How do you calculate moment of inertia for circle?

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SUMMARY

The moment of inertia for a circle not centered at its center of gravity can be calculated using the parallel axis theorem. This theorem allows for the determination of the moment of inertia about any axis parallel to one through the centroid. In two-dimensional space, the calculations typically involve integration, but the parallel axis theorem simplifies the process. Understanding the distinction between centroid and center of gravity is crucial for accurate calculations.

PREREQUISITES
  • Understanding of moment of inertia concepts
  • Familiarity with the parallel axis theorem
  • Basic knowledge of integration techniques
  • Geometric properties of circles
NEXT STEPS
  • Study the parallel axis theorem in detail
  • Learn integration techniques for calculating moments of inertia
  • Explore complex shapes and their moment of inertia calculations
  • Review geometric properties of centroids and their applications
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Students and professionals in engineering, physics, and mathematics who are involved in mechanics and structural analysis will benefit from this discussion.

Josh The Cool
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Hey, not sure if this is the right place to post this, but here it goes. how do you calculate the moment of inertia for a circle that is not at its center of gravity. I am trying to find the moment of inertia for a complex shape made of many circles, and this seems like a good place to start. Forgive me if the answer is simple, because I have spent hours googling this question and have come up empty handed. I would greatly appreciate any help!
 
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Around which axis? In general, with an integral, but sometimes there are some tricks to avoid this, like the parallel axis theorem.
 
This is in two dimensional space. So I think the z axis if I understand correctly.
Edit:
I also looked at that wiki page, but couldn't apply it in any useful way.
 
What is unclear about the Wikipedia page?
 
Are you thinking of a reference point in the plane of the circle but not at the center of the circle?

A circle is a purely geometric figure, and as such, has no cg. It does have centroid; is that what you have in mind?
 

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