3:03 AM
@JohnRennie i was asking yiu a question,
Are you free now
My question since i have no teacher,i am facing problem of mechanices ,which contain problem on constrained
I do not know constrained and how to find its relation
If you can explain this to me by an example

1 hour later…
4:31 AM
@yuvrajsingh Hi Yuvraj. I'm usually around from about 05:00 to 13:00 UK time.

5:23 AM
I am in india
Time difference is around 6 hours
@JohnRennie can i talk to you 2 hour later

@yuvrajsingh I think the UK is 4.5 hours behind India so presumably it's 10:55 in India right now.
Anyhow I'll be around for another four or five hours.

5:42 AM
My question is same that i posted yesterday
@JohnRennie

@yuvrajsingh I can't find where you previously posted the question. Can yu post it again?

I have no teacher @JohnRennie
I study ing constrained
Relationship ,but could not understand can you explain this to me

I'm not sure what that means. Have you got an example question we could look at?

With an example please ,yesterday i have an exam which contain question on it
A block of 5 kg arranged to several pully
@JohnRennie constrained relationship in newronian mechanices

@yuvrajsingh can you post a picture of the question?

5:54 AM

@yuvrajsingh which question?

@JohnRennie
@JohnRennie4
@JohnRennie i am nit wanting the answer i am just asking how constraint relation help to find accelration of various body

6:11 AM
@yuvrajsingh this one?

6:24 AM
@JohnRennie yup
It is the simple example but when there more no of pullys and i need to find constrained relation ,it seems difficult to me

@yuvrajsingh this is ow I would approach it:
Start by calculating the distance $y$ as a function of $x$. This is just simple geometry.
Once you have $y = f(x)$ you can differentiate to get $dy/dx$.
What you're trying to find is $dy/dt$ i.e. the velocity of the block A, and to do this you can use the chain rule:
$$\frac{dy}{dt} = \frac{dy}{dx} \frac{dx}{dt}$$
You've already calculated $dy/dx$, and $dx/dt$ is just the velocity of the loop i.e. 50/3 m/s. Substituting these gives you the expression for $dy/dt$.

6:43 AM
@JohnRennie how to create tension relation with velocity in other constraint problem

1 hour later…
8:02 AM
is it easy to see Alexander horned sphere, is topologically a sphere?
it is gained by: start with a torus — a shape like the surface of a doughnut — and remove a slice. Attach two interlocking smaller tori, one on each side of the gap left by the slice, and repeat the process, slicing each torus and inserting an interlocking pair of smaller tori that you will subsequently slice and insert even smaller tori into. Perform the process infinitely many times.

hello

8:18 AM
hello

2 hours later…
9:54 AM
This chatroom has been so dead recently

2 hours later…
12:02 PM
for the benefit of the star board:

@JohnRennie So should I put surfactant or not?

@DanielSank what did you think of this one?

12:50 PM
Oh man
Apparently there's a paper on the Cauchy problem on discrete non-globally hyperbolic spacetimes with interacting systems!
Better check it out

1:29 PM
One of my biggest pet peeves on this site is when people type "+ve" and "-ve" instead of just typing out "positive" and "negative".
2
"+" isn't "positi" and "-" isn't "negati".

@AaronStevens I just had to google what +ve and -ve mean (I'm sure I've seen them, but probably in poorly written context so I ignore it). If you're going to be that lazy you might as well just leave it at "+" and "-" instead of adding some weird letters that seem like acronyms.

@JMac yep. Exactly. I always edit it to the whole word.

It's strange how such weird conventions manage to get hold

@JMac It makes no sense. I thought maybe people learn it from teachers writing on a board, but that doesn't make sense either.

@AaronStevens I could see like one teacher coming up with it and using it with their students; but I'm surprised that it wasn't something that was quickly questioned and corrected by others.
I've had teachers try to teach nonsense conventions before. My favourite example was my "Grade 11 Advanced Math" teacher. She asked us how we wanted to round, and we agreed as a class with the standard "0.5 rounds up in every case" instead of "0.5 rounds to the nearest even number". For some reason, she concluded that this means that "0.45 rounds up to 1 because 0.45 rounds up to 0.5 which rounds up to 1". I never managed to convince her that it defeated the purpose of rounding.

