anybody know what the moment of inertia for a square about its centre is?

When laying flat

_

Thorugh the centre into the plane of the paper

@JakeRose it must be $\frac{ml^2}{6}$, where $l$ is the side of the square

How did you get that?

I keep getting a 16th instead

Well you just gotta integrate it and then use perpendicular axis theorem

Can I talk you through my method and you tell me where I went wrong

@Tanuj

Sure @JakeRose

Okay so first

Split thd square into two rectangles

Each with a mass m/2

yea

And their CoM a distance of a/4 from the original CoM with a being the side length of the square

okay

Therfore you get $ I= m/2*(a/4)^2 +m/2*(a/4)$

theres meant to be a square on that last one

Giving $ 2*m.2*(a/4)^2$

okay , so firstly why you may be getting it wrong is because you did not consider or take into account , the distribution of mass throughout the whole square shaped plate .

?

Please be more specific than a "?"

I dont understand what you mean sorry?

okay see it this way .

you just assumed all the mass to be concentrated at a single point , i.e. $(\frac{a}{4})$ from the center . Remember $I=\int dm\cdot r^2$ , so the $r^2$ actually takes into account the actual distribution of the mass throughout the plate.

You cant just use a point mass approximation?

Okay so calculus it is

yup , since distribution also matters.

can you carry it on from here ??

I re did it with calculus and now Im getting ma/12

no a^2

Gime one sec to see If i can spot it

Got it

great ! Now just use perpendicular axis theorem !

and there you have it :)

What do I need that for?

I've already got the answer right?

nope

you asked for "moment of inertia for a square about its centre, thorugh the centre into the plane of the paper"

you've just calculated it about a line passing through center but lying in the plane of square

Got back from Hollywood.Buying healthy groceries now

Oh I see

yea

Is there no direct way to get that?

You have to use perp axis theroem dont you

duh , indeed

I hope its sorted now

I mean thats not totally obvious

thanks for the help

Well you can always compute moments of inertia by direct integration, in principle, but sometimes the axis theorems make the calculation a lot easier

I mean to do a square like that though youd have to use mass elements of little square framse right?

@JakeRose Well it should've been obvious , i wrote it like 3 times already. But nvm , now that you get it , is all that matters.

I don't think you get it . How did you integrate ?

I dont know the notation for tha mathjax for integrtion

So ill just say it in words

okay

0 to a/2 of ax^2

with 2 on the outside as well as the mass per area

hmm , i don't get what you did , but seems right , since you also took into account the mass per unit area

what you want to do now is to find moment of inertia of different bodies to get a practice

How would you have done it?

Thats just the way we were taught at uni you see

I'd have considered the center of the square as reference , now since the mass changes with length , i could write $\lambda=\frac{M}{L}$ , where $\lambda$ is the linear mass density

at a distance $x$ from the reference , i would've taken a strip of thickness $dx$ , now the mass of this strip would've been $\lambda\cdot dx$

then from $I=\int dm\cdot r^2$

Ah I see

Yeah we essentially did the same but you simplified it to lengths whilst I did area

yea

Anybody here?

It's round. It's ROOOOOUUUUNNNDDDD

@JakeRose What is it

Well 2 questions really

I might have to go somewhere , just ask

Find the moment of inertia of a hollow thin cubical box of length a and total mass M of axis passing through the centre of two opposite faces

I know Ive got theright method but my answer is far off

whats the answer

5Ma^2/18

Oaky , you remember the previous result right ?

Yeah

moment of inertia for a square about its centre, thorugh the centre into the plane of the paper = $\frac{ml^2}{6}$

yup

Here , just imagine a rod passing through centers of two opposite faces .

Now , divide mass M to 6 faces of cube , M/6 each

okay so far ?

yep

okay so moment of inertia about one of the two faces through which our imaginary rod passes can be given by the same formula

$\frac{ml^2}{6}$ , substitute M for one face and tell me what you get.

