Find Inner & Outer Radius of Hollow Circle from Second Moment of Area

In summary, the conversation discusses finding the inner and outer radius of a hollow circle based on its second moment of area. The equation used is I=π(r1^4-r2^4)/4 and a simultaneous equation is needed. However, there is a need to specify a parameter such as the area of the section or thickness in order to solve for the radii.
  • #1
kazel101
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TL;DR Summary
trying to solve for cross-sectional dimensions with only I. Need another equation to form a simultaneous equation.
Hi! I am trying to find the inner (r2) and outer radius (r1) of a hollow circle based on its second moment of area. I have the equation that I=π(r1^4-r2^4)/4. I think I need to use a simultaneous equation and then sub this in for one of the radii. However, I am unsure of another equation I could use. Any suggestions would be great of places to look or things I have overlooked.
 
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  • #2
There are many solutions for any particular value of I.
You need to specify a parameter such as the area of the section, or thickness r2–r1, before solving for r1 and r2.
 

1. What is the second moment of area?

The second moment of area, also known as the moment of inertia, is a measure of an object's resistance to bending. It is calculated by summing the products of each element's area and its squared distance from a specified axis.

2. How is the second moment of area related to a hollow circle?

In the case of a hollow circle, the second moment of area is used to calculate the circle's ability to resist bending around its central axis. This is important for determining the circle's strength and stability.

3. What is the formula for finding the second moment of area of a hollow circle?

The formula for finding the second moment of area of a hollow circle is I = π/4 * (R^4 - r^4), where R is the outer radius and r is the inner radius of the circle.

4. How do you find the inner and outer radius of a hollow circle from the second moment of area?

To find the inner and outer radius of a hollow circle from the second moment of area, you can rearrange the formula to solve for either R or r. Once you have one of the values, you can then use it to solve for the other radius.

5. Why is it important to find the inner and outer radius of a hollow circle from the second moment of area?

Knowing the inner and outer radius of a hollow circle from the second moment of area is crucial for understanding the circle's structural integrity and ability to withstand bending forces. This information is essential for engineers and designers in various industries, such as construction and manufacturing, to ensure the safety and stability of their structures and products.

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