1:41 PM
@JMac Oh wow that's frustrating

@AaronStevens It was extremely frustrating to me. To the extent that she considered writing me up to administration for being belligerent or something because I kept pushing that issue. I wouldn't drop it until she pushed it that far, because it was just so illogical. I was bringing up graphing calculators and showing that they never did that. I just tried explaining the purpose of rounding; but she wouldn't even budge. It still blows my mind, rounding is so logical.
I got a good laugh out of it one time when I got an extra % because of it though. (countered the % I lost for not rounding that way on a different test)

@JMac You should have gotten a 45% on an assignment and asked why she didn't give you a 100%

@AaronStevens I'm sure the logic of "is 45% closer to 100% or 0%?" came up countless times in our conversation. For some reason it still didn't seem to click.

@AaronStevens hi
Can i ask you a question

@yuvrajsingh Hello
@JMac what even is logic though?

1:55 PM

@yuvrajsingh ok. I'm fine with asking a question, but why not just post it on the main site?

@AaronStevens i feel comfortable here
Basically my question was on the interaction energy
@AaronStevens hiw to describe it

2:55 PM
@AaronStevens Clearly something that we should ignore when doing math. I prefer my numerical analysis to be based off feelings.

@yuvrajsingh Interaction energy?

3:13 PM
@JMac 0.45 really wants to be close to 1 ever since he helped her with her math homework
@yuvrajsingh but what is your question

3:32 PM
@JMac ow

@JohnRennie my teacher told me about electrostatic interaction
@JohnRennie energy

1 hour later…
4:41 PM
@JMac I've always been puzzled at these abbreviations because they seem to imply that '+' and '-' alone mean "positi" and "negati" :P

@ACuriousMind Yeah, it's really strange. + and - in isolation make more intuitive sense to me than +ve and -ve.

I often explicitly mention it in my edit comment when I remove such nonsense.
Something like "Do yourself a favour and never write "+ve" or "-ve" again."

what are they supposed to be shorthand for?
just, the last two letters of positive/negative?
if so that's...pretty silly

4:57 PM
Yeah, that's where the whole mystery of "who came up with that and why didn't it die immediately" comes in. It's really unclear to me why anyone would choose to use that notation.

Personally I like the notation "+ve" and "-ve". Bite me :-)

@JohnRennie But why?

It's shorter than typing "positive" and means the same.

@JMac Cursory googling seems to suggests it's used a lot in handwritten medical records, where writing "positive" and "negative" is too long but especially - alone would be in danger of looking like a smudge

Back in the 1970s (ask your father) this was a standard notation in electronics, and since there were no computers in those days us nerds used to dabble in electronics instead. I picked up the notation then and it has stayed with me.

5:02 PM
@JohnRennie Means the same as long as the person understands the notation. Personally, I would understand "+" to mean positive quicker than I associate "+ve" to mean only positive. It's always evoked a sense of being an abbreviation to me, like +V____ Energy and - V_____ Energy". IDK, it just personally confuses me more than it clears things up.

That's because you're a young whippersnapper!

@JohnRennie Have a minute?

Well at least I understand a bit about the notation. I definitely would suggest people avoid it though. It makes sense in the context of handwritten medical records; but with typed responses it does more harm that just using +/- or positive/negative IMO. Especially since younger people don't really see it and it's not exactly intuitive.

To be honest when I'm typing I would use the full forms because typing is fast so there's no great benefit to abbreviating.
@NovaliumCompany sorry, but I'm rushing to clear up some stuff then I have to go. I'll be around tomorrow.

@JohnRennie Alright, no problem.

5:08 PM
Yeah, that's why it's confusing me I guess. Typing a full word is barely any more effort than the shorthand, and a symbol like +/- doesn't look like a mistaken dash as much. I'll use weird shorthand in my own hand notes if I think it helps, but obviously I wouldn't try to use that notation to explain things to others.

