The h Bar

Slereah

3:00 PM

Yeah typo

0celo7

@b

barrycarter

@Slereah Are you sure? I thought rotational inertia depended on the fact that the point masses can't go flying off in straight lines because they are electrically bonded to each other

@0

3075

xD

barrycarter

Stupid keybord

Obliv

if they were point masses why does it become $r^2$? @slereah

0celo7

3:00 PM

@barrycarter within reason :)

@Obliv prove it

Use the formula for moment of inertia

Obliv

@0celo7 no he's pretty dumb actually. He just recites everything from the txtbook, makes a lot of logical fallacies, lies a lot, and overall clumsy. I think it's because he's fresh.

0celo7

@Obliv he's a prof at a university (community college?)

He's not dumb

Obliv

@0celo7 dumb relative to profs. at any good school.

Slereah

The moment of inertia for a point mass is $mr^2$

For instance for a pendulum

You can consider a solid object as a collection of point masses

skill patrol

Who wrote the textbook? @Obliv

0celo7

3:03 PM

A simple pendulum @Slereah, yeah

barrycarter

@Obliv A freshman? The word 'fresh' has a different meaning.

Obliv

@barrycarter fresh as in new.

barrycarter

THIS IS WRONG: If you rotate a mass in a circle you do m * pi * r^2 work (not sure that helps)

@Obliv Used as a compliment in the US

0celo7

Fresh means frech to me, ask @ACuriousMind for a translation

I can't into English

barrycarter

wet-behind-the-ears amateur unseasoned would be more appropriate

skill patrol

3:05 PM

Rookie

Obliv

@slereah What do you mean by moment of inertia then? Is it simply the rotational analogue to mass in translational motion?

barrycarter

Yes, that sounds about right.

Slereah

Yes.

Obliv

@slereah How come the approach to developing mass in translational motion is different from rotational?

Slereah

$T = I\omega$

Obliv

3:06 PM

is that angular momentum o.O?

barrycarter

I'm torqued about that

Slereah

Torque, moment of inertia and angular speed

barrycarter

I still think there's a fundamental difference between rotational and non-rotational energy/momentum.

Obliv

same.

barrycarter

Thingies don't normally go in circles unless you make them.

Slereah

3:07 PM

Oh wait should be $\dot \omega$

I guess

barrycarter

Yes, change in angular momentum.

skill patrol

planets do

barrycarter

Yes, but that's because something makes them, son.

ACuriousMind

@barrycarter There is - one is the conserved charge associated to translations, the other to rotations.

Obliv

well everything doesn't move in general unless you make them @barrycarter

ACuriousMind

3:09 PM

@Obliv Hello there, Aristoteles!

barrycarter

@Obliv But an object in motion remains in motion (straight line).

skill patrol

That^ is inertia

barrycarter

@ACuriousMind That's what I meant ha ha... you mean the charge between the particles of a solid, right?

Obliv

you knwo what I meant

things at rest won't move unless you make them

barrycarter

Yes, but once you make them move, no force is being applied.

Obliv

3:10 PM

this is why words fail to describe nature :(

barrycarter

For angular momentum there IS a force being applied though we ignore it.

ACuriousMind

@barrycarter No, I mean the Noether charge. By Noether's theorem, there is a conserved quantity associated to every continuous symmetry. Linear momentum is the one associate to the spatial translations being a symmetry, angular momentum the one associated to the rotations.

barrycarter

@ACuriousMind You used a lot of big words I don't understand, sorry.

Obliv

@barrycarter What are you saying? angular velocity will remain constant unless a force acts upon it, no?

Slereah

ACuriousMind

3:11 PM

@barrycarter ummm...without friction, stuff that rotates keeps rotating, e.g. a space station, once in rotation around an axis, keeps rotating.

barrycarter

@ACuriousMind @skillpatrol @Slereah and even Ocelot: are we in agreement that an object's angular momentum remains constant only because some force acts on the object, even if it's only the force that holds a solid together?

ACuriousMind

In that sense, there is no difference between linear and angular momentum

@barrycarter No

0celo7

@ACuriousMind German detected.

ACuriousMind

In the absense of forces, angular momentum is conserved.

barrycarter

@ACuriousMind So you're saying that if the space station disintegrated, its individual particles would remain in rotational motion?

