and the distance between the original and rotated axes. This is an important concept in the study of rotational dynamics and is often used in engineering and physics calculations. I hope this helps answer your question.