@JMac it was more the sort of thing you'd use when drawing circuit diagrams i.e. you'd write "+ve" and "-ve" by the supply rails.
In that case (a) you were writing it by hand and (b) there often wasn't a lot of space on the diagram.
I bet if you dug out a hobbyist electronics magazine from the 70s you'd see that notation all over the place.

kinda reminds me of the notation I use a lot in my own work recently, where I deal with a bunch of triplets like (3,-1,2)
i've gotten into the habit of writing those as $(3,\overline{1},2)$ when i'm doing scratchwork

@Semiclassical Crystallographers do that too :-)

@JohnRennie I think I've seen that before. I always just automatically associated "+ve" and "-ve" as if the "ve" part was some sort of relic notation for voltage, not the "ve" part of positive and negative.

yeah, i can imagine

5:12 PM
I learned that notation in my first year crystalline solids course in 1980!

nice. i wouldn't be surprised if I've seen it in that context as well and am not remembering it

relic notation - as used by us relics :-)
Miller indices form a notation system in crystallography for planes in crystal (Bravais) lattices. In particular, a family of lattice planes is determined by three integers h, k, and ℓ, the Miller indices. They are written (hkℓ), and denote the family of planes orthogonal to h b 1 + k b 2 + ℓ b 3...

yeah
i vaguely remember that from Kittel

See, I can remember stuff from 39 years ago, so why can't I remember where I left my damn phone :-)

on that note, there was a paper I've used a lot in my own work lately, a stats paper from 1937. setting aside the content of the paper for a moment, the paper starts like this:
"In the case of “correlations”, as indeed is often the case, many discussions arise from confusion between different concepts. For a long time we have seen papers demonstrating and repeating that is necessary to distinguish between the concept of “correlation” that is measured by the “correlation coefficient” r (of Bravais), and the concept of “stochastic dependence” defined in probability theory."
@JohnRennie notice a name in there?

5:17 PM
Auguste Bravais!

yeeeep
apparently his other part in math history is anticipating (at a technical if not conceptual level) the Pearson correlation coefficient

I didn't know he devised correlation coefficients as well as classification of lattices.

Well, it's a bit problematic to assign credit to him (as de finetti is in that intro)
What he was dealing with was properly the bivariate normal distribution for the errors in measuring a given bivariate quantity
By contrast, when you get to correlation/regression more properly, you're looking at one random variable as a function of others

I have to go. See you all tomorrow.

later

5:51 PM
-6

The quantum model for the hydrogen atom is a Hamiltonian dynamical system based on Schrödinger operator $H$. When compared with the physical atom it has important shortcomings. First and foremost the quantum system has no trajectories joining stationary electron configurations at different energy...

oooof

yeah, uh, i'm just going to back away slowly

@Semiclassical =P
I know

6:41 PM
@EmilioPisanty I guess you have a >er tolerance for it than I do

Why the graph of chemical potential vs. temperature is linear despite of the fact that entropy is function of temperature?

7:03 PM
A Heat Engine Made of a Single Ion Spin (with PSE's own @MarkMitchison in the mix!)

@AaronStevens I like "greater-than-er" more than "plus-ve" or "minus-ve".

.less ;-)

@Loong I thought you were trying to correct me, as in "less-than-er". I realize now that I completely missed the point of what you were saying, pun absolutely intended.

Mathematica is dumb at times

@JMac So maybe we should write .< for pointless?

7:18 PM
I have a source which states $K_\nu(z)\sim \dfrac{\Gamma(\nu)}{2(z/2)^\nu}$ for large positive $\nu$ so long as $z\neq 0$
And mathematica agrees with that numerically
But, if I ask it to compute the limit of that ratio as $\nu \to+\infty$ (even with $z=1$, for instance) then it just shrugs
I am disappoint.

What do you want this for?

to explain why the series $\sum_{n=0}^\infty I_n(z)t^n$ is fine but $\sum_{n=0}^\infty K_n(z)t^n$ isn't

I couldn't understand how this transformation works
$$\left[i \gamma^{\mu} \partial_{\mu}-m\right] \psi(x) \rightarrow\left[i \gamma^{\mu}\left(\Lambda^{-1}\right)_{\mu}^{\nu} \partial_{\nu}-m\right] \Lambda_{\frac{1}{2}} \psi\left(\Lambda^{-1} x\right)$$
under this law of transformation
$$\Lambda_{\frac{1}{2}}^{-1} \gamma^{\mu} \Lambda_{\frac{1}{2}}=\Lambda_{\nu}^{\mu} \gamma^{\nu}$$
?