0celo7

3:13 PM

Civilization calls him Aristotle.

Slereah

Harris Turtle

Obliv

h is silent

ACuriousMind

@0celo7 Just because you barbarians butcher Greek and Latin names doesn't mean I have to.

Obliv

wow! shots fired

Slereah

@ACuriousMind How do you pronounce De Broglie

AccidentalFourierTransform

3:14 PM

@0celo7 in Spain we say Aristoteles as well (then again, calling Spain Civilization may be too much...)

barrycarter

I don't.

ACuriousMind

@Slereah With great difficulty

3075

lol

0celo7

@ACuriousMind Doch, sonst machen wir uns lustig über dich

:)

barrycarter

Ich bin ein jelly doughnut.

ACuriousMind

3:14 PM

@barrycarter Wait, now I have confused myself.

barrycarter

@ACuriousMind "no, that could never happen"

0celo7

@barrycarter the sum of their angular momenta is constant

Obliv

@slereah how is rotational mass derived? You just gave me a torque equation. What do I do with that? Torque is $I\alpha$ so how would I begin the derivation?

0celo7

if they "spin" depends on the final configuration

@Obliv $F=ma$

barrycarter

Ocelot, even if that's true, it doesn't mean the object remains rotating.

Obliv

3:16 PM

@slereah wait would I use the definition of torque via cross product instead? $r \times F$

0celo7

@Obliv are you on university internet right now

ACuriousMind

@barrycarter No, I'm not saying that. but the total angular momentum is constant. If the station disintegrates, the particles don't continue their rotation, but they still have, in total, the same angular momentum

Obliv

yes

0celo7

@Obliv ok, read this:

Slereah

Torque is defined easily, so is angular speed

0celo7

3:16 PM

rd.springer.com/book/10.1007/978-1-4757-2063-1

Slereah

Or you can use angular momentum

0celo7

Everything is explained in this wonderful book

Slereah

Then moment of inertia is just $I = \frac{L}{\omega}$

barrycarter

@ACuriousMind OK, but I'm saying: while a piece of mass IS revolving around a center, some force is being exerted that prevents it from going off in a straight line.

Slereah

It's not too hard to derive it for a point mass

ACuriousMind

3:17 PM

@barrycarter Yes, that is true by Newton's laws.

Stuff that doesn't move in straight lines has some sort of force acting on it

barrycarter

@ACuriousMind I was just pointing out that we normally assume our masses are connected in a rigid fashion, and ignore that part.

ACuriousMind

Carry on, then :)

barrycarter

It bugged me for a long time, so I like mentioning it :P

It's also why you can't break relativity with really large disks.

Obliv

@barrycarter but can you say the same thing where a force is being exerted on a object so that it doesn't start rotating?

0celo7

@Obliv actually

barrycarter

3:19 PM

@Obliv Umm, what do you mean? If an object's not rotating, it won't spontaneously start rotating

0celo7

I have a legit recommendation for something to read

barrycarter

@Obliv If you apply equal and opposite torque, sure.

0celo7

damtp.cam.ac.uk/user/tong/dynamics/clas.pdf

Obliv

why would an object need a force to keep it from going linearly then?@barrycarter

0celo7

I think that explains everything

3075

3:19 PM

@0celo7 I was re-reading that right now. xD

and damn you were right he does mention that the addition of a time derivative to the lagrangian leaves it invariant.

skill patrol

Inertia @Obliv

Obliv

@0celo7 what do you mean by everything

0celo7

@3075 I think literally every physics book mentions that at some point

barrycarter

@Obliv You mean, why would you need a force to stop it?

Obliv

@skillpatrol that doesn't.. help.. @barrycarter says that a force exists so that an object who is rotating does not stop-rotating(or start moving linearly instead?) but the same cannot be said if you flip the terms around?

3075

3:21 PM

@Obliv those are basically a good set of lecture notes on mechanics that cover a lot of what you need to know from mechanics.

barrycarter

God, I hope I never said that.

I didn't say the last part about flipping terms.

3075

@Obliv you need calc 3 though.

barrycarter

"a force exists so that an object who is rotating does not stop-rotating(or start moving linearly instead?)"

