Rotated Section - Moment of Inertia

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The discussion centers on calculating the moment of inertia for a rotated 2D area, specifically seeking a formula for the inertia moments (Ix, Iy, Pxy) after rotating the area around the origin by a certain angle. The original poster, Eduardo, is looking for a method to determine these values without changing the axis of rotation. A participant suggests that rotating the area can be treated as a negative rotation of the axes, implying that the existing formulas for inertia moments can still be applied. This indicates that the same calculations can be utilized by simply adjusting the angle of rotation accordingly. The conversation emphasizes the relationship between area rotation and axis rotation in moment of inertia calculations.
eriveraa80
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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
 
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Not sure what you mean. Can you provide additional explanation by means of a diagram or other hand waving?
 
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?
 
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.
 

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