The h Bar

fair, sleep well

ill follow suit I think its gone midnight here

dmckee

2:27 AM

Writing a midterm for my modern physics students. Anyone got a good conceptual question on the kinds of rules of thumb that come from early QM?

Something that relies on the HUP, or ad hoceries with the de Broglie wavelength or something?

dmckee

2:57 AM

@SirCumference They have a pretty detailed study list already and this is for a interactive exam component where I ask them to work on problems and explain to me what they are up to.

Even if they have advanced knowledge of one thing they're going to have to answer questions on multiple topics.

And they do know my stack exchange identity.

6:25 AM

Last night dream near the end contains a weird bookshelf where one of the books is written: Classical electromagnetism in variable speed of light. While the book was never read during the course of the dream, looking at it there's a slight translucent overlay to the scene where the following expression is visible: $$c\gamma \frac{dE}{dt}$$

user104729

That's a normal dream.

There are also a couple of pseudophysics, paranormal sounding books (A book called
Mercury Producing Sabuu Particles by Abu (some indonesian spelling name)) and hard copies of journal articles that looks like documents from X files. One of these mentioned about something called the freze Cheryn gene and a couple of printed files showing a group of triplets processing said gene and thus if one of them dies then so will the others. I then tries to video them all to be use for science fiction, but whenever I tried to video the files, the phone switch off, causing me to become frustratd and nee…

12 hours ago, by Phase

http://www.conservapedia.com/Counterexamples_to_Relativity

I probably will blame Phase for giving my subconscious ideas on generating pseudoscience, lol :P

user104729

I am trying to determine the main advantages of the Hamiltonian mechanics formalism, versus the Lagrangian formalism. I think the best reason I have found is as follows:

If a coordinate does not appear in the Hamiltonian, the corresponding momentum is conserved, and we have fewer equations to solve.

If a momentum is conserved in the Lagrangian setting, we still have to solve all of the equations, since the generalised velocities do not disappear.

Is there a better reason? (Other than that it builds into quantum and statistical mechanics)

Q: Why not using Lagrangian, instead of Hamiltonian, in non relativistic QM?

I think I remember someone asking about this in the main site. Let me have a quick search ...

Aha, I was probably remembering this:

40

When we studied classical mechanics on the undergraduate level, on the level of Taylor, we covered Hamiltonian as well as Lagrangian mechanics. Now when we studied QM, on the level of Griffiths, we always dealt with Hamiltonians not Lagrangians. Why is that? I know that QFT and particle physics...

user104729

6:58 AM

Interesting question, nevertheless.

7:34 AM

This is what international diplomacy has become? The US president accuses the president of another country of being short and fat?

Prathyush Poduval

Is he talking bout Kim Jong?

Its just 2 toddlers fighting for each other's candy (nukes)

faketrumptweet.com lol this exist

but it is not smart enough to infuse any arbitrary phrase with trump's tone

7:54 AM

Disappointing ...

8:07 AM

filiph.github.io/markov

Slightly better but not much (and no customisation)

time.com/3966291/donald-trump-insult-generator

Lol, thsi one does does some trump tone

8:28 AM

See, it's not just me!

Q: How do i change my profile picture and display name in physics stack exchange?

It's a perfectly valid question

Physics Meta

8:42 AM

0

How do i change my profile picture and display name in physics stack exchange?.i cant see any link in my profile settings

support profile-page

9:33 AM

holy

physics.se seems better today

right

9:45 AM

"Knowing that I am dreaming, but at the same time not realised I am still dreaming and mistaken this hong kong like place to be the actual hong kong, I then float around the area to explore some outlying islands from the shore and the top of some buildings (which I knew will otherwise be impossible to reach the rooftops of buildings in reality, such as the roof of the ITC)"

"I then tries to video them all to be use for science fiction, but whenever I tried to video the files, the phone switch off"

I have a very strange type of lucidity in my lucid dreams this year

This dream has one of the easiest fly mechanism and in fact, it is the first dream since 4 years ago that I can fly realatively at ease. There's weightlessness when falling from the sky, though whenever I stop doing the flying pose, evidenced by my legs felt heavier than my body as if being stretched

I dreamt of that I picked some coins some rogues left on the street while they were playing aside not noticing. When I crawled away after holding a coin of 50 dollar and several coins of 1 dollar, they found their coins disappearing and hurried up to call on me. I hurried up to flee. Then I waked up by my ear itching.