Oh, OK

Obliv

@barrycarter Oh I get it. You're saying there's a rotational analogue to the concept of inertia?

barrycarter

and I also said "an object moving linearly does not need a force to keep it moving linearly", correct.

Obliv

3:23 PM

@barrycarter I don't think a force must exist for that to happen man.

barrycarter

@Obliv Without force, masses travel in straight lines.

skill patrol

Or stays put

barrycarter

But the force in this case is the rigid force that holds solid things together.

0celo7

@Obliv well

there's also something called the inertia tensor

barrycarter

@skillpatrol I regard a point as a limiting case of a line :)

0celo7

3:24 PM

and the moment of inertia is the trace of it.

barrycarter

@Obliv You might want to ignore what I said earlier. I was being... pedantic.

0celo7

something like that

Obliv

@barrycarter a rigid force that holds solid things together is not the same as what I thought you meant. :p

barrycarter

@Obliv Yes, we normally ignore that force, although we must take it into consideration to avoid relativity paradoxes involving really big sticks or really big disks.

Obliv

@barrycarter OH wtf. did you just mean centripetal acceleration?

barrycarter

3:26 PM

@Obliv No, that's a little different. Imagine if you spun something and it came apart completely... the various pieces would go off in straight lines.

It saddens me that Archimedes was probably sort of wrong about moving the Earth.

Obliv

@barrycarter well how is that different? All of those pieces were undergoing 'centripetal' acceleration. Even if they were not moving in a uniform circle.

skill patrol

31 mins ago, by skill patrol

Newton's first law of inertia. @Obliv says what?

barrycarter

@Obliv Hmmm... to me, centripetal acceleration comes from the center of the orbit. In this case, the acceleration is coming from neighboring particles.

3075

@0celo7 you're right I just looked though some mechanics books and they all mention that.

I missed it somehow.

0celo7

because you skim?

3075

3:28 PM

xD

that's why I fail at life.

Obliv

@skillpatrol newton's first law states that an object's motion does not change unless a net external force is acted upon it.

0celo7

@3075 with that attitude, yes

3075

@0celo7 :'(

Obliv

@skillpatrol I'm just saying the external force that we're both talking about is the centripetal force or whatever you want to call it.

barrycarter

Imagine you have a bunch of M&Ms on a record player.... wait, does anyone know what those are?

Obliv

3:31 PM

yes they're chocolate

barrycarter

OK, good, and a record player?

Obliv

yes a disc rotating about an axis in the center of it

barrycarter

LOL! Best deinfition ever!

@Obliv OK, so M&Ms on a record player. If you start the player, do the M&Ms remain on the player?

Obliv

no

skill patrol

Why?

Obliv

3:32 PM

I KNOW WHY

skill patrol

Think

barrycarter

@Obliv That's all I was saying. Now, if you connect the M&Ms with little sticks and make a giant M&M/wood cookie, then would they stay on?

Obliv

holy shit

barrycarter

An ephiany?

3075

@Obliv fictitious forces dude.

Obliv

3:33 PM

it's not fictitious

barrycarter

@Obliv They're not fictious!

It's the real force of bonds between atoms/molecules.

Obliv

centripetal acceleration is caused by a real force

3075

uh...

but its the centrifugal force that moves the chocolates off the disk.

which is fictitious.

barrycarter

Yes, we've moved on to sticking the M&Ms together with little wooden sticks.

skill patrol

This is fact not fiction

barrycarter

3:35 PM

The sticks are the bonds between the particles, the M&Ms are the molecules making up the rotating object.

All hail @JohnRennie

John Rennie

It's me, large as life and twice as handsome.

skill patrol

HAIL!!

barrycarter

@JohnRennie I have concluded that simultaneity is a bookkeeping measure, and that I can find a better way to do relativity problems.

John Rennie

In the sense that any coordinate system is just a bookkeeping device I agree.

barrycarter

@JohnRennie Sure, but assigning future times to something seems silly.

John Rennie

3:37 PM

This is especially marked in GR, where students get endlessly confused about what the coordinates mean.

barrycarter

@JohnRennie Also, the v * t part of the Lorentz transform is fairly obvious. I think I could modify the transform to take that part as implicit.

