@naturallyInconsistent I was thinking about this energy thing in macroscopic terms, and it was clear to me no matter what I do, this macroscopic formula does not contain the interaction energies at the molecular level. Is there some procedure that somehow averages, say, the energy density or something like that?

@nickbros123 I'm not at all sure. Maybe one of the quantum averaging methods would do that, but I am very seriously of the thinking that nobody is worried about that when we cannot even properly define the averaging process. Maybe you can solve this for us?

@naturallyInconsistent I don't know, but i know one thing, I hate materials physics. Causes massive indigestion issues

The issue im having right now is the ambiguity of the energy formula $\frac{1}{2} \epsilon \iiint E^2 d\tau $ where $E$ is the macroscopic averaged electric field.

One thing I know is, the Lorenz force law somehow holds when we plug in the macroscopic variables too;

my interpretation of this force law is that larger than molecule (ideally many 1000 molecules) sized charges particles, in presence of an external electric field E which is averaged, experiences a force $qE$; I don't even know to what extent this holds but, from here- My interpretation of the energy formula comes from- me bringing these microscopically large "blobs" from infinity and placing them in their stipulated spot

If my interpretation is correct, which I hope it's not, we are losing the information of the interaction energies of the molecular interactions happening within these "blobs"

I also think we must be losing some energy when we do this averaging process. It is very annoying because the Lorentz local E field is actually NOT the E field that appears in E^2 energy calculation, because it is NOT a physically available E field at all. It is the E field felt by a point dipole located at the observation centre point that has the self-field subtracted off.

The real microscopic E field is wildly fluctuating up and down inside a unit cell, we are all in agreement with that. When you integrate microscopic E^2 over the unit cell, it needs to be way more than the averaged, smoothed E^2 integration.

@naturallyInconsistent yes, even in some simple symmetry cases true local field has significant difference from averaged out field, near an atom let's say. But people nonetheless use the formula for calculations, right? Are they ignoring any errors that could come from ignoring the lost energy, or somehow it's shown that he lost energy is negligible compared to the total?

In my blob by blob kind of picture, it is clear that we get an approximate tally for the interactions of molecules of one blob, with molecules of all other blobs, so the energy lost is interactions within a blob, for each and every blob, which I suppose is of the order 10^20 ish?

I have a gut feeling, motivated by no physical insight, that one can neglect these lost energies in the case of non dielectric/ non polarisable media, but when one considers polarisable media, he can no longer neglect it

Hello Everyone..

Hi @nickbros123

I want to understand how perpendicular force change direction of an object in small interval of time.

@Slereah @Relativisticcucumber Wittgenstein's view of language is the correct one ;)

@naturallyInconsistent I need to your help in understanding direction change phenomenon. When your time permit.

@123 why are you randomly tagging me? And Ive been avoiding you as much as I can. I don't have the kind of patience with your kind of questions.

@SillyGoose Language can easily encode nonsense, so obviously Wittgenstein is HONK HONK

@naturallyInconsistent Ooooh no. I am naive. When i become tired by searching, thinking, reading, writing and found no solution. Then i asked here.

@123 Ask. If someone likes it, they will reply.

h o n k

If you have knowledge you have to help others and sometime there are students that are like me.

@123 Not at all. Nobody owes us an answer. I help a lot of people; your kind of questioning makes my blood pressure spike and so I am not at all inclined to help you.

@naturallyInconsistent Ooooh no.

I teach as a profession and like it.

When I am not paid to deal with students that I don't like, I can choose not to teach at all.

But following definition by not understanding it deep is similar to accept everything with closing eyes.

@123 that is your assumption. Do not assume that other people are not understanding things deeply

at least without evidence

So as i said if you have knowledge you to share with others.

My questions are always valid.

@123 They are most often not.

I never asked irrelevant questions.

Also, I just answered on the site the thing about direction changing. I am so not surprised that the person who received the answer did not do anything about it.

Pls share the link.

I have read many threads. They just saying if force perpendicular then direction change. Nothing else. My question is how it is happening.

@naturallyInconsistent Thanks. Let me read

@naturallyInconsistent This answer mostly related to math. I understand the math . I want to know what happened physically at small interval of time using velocity and centripetal acceleration vector?

Mathematically it's there @123, if u want a physical picture grab a high fps camera, tie a rock to a thread and spin it

@123 I was particularly NOT interested in the maths when I wrote that. You draw it out, and you will understand.

@naturallyInconsistent I asked one of my institute professors who works in statistics and fluid mech about this average energy thing and he doesn't seem to think the question is important. And he has hardly read material on it. It surprised me. I got the same answer from another prof who was a string theorist. Though, They were all in agreement in saying that the building up of macro, from microscopic considerations is a very difficult one.