Pretty typical chase scenes

10:01 AM

whenever I dreamt of being chased, I have never dreamt of being caught.

Last night I dreamed that I woke up and reached out for my spectacles only to find there was a large pile of spectacles on my bedside table, and I couldn't find my spectacles in the pile. What this means I have absolutely no idea.

Anonymous

10:15 AM

Maybe it's an indication that there's a *spectacular* burglar
in your locality. Keep your doors and windows tightly locked tonight. :'P

I often lost my spectacles in reality but have never dreamt of losing them in my impression.

In my chase dreams in the past, I sometimes get caught, and killed many times

(screen fades to black, or a 3rd person avatar representing me fall to the floor, or sometimes 1st person view of me faint and black out)

Anonymous

I didn't have any dream in the past few years (weird)....at least I don't remember any

I almost always dreamt as long as I sleep, even just while dozing accidently for 1 minutes.

Anonymous

Also, I if I ever had dreams those were mostly nightmares

Anonymous

10:21 AM

(Not as extreme as @Secret though)

Anonymous

@CaptainBohemian Strange

In general, I cannot naturally wake up from nightmares if no one wakes me up, thus over time I learn to face the chasers and tries to twist the dream's narrative from within to force a good ending so I can wake up

Q: Calculate a two wheeled robot wheels rotation velocity for different movement

once I accidently dozed just for several minutes in a chair in a computer room, and I waked up finding I made a vivid dream in which my country was in a catalysm and everyone was hurrying to flee and my friends and I had been ferried to a desolate island from my homeland safely.

Qmechanic

1

Consider the following situation. I have a two-wheeled robot like that I have required information: size of a robot, radius of wheels and so on. Also I have an object that the robot should pass around. I know its absolute position and the robots position as well. I need to calculate the w...

classical-mechanics electric-circuits velocity rotation geometry

Off-topic? Close as HW?

My dreams rarely have movie like content when the sleep is dosing like you described above (I usually have movie dreams when full sleep). The dreams I had while dosing, however are often the dreams I am most interested in: They contain a variety of exotic physics, chemistry and mathematics as well scifi materials.

The catch: These dreams are by far the hardest ones to recall, I am still trying to improve my recall on these

10:30 AM

Suppose you have a system like this:

@Qmechanic Looks more like either a robotics or engineering question, more than physics

suggest migrate to engineering type SEs?

Both are connected to a stable wall. If there's mass M on the right sid green bob, then what would be the tension at the left green bob ?

My intuition tells it is M, but the book says it to be 4M/5

I sometimes dream of some physics principles and results, usually during those days I am overwhelmed with studying physics, but I don't believe those principles or results I dream are true.

Anonymous

@Secret Nightmares seem to be an interesting area of research. I wonder how much progress they have made in relating dreams to real life experiences. My dreams are mostly totally unrelated to real life occurrences.

What is the tension on the left side, then ?

10:36 AM

I don't know what are counted as nightmare. Usually if I dream of disasters, I dream of escaping from them safely, even when I was fleeing, I was in panic. I have never dreamt of failing to escape.

Well, I recall reading a NewScientist issue which talked about various groups researching about dreams with fMRI, and they mostly suggest that dreams are assembled from daily experience being rearranged in certain ways with memories.

My dreams can be mostly traced to activities occuring within 3 hours before sleep and within the past 3 days, but sometimes, more older memories many years ago were being used in some highly altered forms

Anybody won't tell ? (Why the hell everybody is talking about dreams rather than physics ?)

@AlexKChen I would have said the tension in the left string is $2Mg$, but obviously not as that doesn't agree with the answer provided.

@JohnRennie No obviously the tension is less than (assume g = 1) or equal to $M$, as the pullyes are masless. My confusion comes from the fact that why it is not equal to $M$ ?

The tension in the right string is $Mg$. Yes?

10:39 AM

I am terrible at pully newtonian mechanics, I need to knew where exactly is the red thing on the right pulley attached in order to figure out how the righ pully pulls the left one

Anonymous

@AlexKChen Umm, because it's interesting? :P

Anonymous

Also, I don't know...but there might be some physicists working on it

@JohnRennie Yes, then ?

