Sierpinski carpet - Moment of inertia

In summary, the conversation is about finding the moment of inertia of a Sierpinski carpet with a mass of m and length of a, with O and O' perpendicular to the plane. The person is unsure of how to calculate the moment of inertia, but it involves finding the moments of inertia of smaller squares and subtracting them from the moment of inertia of the entire square. There is also a mention of calculating Jx and Jy, but the issue is finding the moment of inertia along the z-axis. The solution is given as using the perpendicular axis theorem, where Iz equals Ix plus Iy. A link is also provided for further reference.
  • #1
zl64c
3
0
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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  • #2
Welcome to the forum!

I'm sorry to say that I don't understand your question. What exactly are you trying to compute?
 
  • #3
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)
 
  • #4
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.
 
  • #5
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
 
  • #6
i just calced it. thanks
 

FAQ: Sierpinski carpet - Moment of inertia

What is a Sierpinski carpet?

A Sierpinski carpet is a fractal shape named after mathematician Waclaw Sierpinski. It is created by starting with a square and dividing it into 9 smaller squares, then removing the center square and repeating the process on the remaining squares infinitely.

What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation.

How is the moment of inertia of a Sierpinski carpet calculated?

The moment of inertia of a Sierpinski carpet can be calculated by summing the moments of inertia of each individual square within the carpet. This can be done using the parallel axis theorem, which takes into account the distance of each square from the axis of rotation.

What is the significance of the moment of inertia of a Sierpinski carpet?

The moment of inertia of a Sierpinski carpet is a measure of its rotational resistance, and can be used to analyze its behavior when subjected to rotational forces. It can also be used to compare the rotational properties of different fractal shapes.

Are there any real-world applications of the moment of inertia of a Sierpinski carpet?

The moment of inertia of a Sierpinski carpet is primarily used in mathematical and theoretical contexts, but it can also be applied in engineering and physics. For example, it can be used to analyze the stability of complex structures or to study the behavior of materials with fractal properties.

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