@Semiclassical what criteria define the bar on "explain"?
Presumably you can just lift this from the DLMF, right?

especially the factor $$\Lambda_{1/2}$$, normally it is attached to $\gamma^{\mu}$ only?

7:24 PM
that's what I thought too. But when I try the DLMF one numerically, I don't actually get the limit going to 1 :/
(DLMF has that expansion but with the Stirling approximation for Gamma(nu) )

@Semiclassical dlmf.nist.gov/10.30#E2 ?

that's the $z\to 0$ limit
what I had in mind was dlmf.nist.gov/10.41

interesting that they're so similar. probably an obvious reason for that

@Semiclassical and that's not enough?

7:27 PM
it's probably enough. I'll admit, I was partly trying to track down why that last DLMF equation was seeming to fail in mathematica
numerically
hmm, I'm not reproducing what I was seeing before. so I probably just had a typo
I'm still annoyed at mathematica, though. It seemingly can't do a limit as simple as $$\lim_{\nu\to+\infty}\frac{K_{\nu+1}(z)}{n K_{\nu}(z)} = \frac{2}{z}$$

7:46 PM
@JMac Something that could work is :oscopy

Why
$$\mathcal{L}_{\mathrm{Dirac}}=\overline{\psi}\left(i \gamma^{\mu} \partial_{\mu}-m\right) \psi \neq 0$$

8:02 PM
@EmilioPisanty one thing this makes me curious about: Given the above limit, it should be the case that $\displaystyle \sum_{n=0}^\infty \frac{K_n(z)}{n!}t^n$ should have radius of convergence $|t|<1/z$
@EmilioPisanty also, the context for all of this was my putting together an answer for this question: math.stackexchange.com/q/3329779/137524

1 hour later…
9:25 PM
someone is here?
@Semiclassical Are you here?
I need help in a simple problem
@EmilioPisanty can you help me?

@ABC Please don't ping random users if you just have a question. Just ask your question and if someone can and wants to answer it, they will.
6

Ok, sorry. I'm new here, I don't know rules.

Just saw this question on the math site:
0

When I read physics explanations of "quantization", I am confused, because they talk about particles, momentum, and other specific things. It seems to me that quantum formalism is much more general than this (e.g. in quantum computing there are no "particles"). What is the most general statemen...

9:41 PM
Image of problem: https://ibb.co/6HPQxHJ
My question is: if i need to write equation Module of forces about this mass that rotate in a circle with radius $R$, why that way: $ma_n=mgcos(t)+T$ it isn't correct? My book show this equation $ma_n=mg+T$.

$a_n$ is normal acceleration.
$a_t$ is tangetinal acceleration.

@ABC t = angle here, rather than time?

Yes, it is angle

Ok. Can you link a pic of the source of this? There are cases where what you report from the book would be right

Photo of system is on the top of my message

That’s not a pic of what your book is doing, though

9:53 PM
Oh sorry wait. Now I'm going to explain better the situation
In general, I'll explain what happens. I have this ball of mass $m$ running through this circumference. I need to set the minimum speed to travel around the circumference. The problem is perfectly clear to me I don't have a problem with it.
To find the critical speed I set $T = 0$. Well I say that my book writes that equation because the result it writes is $v = \sqrt {gR}$ while to me $v = \sqrt {gRcos (t)}$. Is it clearer now?

I take it the ball is moving in a vertical circle? The gravitational force wouldn’t matter if it were horizontal

I know that $a_n=v^2/R$
Yes is a vertical circle but $ma_n$ it isn't horizontal force, it's normal force

Sure
Well, I’m not sure I understand how the book is getting its answer (I’m having to visualize) but your answer doesn’t make much sense: if the ball is to keep moving around the circle, then having an angular dependence to the minimum speed doesn’t make sense to me
For one, when t=180 degrees your answer would require v^2 = -g R

I admit that the final result I get is also strange to me. But if you think about it if I'm writing the equation of the normal forces module I have to write like that, don't you?
I mean that it's only a problem of definition of angle?
I'm very confused

I’ll agree to this much: If the tension force is constant, then Newton’s second law does give ma_n = T + mg cos(theta)
Actually, is the mass assumed to move at a uniform speed around the circle?

