# Mohr circle of inertia-product of inertia

• chandran
In summary, the product of inertia is a measure of how a body's mass is distributed about a given coordinate system. It is required in order to draw the mohr circle for inertia and is important in understanding the rotational motion of a body. Further resources are available to help understand and visualize this concept.
chandran
I want to draw the mohr circle for inertia about some coordinate. I know
moment of inertia about x,y coordinateas IX AND IY. Theory says that
product of inertia is required. What is this product of inertia and what is its
physical significance?

chandran said:
I want to draw the mohr circle for inertia about some coordinate. I know
moment of inertia about x,y coordinateas IX AND IY. Theory says that
product of inertia is required. What is this product of inertia and what is its
physical significance?
To avoid the blind leading the blind I will defer to the following sites which I think you will find very useful:

http://kwon3d.com/theory/moi/prin.html
http://isb.ri.ccf.org/biomch-l/archives/biomch-l-2002-02/00020.html

I found this excellent site that has a series of animations that will take you step by step through it.
http://www.engin.umich.edu/students/support/mepo/ELRC/me211/flash2/coach_inertia_00.swf

Hope that helps.

AM

Last edited by a moderator:

The Mohr circle of inertia is a graphical representation of the moments of inertia about a certain coordinate system. It is commonly used in structural engineering to analyze the distribution of stresses and strains in a structure. In order to accurately draw the Mohr circle, we need to know the moments of inertia about the x and y coordinates, denoted as IX and IY, respectively. However, in addition to these moments of inertia, we also need to know the product of inertia.

The product of inertia is a measure of the distribution of mass around an axis. It is the sum of the products of each element of mass in a body multiplied by the perpendicular distances of these elements from the axis. In simpler terms, it describes how the mass is distributed in relation to the axis of rotation.

The physical significance of the product of inertia is that it affects the rotational motion of an object. When an object rotates, its mass is distributed around the axis of rotation. The product of inertia helps us understand how this mass is distributed and how it affects the rotation of the object. In structural engineering, the product of inertia is important in determining the stability and strength of a structure, as it affects the distribution of forces and moments acting on the structure.

In conclusion, the product of inertia is a crucial factor in accurately analyzing the moments of inertia and understanding the rotational motion of an object. It plays a significant role in the design and analysis of structures and is an important concept in the field of engineering.

## 1. What is the Mohr circle of inertia-product of inertia?

The Mohr circle of inertia-product of inertia is a graphical representation of the moment of inertia tensor, which describes the distribution of mass in a rigid body. It is used to analyze the rotational motion of a body and determine its principal moments of inertia and axes of rotation.

## 2. How is the Mohr circle of inertia-product of inertia calculated?

The Mohr circle of inertia-product of inertia can be calculated by plotting the principal moments of inertia as points on a circle, with the horizontal axis representing the product of inertia and the vertical axis representing the principal moments of inertia. The center of the circle represents the centroid of the body, and the radius of the circle is equal to the radius of gyration of the body.

## 3. What is the significance of the Mohr circle of inertia-product of inertia in engineering?

The Mohr circle of inertia-product of inertia is an important tool in engineering as it allows engineers to analyze the rotational behavior of complex bodies and calculate the moments of inertia for different orientations. This information is crucial for the design and analysis of structures and machines that experience rotational motion.

## 4. Can the Mohr circle of inertia-product of inertia be used for non-symmetric bodies?

Yes, the Mohr circle of inertia-product of inertia can be used for both symmetric and non-symmetric bodies. For non-symmetric bodies, the product of inertia and principal moments of inertia will vary for different orientations, but the Mohr circle can still be constructed to determine the maximum and minimum moments of inertia for any orientation.

## 5. How does the Mohr circle of inertia-product of inertia relate to the stress and strain of a material?

The Mohr circle of inertia-product of inertia is related to the stress and strain of a material through the concept of Mohr's circle in mechanics of materials. Mohr's circle is a graphical representation of stress and strain in a material, and the Mohr circle of inertia-product of inertia is an extension of this concept for analyzing rotational motion. Both circles use similar principles and can be used together to analyze the behavior of materials under various loads and orientations.

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