M/36 *l^2

?

good , what about combined MOI for two faces

twice that

which is

M/18 * L^2

yup. Lets call it result 1

cool

okay now coming to the four remaining surfaces , i suggest you should draw a diagram to get the 'feel'

or just imagine it ! lol

theres four

theres. four.

not two

fuck

Thatll be exactly where Ive gone wrong

okay so what is the MOI of a square , about an axis passing through the center and lying in the plane of the square (parallel to one of the sides ) ?

Okay , can you try it now ?

Yup got the right answer now

thanks man

sure thing :)

@JakeRose what was the other question ? Did you get it too ?

Its have that cube hung from an edge and displaced by a small amount

Show it performs shm and find its time period

okay

Ive went through it and I think Im doing everything right

but my answers is off again

Can I walk you through it and you tell me where Im wrong?

sure

but what does it mean ? As in what edge ?

Like a length if ygm

So if you looked at it perpendicular to the direction of oscillation youd see a square

Can I see the whole question ?

The box is suspended from a horizontal hinge along one of its edges. The box is displaced slightly from equilibrium. Show that it undergoes SHM and find its time period

Horizontal hinge ? I'm sorry I'm not getting the actual situation.

It essentially looks like a diamond

Hanging from the top vertices

hmm idk

@JakeRose how are you approaching this ?

Conservation of energy

Take derivative and get an shm equation

I just get the wrong numbers sadly

can you just run me through everything that you've done

Sure can do

looks like a good question but awfully phrased , atleast for me

Okay so the distance from the hinge to the Com is 2^1/2 / 2

*a

multiplied by a that is

oh so the cube is hanging from one of the vertices ?

yea

okay

Next as it is displaced its change in GPE is $Mgl(1-cos(theta)$

with l being the root 2 thing

okay

Rotational kinetic energy is $1/2 * I * dot/theta$

Whats the theta dot notation funciton?

$\cdot$

But how do you tyoe that in the mathjax?

it is in the mathjax

Yeah but it doesnt show what I have to type for it

$\cdot$ copy and paste this ! It can't be any simpler than that

I took a lot of pictures today.

$\dot{\theta}$

Some at Hollywood, others at a private airport , and some at spacex

Is what I meant

That didnt work when I tried

wow ! Really ! I don't want to be rude but man , you test my patience

When I copy and paste what you typed it doesnt go in with the mathjax

This is just putting me down Ill see you later

$\cdot{\theta}$

it is working , idk what you're doing man , but alright

@RyanThorngren Woah !! It says you last talked 1413 days ago !

That's a long ass time !

hello world

again

welcome back man !

haha thank you. things have been quiet over at physicsoverflow

yea , i don't know a thing about it , but have heard it from the more experienced users here

I like to think that physicists are too busy out having a good time than going home to chat about physics on the internet too :)

but my brain's been working better at night these days

so what's new and interesting?

I'm revisiting this old classic terrytao.wordpress.com/2010/04/10/…

Welp now I sound like an idiot in front of my professor...

@SirCumference yep.

with luck they'll forget in a week

lay low for now

I'm looking for folks with whom I can discuss ways to find stationary solutions to nonlinear field equations. If anyone is interested, I'll start a chat room for the topic.

@JohnRennie Hi :) Good Morning .I heard you're on a business trip ?

@Tanuj Some of what I'm seeing up the page in your conversation with Jake is a little overbearing. If you find yourself in a situation like that again, where you're trying to help someone and it's testing your patience, I suggest taking a break before you get to the level of posting things like "are you kidding me?" and "you're doing something silly then"

@SirCumference is that piazza?

@loocsieulb Nah it's gmail

I don't think I ever figured out how to use Piazza

@SirCumference profs dont give a fuck dude

trust me unless ur working with them

Yeah but it's still embarrassing...

he probably forgot already

True

nah its fine

dont feel bad

@SirCumference what did you ask anyway

just curious

He got back to me

btw kind of off topic i used to send long elaborate emails to profs with really polite language etc and realized that every one of them just replied with “k” so i decided to send my emails as badly as possible like “hi can i meet you about ___” with all lower case and no formatting and i found absolutely no difference in how they replied or behaved afterwards.

so i do that now

@SirCumference sounds like a dick tbh

is he mocking you?

i didnt see your first email so idk

I dunno what to make of that

what did you ask?????