10:09 PM
I know that mass has initial velocity $v_b$(at the lowest point of the circumference) and there are force of gravity and Tension.

Ah. One thing to note in that case: If the mass successfully moves around the whole circumference, where do you expect it to be moving slowest?

at the highest point

Right.
That said, I’m still not sure what your text is doing: I can maybe see an argument for 2*sqrt(gR) on energy grounds
But I’m not sure I have their assumptions right

My text write:"In order for the ball to describe a circle, at point B higher the speed must be $v_b ^ 2 = gR$"

That’d make sense if B is the top of the circle
But if it’s the bottom I don’t really see what they mean

10:18 PM
yes it is
B is the top of the circle
why are you saying that B is the bottom ?

because you said v_b was the speed at the bottom

In another exercise it's write:"The limit condition to be able to make the turn around the pin along the circular trajectory of the radius R is obtained by imposing that the thread tension is zero at the moment when the mass is on the vertical above the pin: "write initial equation""
oh sorry yes
my error
error

Note that their claim makes sense if B is the top of the circle and v_b is the speed at that moment

v_0**
not v_b

Since then the centripetal acceleration is due entirely to gravity

10:21 PM
Then the problem is: the mass has initial velocity $v_0$ (at the lowest point). Find $v_0$ for the mass to travel around the entire circumference.

Ok. Is sqrt(gR) their answer for v0 or for vb?

$v_b$

Ok. Then what they’re saying is right.

ok perfect, but my problem is here again. Why is my equation false ?
I understood the problem perfectly. I don't just understand why it is right to write their equation, but not mine.

Because they’re talking about what’s going on at the top of the circle, not at an arbitrary point along it

10:25 PM
Perfect!!!
Wooww Now I understand!

And it’s sufficient to consider the top: if you don’t have at least a little speed at the top, you won’t get around

So my equation is correct in the general case?
Should I not also find their case from my equation?

Seems legit. Note, though, that you need to be careful about what your theta means.
Is theta=0 the top or the bottom?

bottom
to my definition

Ok. Then when theta = 0 you’ll have the force of gravity pointing away from the center

10:30 PM
yes

So the radial force towards the center is T-mg cos(theta)

perfect
I understand
All clear!
Thanks you!!!

You have been of great help to me. I thank you for your patience !!

I have a problem when performing a transformation in the spinor representation

\begin{aligned}
\psi \rightarrow \Lambda_{\frac{1}{2}} \psi &= \left(1-\frac{i}{2} \omega_{\rho \sigma} S^{\rho \sigma}\right) \psi \\
&= \left(1-i \left(\omega_{ij} S^{ij}+\omega_{0i} S^{0i}\right)\right)\psi
\end{aligned}

where
$$S^{0 i}=\frac{i}{4}\left[\gamma^{0}, \gamma^{i}\right]=-\frac{i}{2}\left(\begin{array}{cc}{\sigma^{i}} & {0} \\ {0} & {-\sigma^{i}}\end{array}\right)$$
\( S^{i j}=\frac{i}{4}\left[\gamma^{i}, \gamma^{j}\right]=\frac{1}{2} \epsilon^{i j k}\left(\begin{array}{cc}{\sigma^{k}} & {0} \\ {0} & {\sigma^{k}}\end{array}\right) \equiv \f

10:37 PM
I have caculated the transformed left hand Weyl spinor and found it correct, but the plus sign of right hand Weyl spinor in front of $$\beta$$ is fuzzy
$${\psi_{R} \rightarrow\left(1-i \boldsymbol{\theta} \cdot \frac{\sigma}{2}+\boldsymbol{\beta} \cdot \frac{\sigma}{2}\right) \psi_{R}}$$
I got it! it is multiplication of a matrice by a column vector $$\psi_L$$ contrasts $$+\sigma$$ and $$\psi_R$$ contrasts $$-\sigma$$