# Rotated Section - Moment of Inertia

• eriveraa80
In summary, there are formulas available for calculating the moment of inertia of a 2D area and for a rotated axis. However, there is not a specific formula for calculating the moment of inertia of a rotated section. It is suggested to use the same formula for a rotated axis, but with a negative rotation angle.
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) ??

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.

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.

## 1. What is a rotated section?

A rotated section is a cross-sectional shape of an object that is obtained by rotating the object about a given axis. This allows us to analyze the moment of inertia of the object about that axis.

## 2. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to rotational motion. It is calculated by summing the products of each small element's mass and squared distance from the axis of rotation.

## 3. How is moment of inertia different for a rotated section?

For a rotated section, the moment of inertia is calculated with respect to the rotated axis, which may not be the same as the original axis of rotation. This results in a different value for the moment of inertia compared to that of the original object.

## 4. What factors affect the moment of inertia for a rotated section?

The moment of inertia for a rotated section depends on the shape of the cross-section, the axis of rotation, and the distance of the cross-section from the axis of rotation. The distribution of mass also plays a significant role in determining the moment of inertia.

## 5. How is the moment of inertia used in engineering and physics?

The moment of inertia is an important parameter in analyzing the rotational motion of objects in engineering and physics. It helps in determining the amount of force needed to rotate an object and predicting how it will respond to external forces. It is also used in designing structures and machines to ensure their stability and efficiency.

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