@loocsieulb It was just along the lines of "how am I supposed to get #3 in the form it's asking for?"

I don't recall what the problem itself was

oh

well then why would he reply that

Although this was for a physics class so I'm wondering if that was a mocking comment...

whatever

Welp, how's life

if he was a good prof and researcher he wouldnt waste time like that mocking you in an email

probably a loser

idk lol im just living

My experience would suggest he could be kind of a jerk, or he could honestly be wondering if you're a physics major. It's hard to tell.

@DavidZ jerk because he said “aren’t” not “are”

super dumb move on his side because it accomplishes nothing and is a waste of time to read or write an email like that

@loocsieulb Yeah, I can't argue with that

Welp, what's happened happened

It's probably a joking reference to the meme that physicists aren't supposed to be able to do mathematics. Sadly, it's often true.

@dmckee Yes.

Do it.

@Tanuj Hi.

@DawoodibnKareem Funny, it's a running gag here that physicists are often better at actual computations than mathematicians.

@ACuriousMind Really? And where's "here"?

Heidelberg, I guess

But I've heard the sentiment from other Germans as well

@DavidZ Noted , I'll try to handle such situations better , thanks for the valuable advice !

@DanielSank Hey !

I remember when I was studying third year electromagnetism. The professor set an assignment question that was a complete non sequitur. In other words, there were a bunch of equations from which we had to prove another completely unrelated equation. It was entirely nonsense.

After convincing myself that it couldn't be done, I combined all the required equations in a more-or-less random fashion, took the positive square root on one side and the negative square root on the other, then added and multiplied by whatever I needed to, to make the final equality appear true. Got an A for that assignment, and the professor's only comment on that question was "there must be an easier way, Dawood".

LMAO Guys ! All this time and I didn't know you could have Mathjax in the chat !

it helps

I just advanced from the Stone Age to 2018 !

Oh god

Geometrothermodynamics is so awful

You have probability distribution-valued manifolds

that does not sound very crazy, you already have information geometry which is basically a manifold of pdfs

well yes, that is what it's based on

does curved space QFT involve operator valued manifolds?

It does not.

How to produce a standing wave?

step 1 : stand

step 2 : wave

Bahaha

@ACuriousMind Hi there

@Slereah I'm so stealing this :P

where is "property"

Welp, if anyone likes this, here's a shameless request to upvote it

" The gravitational field of a cube was first calculated in 1958"

Also question, does it look a little too much with the A as a tripod?

"Could a moon or satellite, orbit this cubic planet? We notice that there is slightly greater gravitational force of attraction over the corners of the cube, and hence an orbiting satellite would significantly couple with the spin of the cube"

Someone asks the real questions

"I would not recommend emulating the style of Lev and Landau in research papers, unless you can emulate their physics."

L&L=Landau and Lifshitz* :p

Three rods A,B and C having identical shale and size are hinged together at ends to form an equilateral triangle. Rods A and B are made of same material having coefficient of linear thermal expansion k1 while the material of rod C has the coefficient of linear thermal expansion as K2. By how many Kelvin must the system of rods be heated to increase the angle opposite to rod C by 0.01 degrees.

Can someone pls help me in this^^

@Blue can you have a look?

Is this an appropriate promotion ad

he shines on us all

@ACuriousMind if I posted that ad in the thread, would I get in trouble

Praise be the way

motls.blogspot.com/2007/11/exceptionally-simple-theory-of.html

@bolbteppa a good paper

exceptionally so

"A. Garrett Lisi and his 222 close personal friends. He needs 18 more to reproduce the roots of E8 and make his theory complete. Click the picture for more details."

