Moment of inertia of Sierpinski carpet

[player1_1_1]

Homework Statement

Hello
sorry for my english, i know its bad.
The problem i have is to count the moment of inertia of Sierpinski carpet around the point lying in middle of this figure. I would be very thanks to you for solving my problem :)

Homework Equations

i don't know what it mean in english..

The Attempt at a Solution

to use integrals, limes, other analysis methods

 

[player1_1_1]

up up

 

[merryjman]

what figure?

 

[player1_1_1]

Sierpinski carpet: http://en.wikipedia.org/wiki/Sierpinski_carpet

 

[ununbium]

If you are writing "Olimpiada Fizyczna", you shouldn't ask for solution there. If you are not I'll show you the answer in 2 days.

 

[player1_1_1]

what i am writing?
can be in two days, not a problem...

 

[player1_1_1]

but what is a difference if you answer now or in 2 days?

 

[Borek]

I suppose that's the deadline for submitting answers - rules prohibit pariticipants from discussing questions and solutions on public forums earlier.

 

[ununbium]

Borek is right.
I don't know English good, so please forgive me mistakes.
"Olimpiada Fizyczna" is some kind of competition in Poland.

If we have big carpet with size 3r and bulk 8m (not 9, because middle of carpet is empty), x is a factor in moment eguation (I don't know how to name it)
I- moment of small carpet (r,m)
I=x*m*r^2
Ic-moment of big carpet 8m,3r
Ic=x*8m*(3r)^2 //I can't prove it, but i know taht it works (from simulation in Excel...)
From Steiner: (http://en.wikipedia.org/wiki/Parallel_axis_theorem)
Ic=4(I+mr^2)+4(I+m(r*2^0,5)^2) //r*2^0,5 is distance from the middle of big carpet to middle of small carpet in corner.
Everything in 4, because we have 4 small carpets next to centre of empty carpet and 4 in corners
first Ic=Ic sceond and for I in second Ic equation we substitute x*m*r^2
and finally we get
x=3/16

 

[Borek]

"Olimpiada Fizyczna" is some kind of competition in Poland.

Physics Olympiad, national level.

equation we substitute x*m*r^2 and finally we get

So once you have explained that I am right you have posted solution two days before the deadline? Am I missing something?

Edit: looks like the deadline was yesterday:

http://www.kgof.edu.pl/

"Termin wysyłania części I" means "deadline to submit 1st part".

So far link to solutions is inactive, perhaps they will be pubslihed on Monday.

 

[player1_1_1]

interesting... it is a coincidence anyway :P
thanks for solving this, it took a long time for me to solve it :)

 

[ununbium]

I wrote 2 days 2 days ago.
Deadline was 15.10.2009 (I am sure), so I think, that i could post the solution.
Am i right?

 

[Borek]

Yep, seems everything is OK - hence my edit, I checked details after posting.

Startujesz czy kibicujesz?

 

[ununbium]

Startuję

 

[Borek]

Powodzenia

Just before Mentors will ban us both - I have asked ununbium if s/he starts or just follows the competition. "Startuję" means "I take part", "powodzenia" means "good luck". That's probably enough Polish for October.