John Rennie

@barrycarter time doesn't flow in relativity, it's just a dimension. Assigning a future time is no different to assigning a positive value of x.

barrycarter

@JohnRennie Yes, but that annoys me. I want time to go only forward!

John Rennie

@barrycarter time doesn't go anywhere

barrycarter

I'm starting to think like that guy we don't mention :)

@JohnRennie The arrow of time points forward.

John Rennie

3:39 PM

@barrycarter that's an artefact of the way human brains work. See:

23

Q: What is time, does it flow, and if so what defines its direction?

This is an attempt to gather together the various questions about time that have been asked on this site and provide a single set of hopefully authoritative answers. Specifically we attempt to address issues such as: What do physicists mean by time? How does time flow? Why is there an arrow of ...

The last section in particular.

skill patrol

@barrycarter did you read the link yet?

barrycarter

@skillpatrol The one you sent?

@JohnRennie OK, let me put it this way. 1) in everyday life, do we agree that we can't go backwards in time?

skill patrol

@barrycarter yes

barrycarter

2) In relativity, you can assign things times and then assign them a lower time coordinate later. Agreed?

Agreed on point 2, @skillpatrol or were you just editing to include my name?

Remember, arrow-up does not mean repeat last message :)

skill patrol

A coordinate is just a number.

barrycarter

3:45 PM

@skillpatrol But you agree with what I said, correct?

skill patrol

which part?

barrycarter

I'm THIS close to pulling in my diagram of awesomeness that I've already pulled in twice...

That, in relativity, we can assign something a time and later assign it a lesser time, effectively saying the object's time went backwards for us?

skill patrol

Who is us?

John Rennie

>we can assign something a time and later assign it a lesser time

Eh?

barrycarter

An observer... OK, you asked for it

In the diagram above, Black assigns time 2008 to Earth, correct?

skill patrol

3:48 PM

Which observer in which reference frame?

barrycarter

In the diagram above, Black, in his 0.8 c reference frame.

skill patrol

ok, go on

barrycarter

I have a link to my git thing of awesomeness if you'd like to see the calcs, ok good.

John Rennie

No, you're throwing around the phrase assign time willy nilly. In Black's coordinate system when the Earth is at the spacetime point (0, -6) a clock on Earth that reads +12.5 years when they meet will be reading +8 years.

barrycarter

Now, if Black were to come to a screeching halt, ... ok, wait

OK, but we agree that Black assigns the coordinates x=6 and t=8 to Earth, correct?

(note that I've reverse the directions, so x is towards Earth)

John Rennie

3:51 PM

>but we agree that Black assigns the coordinates x=6 and t=8 to Earth, correct?

No, that's a meaningless statement

Black assigns the coordinates (0,6) to Earth

barrycarter

Hmmm. Would you agree that Red assigns coordinates x = 10 and t = 0 ?

John Rennie

@barrycarter Yes

barrycarter

@JohnRennie And would you agree the Lorentz transform of 0.8 c applies? (I think you actually read my argument earlier and agreed with me, but OK).

John Rennie

Or more precisely, in Red's coordinate system when Red's clock reads zero Red assigns the coordinates (0, 10) to Earth.

Obliv

@0celo7 can I read tong or does it require some math I don't know?

0celo7

3:53 PM

@Obliv I don't know what you do and don't know

Obliv

@0celo7 does it require calc 3 or any abstract/linear algebra?

barrycarter

Actually, let me update. Would you agree that Red assigns coordinates x=10 for ANY value of t?

0celo7

@Obliv Yes

John Rennie

@barrycarter Yes, when Red's clock reads t Red assigns the coordinates (t,10) to Earth

barrycarter

And may I apply the Lorentz transform for 0.8 c to get Black's coordinates?

Obliv

3:55 PM

@0celo7 Do you think learning the math prior to the applications is better than learning the math as you apply it? I'm accustomed to the former so I don't think I can read it.

barrycarter

@Obliv Math is awesome in and of itself. Know math, know peace.

John Rennie

The Lorentz transform will tell you what point in Black's coordinates the point (t,10) maps to.

barrycarter

@JohnRennie OK, good, but it's legit to apply it, right?

John Rennie

Yes

0celo7

@Obliv Just learn calc 3 holy shit

@barrycarter Some math.

barrycarter