I still don't know whether he really is adding apples and oranges

motls.blogspot.fr/2005/08/common-crackpots-errors.html

also good

Last ridiculous thing

Oh man

I think I know who that guy is

He's the guy 't Hooft talks about

staff.science.uu.nl/~hooft101/gravitating_misconceptions.html

"Crackpots will often do many typical things - which are unusual among scientists - such as to emphasize that they deserve a Nobel prize; offering money for proving or disproving their theories; naming things after themselves."

This vixra stuff is a bit unbelievable

'the virasoro problem is solved'

vixra.org/pdf/1802.0078v4.pdf

I mean, how do people do this

Some of this is hilarious, e.g. vixra.org/pdf/1801.0168v1.pdf but then you get (what seems like) real math in them like the one above

'Paper send in for the fqxi contest... The intention was to give the most accurate answer possible (within the limitations of the format of the contest and my insights at that moment), embedded in a historical background and written in my usual witty style with some extra provocative spice (which I added on purpose). I think it brilliantly succeeded in doing so. Unfortunately, the competent jury members did not deem my efforts worthy of passing the first round.'

I can't even

@JohnRennie John ! Hi :)

@JohnRennie man , I miss you pinging me back with that :-)

@JohnRennie Really miss you , have a great business trip ! :)

Putting the Laplacian in ellipsoidal coordinates the long way instead of using covariant notation is why it took so long, poor customer

Is there such a thing as the L'Hôpital of a function?!

@lılostafa not really, no

@ACuriousMind Someone has created an article on Persian Wikipedia that reads:

@Blue Sorry for disturbing, I just wanted to ask that are there multiple integer type questions too in the exam?

Like questions where multiple integers can be correct...2,4, etc.

That's nonsense, right? :/

@lılostafa It would appear so.

What are f and g supposed to be there? Is y the extremum of f/g and does g approach 0 or infinity at c?

It actually says "Let's assume a function $f$ has a relative extremum..."

Otherwise, that's exactly what is written in that article

(Doesn't say what g is)

Then that first equality only makes sense if $g (c) = 1$, and the second is indeed true by l'Hospital's rule but it's completely unnecessary, so yeah that sounds like nonsense :P

"Integer type questions"?

@ACuriousMind In JEE, per subject, there are generally around 8- 10 "integer type questions". These are numericals whose answer varies between 0 to 9

I don't see how that's a useful distinction, but then again I never claimed to understand anything about JEE :P

@ACuriousMind After some Googling I found that he's a crackpot that uses the (nick)name biowrn to refer to himself, and has created a couple of other theorems with names like Biowrn-Euler theorem on Wikipedia :)

@lılostafa Did you get the info about L' Hospital ?

@Tanuj What info?

@lılostafa I thought you didn't understand it

I think I have a fairly good understanding of it (at least at the level of a standard calculus book)

lol okay , all good then.

@lılostafa Biowrn looks weird as a name (and unpronouncable). Is that a transliteration from Farsi?

@ACuriousMind No I first thought it may be swedish or something

his Instagram account instagram.com/biowrn/?hl=en

Well, if I take the 'w' as a u-like sound, that sounds eerily like my name, which is indeed Scandinavian :P

lol :)

Oh boy

"Introduction to the relativistic string theory" has arrived

@Slereah arrived where? Amazon or libgen? ;)

Amazon

Wouldn't be much point to be excited about libgen

@Slereah unless it costs a couple of hundreds of dollars

Nah it was fairly cheap

Like 30 bucks

Hence why I got it

Nesterenko?

My answer here is based off the appendix of it

Early sections are incredible

Want to read the appendix explaining dual models

The appendix is a tiny bit unclear, the Noether variation has a minus which drove me crazy and is in some old paper of his, need to double check the logic of it

@bolbteppa yeah

I got sidetracked from Nest/Scherk with these videos following GSW a while back (then from these too and 30 more things :( )

youtube.com/playlist?list=PLNMIACtpT9BdBY7o4HWmD4udR-T8ru6Pn

@Slereah some attractive friends there! obv far smarter than einstein :P