Sierpinski carpet - Moment of inertia

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Homework Help Overview

The discussion revolves around calculating the moment of inertia (MoI) of a Sierpinski carpet, a fractal shape known for having no area. The original poster presents a specific scenario involving mass and length, questioning how to approach the integral needed for the calculation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the idea of calculating the MoI by first determining the MoI of a larger square and then subtracting the contributions from the smaller squares. There is also mention of the challenge posed by the axis of rotation being perpendicular to the plane of the carpet.

Discussion Status

Some participants are exploring different interpretations of the problem, particularly regarding the application of the perpendicular axis theorem. The original poster has indicated progress in their calculations, suggesting that some guidance has been helpful.

Contextual Notes

The original poster notes a specific challenge related to calculating the MoI about the z-axis, which may indicate constraints in their understanding or approach to the problem.

zl64c
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Hi, its my first post here, so i say HI :D
hm, i have a little problem with moment of interia. I know, that sierpinski carpet has no area and that's why with normal situation it also has not moment of interia (MoI). but now, i have special situation: mass - m, and length a. O and O' is perpendicular to the plan. i think is simple integral but maybe I am wrong? waiting for any ideas or any integrals to calc( love it ) :D:D

greetings form Poland
 
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Welcome to the forum!

I'm sorry to say that I don't understand your question. What exactly are you trying to compute?
 
Well what I am seeing is that it is basically a large square with squares in it cut out. So you can find the moment of inertia of the entire large square and then subtract the moments of inertia of the smaller squares (which may be a bit tedious as it looks)
 
rock.freak667 said:
Well what I am seeing is that it is basically a large square with squares in it cut out. So you can find the moment of inertia of the entire large square and then subtract the moments of inertia of the smaller squares (which may be a bit tedious as it looks)

yes, that's true. But i know how to calc MoI only Jx and Jy and here i have axis z. that's a problem.
 
zl64c said:
yes, that's true. But i know how to calc MoI only Jx and Jy and here i have axis z. that's a problem.

By the perpendicular axis theorem, Iz=Ix+Iy
 
i just calced it. thanks
 

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