@Secret Do you have K&K ? I'm talking about exercise 2.13

Nah, I only have Goldstein

Anonymous

@Secret I partially agree. But often dreams are also totally unrelated and weird (from personal experience and from what I heard from others)

10:40 AM

@AlexKChen So the string exerts a downwards force of $2Mg$ on the right pulley. That means if the pulley is stationary there must be a balancing force of $2Mg$ upwards.

Oh hang on. Are the two masses both $M$? In which case the system isn't in equlibrium?

Here's one of the most entrapping and spiritual one I had: http://secretlabsultraviolet.blogspot.com.au/2017/10/a-groundhog-day-like-dream-10102017.html

Actually, back in late october, I had a lot of dreams which I cannot really trace to any events in reality, and they are highly surreal movie dreams

Anonymous

@Secret Interesting. I'll read it

Anonymous

thanks

JohnRennie: One thing I don't really understood about that problem is how is the string attached at the top of the right pully. Without that I have no idea how will the two mass be connected

Anonymous

Yeah, it looks like an incomplete diagram

Anonymous

10:46 AM

The right pulley will fall down

@JohnRennie No I mean given the bob at right side is M, and the bob at right side N, the exercise askes to determine the tension at right and left side.

OK, I'm giving a more accurate diagramme. Very sorry for the confusion created

[cc: @JohnRennie @Secret Accurate picture ^]

What is the best Q&A forum for physics?

Anonymous

Yahoo

Why?

10:50 AM

Also Can i use latex there

Hmm..., how does the tension get resolved at the junction... (also typo on the left, should be $M_1a_1$)

or what kind of physics questions can i ask on yahoo

Anonymous

@AlexKChen Okay, so take the tension in lower string to be $T$ and upper string as $2T$.

Anonymous

Then write the equation for each block

Anonymous

Solve for accelerations

Anonymous

10:52 AM

Two equations, two unknowns

Anonymous

You're done

Blue

@Lagranian Here's a brilliant question that I saw on yahoo: Is the bartener in Rickroll video Barack Obama ? You can find such thought provoking question in yahoo (Well, troling aside, Physics SE and physicsforum is good, DO NOT use quora)

Does yahoo answer schrondinger wave equation problems?

@AlexKChen However, physicsforum seems not good.

@Blue Why the tension in the upper string will be twice the lowe string ?

10:53 AM

why is physics forum not good?

@CaptainBohemian I've heard something about that.

Anonymous

@AlexKChen Mass of the lower pulley is taken 0, so

Anonymous

Write the force equation for the lower pulley

So, I'm tryna find a site where I can post my all questions.

I have only asked questions in physics forum and quora.

10:54 AM

If I post on physics.se, It'd be off-topic.

But I want to upload my picture like here.

and wanna use latex

Anonymous

@Lagranian Don't expect hw question answers for free. You won't get it anywhere on the internet

@Lagranian You can ask in the problem solving strategies chat room.

What about paid sites?

@Blue the tension at the string just above M_2 is M_2g, and what's the tension in the string just above the pulley holding M_2 ? (No sorry I don't understand how you're getting 2T)

Anonymous

@Lagranian Yeah, plenty of paid sites like Chegg

10:56 AM

To get MathJax see this link

yea, people in physics forum and quora never give me complete answers.

@JohnRennie It seems too great! What kind of questions can I ask on that chat room?

Anonymous

@AlexKChen "tension at the string just above M_2 is M_2g"

Anonymous

It's NOT

Oh I don't want to get complete answers.

I just want to get an equation or hint.

10:57 AM

@Lagranian you can ask anything, though of course there's no guarantee you'll get an answer.

Hello!
I am looking at the following exercise:
Find the energy function for the simple pendulum that moves on a vertical plane at constant gravity field.

Does it hold that E = mgh ?

I'm so confused right now.

my complete answers mean what I really want to know. I never post exercise questions.

@Blue I mean the tension at #1 is clearly M_2*g. What's the tension at #2 ?

10:58 AM

Stack exchange seems greatest I've ever seen.

But don't know physics.se

@MaryStar I would guess that means the potential energy change for a vertical displacement x is mgx.

Anonymous

@AlexKChen No, tension in the lower pulley rope is not $M_2g$

Anonymous

The mass $M_2$ is accelerating

Anonymous

So is $M_1$

Anonymous

The only correct equation is $T_1=2T_2$

11:00 AM

i never knew there are also paid website. Then I would just go to ask professors.