@naturallyInconsistent Yes i am doing this. Let me sharing you video simulation

But I don't know, I have a feeling one can actually, through some or the other averaging, show that the unaccounted energy is quite negligible, at the very least when one doesn't have polarisable material

The funny thing is I would've totally believed in the definition P= dipole moment per unit volume, child's model of polarisation they show usually, working in that naive pic but when I went into this macroscopic rabbit hole, nothing is the same anymore. Sometimes I wish I didn't learn this xD

@nickbros123 I don't think so. I don't think there is a way for us to pick smoothed stuff to agree with fluctuating stuff, because the squaring causes a huge discrepancy. If you said that the mean values agree, then fluctations doesn't matter. root mean square is sensitive to fluctuations.

@nickbros123 I was very happy to have learnt the Lorentzian averaging, because it seemed to be important and good, but yes, we have been mentally raped by learning macroscopic fields. It is after a lot of learning that I really think we should just use microscopic fields and never deal with macroscopic shit.

Note that the various averaging processes are empirically amazingly successful. It is just that they seem to be mathematically nonsense.

I got some motivation from this answer physics.stackexchange.com/a/765066/346785

Not entirely satisfied by that answer, for this seems too ideal a picture

But it was a good place for me to start thinking

@naturallyInconsistent imgur.com/nirmNOE Pls see link video.

In this i have made tangent velocity vector at the origin. It clearly shows it preserves magnitude but continuously changing x and y component of velocity. When one component is decreasing another is increasing by the amount so magnitude remain the same.

Pls look at another video example imgur.com/77Pz3AX this link.

From C frame of reference initially B is at rest when they are moving same direction and with same velocity. When force is applied for a moment to the B. Then from C frame of reference B is moving with constant velocity and moving toward C.

But from A frame of reference initially B & C moving in a straight line in same direction. When perpendicular force is applied for a moment to B. Then B changes direction and gain y-component of velocity. But B maintain x-component of velocity. It means resultant vector $V$ after force is greater than before force is applied. My question is that perpendicular force should preserve magnitude. But in this example magnitude increases.

i.imgur.com/bK1lVuB.png In this picture another example from projectile motion. Where force perpendicular to direction of motion at maximum height.

@nickbros123 yes, too ideal. We know from the difficulty of evaluating the Madelung constant (i.e. do the usual spheres sum and you will definitely get a divergence) that the electrostatic energy is difficult to compute!

For a moment this should only change direction by the rule. But it increases y-component of velocity and maintaining x-component velocity.

@123 this is tolerably correct

@123 That you are asking this means that you totally failed to understand what Amit was telling you yesterday.

Yes i understand Amit discussion. In example where A,B,C objects force has larger $\Delta{t}$.

What i think. Let say we have very short $\Delta{t} = t_2 - t_1$ when particle is at t_1 in my all examples where force is perpendicular to the direction of motion. Now at this moment nature will not decide whether nature increase speed or direction change preserve magnitude. It will be decided at $t_2$ after nature watches what is the direction of force at $t_2$. If at $t_2$ direction of force still perpendicular then nature rotate the vector by $V_x$ decreasing and $V_y$ increasing.

If at $t_2$ force remains the previous direction so it increase speed. My all point is that. Nature decide whether preserve velocity or not depend on looking what is the direction force at $t_2$ not at $t_1$.

Am i correct or totally wrong.

I have to parse your English because it is not correctly English enough to be easy to understand.

@naturallyInconsistent I know my English is not good enough.

And then I have to think if your question is even valid or not.

And stop tagging me when I am already replying to you right now

Okay

In my opinion at first moment $t_1$ when force is perpendicular to the direction of motion. Nature will not decide whether preserve magnitude of velocity or increase velocity. Nature will decide this at $t_2$ by looking what is the direction of force now.

If at $t_2$ direction of force still perpendicular then nature maintain velocity by decreasing $V_x$ and increasing $V_y$.

But if at $t_2$ direction of force is same as previous like $F_y$ then nature increase $V_y$ also maintain $V_x$ remain the same. Which causes increase in speed.

It is my point of view. Hopefully i am clear now in my view. What you think am i correct or wrong.

Nature decides changing only direction or increase speed at $t_2$. Where $\Delta{t} = t_2 - t_1$ is very small $\Delta{t} \rightarrow 0$

nature doesn't "decide" anything

Hello @ACuriousMind pls clear me. Where i am lacking in understanding the phenomenon.

the problem is that you seem to insist on thinking about this as isolated instants in which "nature decides", but time is continuous and nature doesn't "decide" anything

@ACuriousMind Aaah Okay.. We take only two examples. Circular motion and projectile motion at maximum height at $t=0$.