@AlexKChen: you probably ought to take this to the problem solving room

Anonymous

@CaptainBohemian Chegg is a good website

Anonymous

For paid homework :P

So, the energy function is potential energy in respect to x, right? @JohnRennie

lmao

Anonymous

11:00 AM

I don't use it nowadays though

My questions aren't homework. I'm just tryna find the correct equation

I never get a complete answer.

but idk if chegg is gd

I have no homework for long. I have never known homework can be asked from web. All questions I asked are research related.

also I'd be great to ask professors.

How can i?

@MaryStar I don't what the question means by the energy function. If it means an expression for the total energy then it is the kinetic energy plus the potential energy.

Is there any site/forum to ask professors?

11:02 AM

I need to revise how to determine the tension for that portion of the string attached to the wall..., hmm

I mean to ask professors you know in your university.

Oh they are so so so angry

lmao I fear

almost all professors I have asked questions are so glad to answer me. They talked to me for a long time.

Anonymous

Professors are busy people. So you won't find them lurking around in websites. But you can visit them during office hours.

Anonymous

I don't see what's your problem in asking questions here

11:04 AM

o wait, the horizontal components cancel out, leaving behind the vertical ones. which means the tension in that portion has to be whatever the net tension in the vertical components of the two block system

I love solving problems about physics but

sometimes I'm being stuck.

and using the internet for it makes sense.

Ah ok. We have that the potential enery is PE = mgx, where g is the acceleration due to gravity and x the vertical displacement, and the kinetic energy is KE = 1/2mv^2, where v is the speed of the pendulum.
Therefore, the total energy is E = PE + KE = mgx + 1/2mv^2, right? @JohnRennie

Anonymous

@Lagranian Sure, you're welcome to ask your questions in the problem solving room.

Anonymous

Or even here

yea, professors only talk to you a lot when you ask them face to face. They don't talk on web very much.

11:05 AM

@Blue What a friendly! thanks ;)

I was going to join the physics olympiads

If I was enough

@MaryStar yes

Is problem solving room active?

need...more...information...

hmm, where to put that m1g component of the force...

@Secret Come in the PSS room

Great! I have to find also the equations of motion and their general solution.
Do we use here Newton's laws of motion?
If yes, we have that F = m*a and that a = x''(t), so F = m*x''(t), so x''(t) = F/m. m is a constant, right? Is F a function of t? @JohnRennie

11:15 AM

@MaryStar It sounds as if you're learning about simple harmonic motion, as the motion of the pendulum is approximately simple harmonic motion - approximately because the motion is only simple harmonic if the angle of swing is small.

11:40 AM

That the angle of swing is small means that sinθ = θ (approximately equal), or not?
In generally in holds that F=gsinθ, and so we get F=gθ.

Could we apply here also Hooke’s Law? If yes, then we get F = ma, with F=-kx, and so we get ma = -kx, so mx''(t) = -kx(t), so x''(t)+k/mx(t)=0. Is this correct? @JohnRennie

@MaryStar yes, the small angle approximation means $\sin\theta \approx \theta$

And yes your final equation is the general differential equation for simple harmonic motion.

@JohnRennie So, at thie exercise we are looking for the equation x''(t)+k/mx(t)=0 and its solutions, right? @JohnRennie

@MaryStar yes. To solve the equation we basically guess the solution and plug our guess into the differential equation to check it works. Mathematicians call this technique for solving differential equations ansatz, which is just a posh word for guess :-)

Can you guess the solution or do you need a hint?

Ah ok! Thanks! I will think what solution we can guess.

Anonymous

If you don't like guesswork, then read up up the general method of solving second order DE's :P

11:51 AM

@JohnRennie mumbles something pedantic about you don't need to guess it

@BalarkaSen I don't know why you mathematicians are so reluctant to admit it's all smoke, mirrors and guesswork :-)

@Blue You can reduce it down to solving a first order system of linear ODE's

And then solve it

Anonymous

Actually if you know how to integrate $\frac{1}{\sqrt{2E/m-k/m x^2}}$, then also it's done

Anonymous

@BalarkaSen Yeah, I was going to say exactly that

Anonymous

Use integration

Anonymous

11:55 AM

But then deriving the integrals from scratch is also a pain

Well, no, you don't need to use integration.

Anonymous

@BalarkaSen Maybe you're talking about some other method

Anonymous

The one I know uses standard integration

@JohnRennie Sometimes I feel like it's true that mathematics is an inherently naive subject because truths are absolute in that world.

But I don't go around saying that publicly

:P

Anonymous

I was talking about this: en.wikibooks.org/wiki/Ordinary_Differential_Equations/…

11:58 AM

@BalarkaSen your towers are made of purer/whiter marble than ours. But that's OK - we aren't envious - honestly! :-)

Anonymous

Well, mathematicians do all the hard work for us. We should be rather happy. :P

@Blue Say you have $y'' = y$. Write $u = y$ and $v = y'$ to get the 1st order system $u = v', v = u'$. Then let $X = (u, v)^\sf{T}$ be a column vector. We can write the system as $X' = AX$ where $A$ is the matrix [0, 1; 1, 0]

Anonymous

@BalarkaSen Oh, converting it to a system of first order ODE

Anonymous

Actually a single ODE

Anonymous

Due to the property of the equation

Anonymous

12:02 PM

I had seen it somewhere, it's nice

Right, a matrix ODE. Now use that the general solution is $X(t) = e^{tA}(p, q)^\sf{T}$ for some constants $p, q$

Anonymous

The main trick is $u = v', v = u'$

Anonymous

Yup, I remember :)

You'd need to write down explicitly what e^[0, t; t, 0] is, which I leave as an exercise to the reader

Anonymous

@BalarkaSen lel

12:03 PM

I can't type today

Anonymous

You'll be a good author

Anonymous

I am learning about Countour Integrals today. Will ask you if I get stuck :P

@BalarkaSen There's something in there about maths/mathematicians that occasionally makes me a bit twitchy - sometimes maths seems to affect the viewpoint of mathematicians outside of doing maths to the extent that I just want to scream "But the real world isn't like that!" at them

fahd

Is therevpersonal chatting in this stack exchange?

@Blue For sure!

@JohnRennie Hah.

12:06 PM

@fahd personal chatting?

fahd

Yes

@Blue And if you come across any good resources on Riemann surfaces, would you be kind enough to tell me about them?

fahd

Did any one found vishualisable meaning of complex integration

Anonymous

@Mithrandir24601 I'm sure @BalarkaSen can suggest you a good book. :) I don't think I'll come across Riemann surfaces in complex analysis :P There's an MOOC here if you like: nptel.ac.in/courses/111106044 (I don't know how it is)

@Mithrandir24601 It is true without a doubt that the complexity of the physical world is tenfold the complexity of the concrete logical world of mathematics. But I think what amazes me personally is even in this "fake, made-up" world, there are thousands of countless fallacies. Do you know hyperbolic geometry, or the story of how it was discovered?

12:10 PM

@Blue Someone on here did give me a name of a textbook with a relevant chapter. It was a good start, but nowhere near enough :P

And thanks for the link!

Yeah I can't suggest a good book for Mithrandir's purposes. Hm, I saw a set of notes somewhere, let me look up

@BalarkaSen I definitely don't the story of how it was discovered...

This might come in handy: math.berkeley.edu/~teleman/math/Riemann.pdf

@Mithrandir24601 So, one of the stepping stones in mathematics is Euclid's "Elements", right? Euclid constructed a completely axiomatic, synthetic setup in which to do geometry, where every other proposition is derived from the fundamental axioms and the previous propositions iteratively and inductively, in a complete, total fashion.

But there was a gap in the game.

Namely, Euclid's fifth postulate (/parallel postulate). He couldn't prove it from his first four postulates.

Anonymous

@Mithrandir24601 You might find the Indian accent weird but the lectures seem to be extensive. They can be sometimes too slow, so you can watch them at 2x. 45 lectures on Riemman surfaces should be enough for your purpose. :)

Anonymous

Also, the references section suggests these books:

Anonymous

12:16 PM

H. M. Farkas, I. Kra: Riemann Surfaces, Graduate Texts in Mathematics 71, Springer-Verlag, 1980
R. Miranda: Algebraic Curves and Riemann Surfaces, Graduate Studies in Mathematics vol.5, American Mathematical Society, 1995
O. Forster: Lectures on Riemann Surfaces, Graduate Texts in Mathematics 81 / Springer-Verlag, 1981
R. Hartshorne: Algebraic Geometry, Graduate Texts in Mathematics 52, Springer-Verlag,
E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris: Geometry of Algebraic Curves - I, Grundlehren der mat.Wissen.267, Springer-Verlag, 1985

Anonymous

I hope you can get them on libgen, lol

About 2000 years later Gauss gave a proof that Euclid's fifth axiom CAN NOT be proved from the first four. The proof is a great exercise in logical reasoning: He constructed hyperbolic geometry, where the Euclid's first four axioms are true, but the fifth is false.