At any instant of time, $F=ma$ just says that the force is the derivative of velocity. What happens in nature are solutions to this differential equation.

In particular for perpendicular forces, when the force is always perpendicular, we conclude the magnitude of velocity won't change over the entire motion

but when it's only perpendicular in one instant, as in projectile motion, all we can say is that that instant will be some sort of "turning point" for the motion, nothing else

@ACuriousMind Ooooh.. Your answers are mostly satisfactory.

I seems to me we take it as natural phenomenon. We can not understand it at microscopic level.

what do you mean? it doesn't matter how large the object that's moving here is

short time interval level.

Means we can not understand the phenomenon bit by bit. Only gross mechanics is known.

No, we know the phenomena even at short times.

If you drew out the thing I was talking about for uniform circular motion, you should be able to understand how perpendicular forces cause uniform circular motion.

@123 you can think about physics at arbitrarily short times

At the instant at the top of the motion, there is a best fitting circle that will be tangent to the motion at the top, and also curving in the correct form at the top.

what's wrong is your attempt to understand it as a sequence of discrete instants; time is continuous

@naturallyInconsistent Ookay. Let me simulate your answer

what we do need to assume, however, is that the forces are finite.

In the case of the ABC thingy, what you have is an infinite force over an instant, giving a finite impulse so the velocity suddenly jumped in a bad way.

@ACuriousMind I am taking time as continuous . But for small interval.

@naturallyInconsistent Aaaah.. Ookay. Now i understand what happened at ABC exmaple.

@123 your insistence on simulations suggests to me otherwise

it's actually non-trivial to write simulations/numerical approximations correctly so that they preserve the physics we care about

e.g. in many cases it's easy to write a discrete version of the equations of motion that does not conserve energy, even if the continuous version did

@ACuriousMind You said at maximum height of projectile it consider as turning point. But what if this turning point turn into the force suddenly centripetal. It means later time if force become perpendicular then it become circular.

@ACuriousMind Aaaah Ookay.

@123 I have no idea what this means

The gravitational force in projectile motion always points down, it can't "turn centripetal" just because it's perpendicular to the motion at some point

@123 There is only one specific time, namely the max height point, at which the constant downward force can be considered as centripetal. Because of this, there is a best fitting circle that can be superposed onto the actual trajectory that you can work it out. Any time else, it is not at all like that.

@123 Correct, and you see that it will only fit being a circle right there and nowhere else.

If you want to find the best fitting circles elsewhere in the trajectory, you have to work it out point by point, using the perpendicular part of acceleration (which might not exist) at the point you are checking out, working backwards to find the radius of curvature.

@ACuriousMind I know gravitational force always points down. Let's consider suddenly we removed gravitational force. and force become centripetal the this turning point become circular motion. This is what i emphasizing to think. Nature decide later moment $t_2$ what is the direction of force.

These are really well-known stuff; if you bothered to study some of the mathematics involved, you would not have had to ask us.

@123 again, I have no idea what "force become centripetal" means

if we assume magic happens then sure, magic happens, but that's not physics

@123 If you turned off gravitational force, then there will not be centripetal along with it. Some physical force must supply the centripetal force. It does not exist otherwise.

@ACuriousMind Let simulate the situation in mind as an example.

@123 And this is particularly invalid.

For example i provided suddenly centripetal force and turned off gravity.

@123 Again, such magic is invalid.

@naturallyInconsistent imgur.com/366jufo pls see the link. I think this is you were talking about. tangential and normal component of acceleration. Radius of curvature and tangential component of velocity, normal component of velocity has zero magnitude.

@123 This simulation is correct. You can see the radius of curvature and the osculating circle makes very good approximation of the trajectory everywhere along the trajectory as long as you redraw it for every point you look at. The perpendicular part of acceleration rotates the existing velocity, and the tangential part of acceleration changes the velocity vector's length. There is nothing much to be confused about once you understand what the maths is doing.

@naturallyInconsistent I understand this. You also notified me this point thanks.

It is rather silly that you say you want to understand this thing physically, but you are asking maths questions rather than physics questions. The physics questions should be answered by drawing the vectors and seeing how they converge to the correct behaviour in the short time limit. It is a standard thing to consider.

In the case of projectile there are two ways of thinking or looking at it. One as cartesian with uniform acceleration along y-axis. Another is tangential-normal, where tangential acceleration is variable which changes speed at every point and normal acceleration which changes direction different at different point. Because both components of acceleration are variable.

What i plotted simulation. In projectile motion i have fixed my frame of reference along x-axis and i am moving with the object along x-axis. So this way projectile motion looks me simple motion under gravity 1D like object goes up and down. When i take frame of reference along y-axis and me moving with object along y-axis it looks motion in 1D with constant velocity.