@Blue I do know some Indians in real life, y'know :P

Since there is a model of geometry where the first four axioms are true, but the fifth is false, this means that in Euclidean geometry the fifth cannot be proven from the first four.

@BalarkaSen OK

@BalarkaSen Sure

@Blue Excellent! The library'll have them anyway, thanks :)

12:20 PM

But it took 2000 years to realize that to prove a certain thing is unprovable in an axiomatic system you'd need to construct an entirely different axiomatic system based on the same axioms where the same statement is false. I feel this is a great example of the various viewpoints in mathematics.

Also it says something about how the axioms are not the end in all in math.

@BalarkaSen I see at least some of the problem :/ And they're constantly arguing over this axiom of choice... To be honest, I can't really care that much. I mean, how do you argue over something that's so fundamental?

After all, hyperbolic geometry is not constructed axiomatically; it's constructed using working out the equations in upper half plane using the metric $(dx^2 + dy^2)/y^2$. Gauss once said his motivation was physical based on measurement of triangles on mountains and showing the total angle of the triangle becomes less than 180

@Mithrandir24601 It's interesting because if you assume axiom of choice (something super obvious) it implies various other things which are super counterintuitive

Banach-Tarski is a good example. That's a corollary of AoC

I can see why you'd think it's a little droll, but you can't deny it's weird

Anonymous

@BalarkaSen Can you identify whether $e^{-z^2}$ is analytic without applying C-R equations? It's troublesome to check C-R equations always while doing complex integration. I suppose, no because certain things like $\bar{z}$ (although simple looking) is not analytic.

@Blue Well, that has a singularity at $z = 0$.

(What kind of singularity?)

Anonymous

Does it? $\frac{1}{e^{z^2}}$ at $z=0$ is $1/e^{0}=1$

12:30 PM

@Blue Careful! $e^{-x^2}$ has no singularity at $x = 0$ as a real function

But, consider approaching $z \to 0$ along the imaginary line

What happens to $e^{-z^2}$ then?

Anonymous

Take $z=ix$ and put $x\to 0$. We get $e^{x^2}$. At $x=0$, I see $e^{0}$.

Anonymous

i.e. equivalent to approaching along imaginary line

Ugh. Forget what I said. I misread it as $e^{-1/z^2}$

Yes, that is analytic.

Anonymous

@BalarkaSen Yes, but how did you say that without checking C-R equations?

Anonymous

That's what I wanted to know

Q: Proof composition of analytic functions is analytic

12:34 PM

Composition of analytic functions is analytic.

It's $f(g(z))$ where $f(z) = e^z$ and $g(z) = -z^2$.

Anonymous

@BalarkaSen Ooooo, awesome

Anonymous

2

Title says it all I looked for a proof on this site but couldn't find one. Prove if $f$ is analytic on $D$ and $g$ is analytic on $\Omega$ containing the range of $f$ show $g(f(z)$ is analytic. The statement seems obvious but I can't seem to be able to prove it.

complex-analysis

Anonymous

That makes it much easier

What is a true statement is that $e^{-z^2}$ has a singularity "at $z = \infty$"

Anonymous

@BalarkaSen Yes, that's true

12:37 PM

In fact it's an essential singularity

Anonymous

Right

What is an analytic function? Just one that's differentiable?

for all of its domain?

Complex differentiable, yes

Anonymous

@Phase For a certain "region" would be better description. 1/z is analytic for all points other than z=0

Anonymous

Some functions are analytic over certain regions which are in domain, not all regions in its domain

12:46 PM

analysis sounds cool

Anonymous

It is hard tbh :P

Anonymous

At some point of my life I would like to learn analysis rigorously.

The radius of earth is $6.371$ km. The earth is rotating around itself in $24$ hours. Then, calcuate the radial acceleration of an object that is in equador.

Okay, so we know that

$a_r = \frac {v^2}{r}$

and the radian is given

by the way $r = 6.371$

I mean

How do we find the velocity $v$ then?