@123 This is tolerably correct

@123 This does not even begin to make sense.

How to set frame of reference to see only tangential velocity only and then normal velocity only. I don't know what is my frame of reference

I mean...yes, if you imagine sitting on an object that moves (the frame comoving with the projective) and there are no other objects in the universe, then you'll think you're moving with constant velocity 0 :P

but in the real world you can detect that you're in an accelerated frame by looking at the resulting fictitious forces on the other objects you can see

And you can feel the accelerations on your body.

@ACuriousMind I made it simulation. I can share with you.

you keep saying "simulation"

I don't know what is my frame of reference, where i set it. To see only tangential displacement and then normal displacement only.

what exactly are you doing when you're "simulating" things

just using some tool to determine and draw the forces/velocities at each point is not what I (or anyone else) would call a "simulation"

@ACuriousMind He seems to be numerically or analytically integrating, and plotting the solutions on a computer, making videos with them. If you click the links to imgur, the videos are rather neat.

@ACuriousMind Oookay. It means simulation have errors. not a real picture

@naturallyInconsistent yeah, my question is whether we're looking at some numerical solver or whether this is just something that plugs numbers into the analytical solution for projectile motion

I'd not call the latter a "simulation" in the usual sense

@123 What? I didn't say your simulations have errors, I just asked you what exactly you're doing to produce them

@ACuriousMind you mean what website or software i am using?

That would be part of the answer, yes :P

I am simulating this with javascipt. creating sliders to simulate objects. applying formulation and creating different objects using valid equation.

Then i convert this simulation into video.

and how are you producing the solution to the equations of motion?

is this a numerical solver or do you just have the analytic solution for the parabola of projectile motion and you're putting different times into that solution to produce the plot?

First i wrote every formula or everything on page then i apply it in calculation. using numerical solver.

@ACuriousMind you can pry mah anal-ytic from mah cold dead hands

Mainly because the simulations we sometimes have to deal with are so difficult that we have to have some patchwork of analytic and numerical work. For example, some computations will only work well if we have the leading asymptotic behaviour done correctly, and those are still considered simulation results, even if they are exact solutions to some exact subproblems.

These are my calculations for a projectile in cartesian which is easy. and then for tangential-normal coordinates then for polar coordinate. All are written here.

Yes, we can see that.

Pls help me. What is the frame of reference when looking the projectile motion from tangential perpespective only and then normal frame only.

@123 There is no normal frame...

And while you can write down the acceleration in the tangential perspective, there is no way to work out what it would be doing, because when you are in that frame, the acceleration is going to be acting on everything else. ACM already told you this earlier.

When I simulate to move along x-axis I can the behavior of y-axis motion and vice versa. Same I wanted to see from other coordinate system.

@123 don't move ur coordinate system with the body, if you want to calculate anything about the trajectory. You can always simply decompose ur vectors in any orthogonal system u want, but I don't think it'll be useful, it is useful when you have rigid body constraints, like a block on a wedge type of problems

@nickbros123 okay. But if I want to simulate and see how trajectory look when I move only tangentially and look what happened in normal

Fitting frame of reference along x or y axis is very easy to think. But I can't think for polar and tangential-normal system

I don't know the first thing about simulations, but if you want to "draw" the tangential n normal reference frame, simply write the trajectory in parametric form, find the slope at the desired point, draw a line with that slope at that point, and another one with the inverse slope. I don't know how to say this in computer language

Here your parameter comes out to be time

@nickbros123 Thanks a lot for sharing helpful information. I have work for 3 to 4 hour. As I will free I will simulate it.

Thanks a lot everyone to help me.

@nickbros123 On this point, he has successfully done it, so that you do not have to teach him how to do it. YAY!

Oh, he actually has! Nice!

I need to learn how to do cool stuff on a computer. If I'm able to plot the ugly charge distribution functions that I get in calculations, it's over for everyone

what is the condition on dimension of the matrix x

i mean is X a column vector or any general matrix?

@nickbros123 There are nice tutorials for basic stuff. What languages are you thinking about learning? What end goals are you looking forward to doing? Would LaTeX be a good thing to learn?

I guess i ll start with python? Idk my end goal really, i just know to be a physicist one needs some computer knowledge. It also wouldn't hurt if I learn how to solve craze integrals on the computer, will save me lot of time

once you get good with one programming language it's much easier to learn others

for integrals or other calculations, you probably rather want Mathematica or Matlab than a general purpose programming language

but python's a good starting point for physics

@ACuriousMind Oh no Matlab. That's a horribly ugly language.

@naturallyInconsistent I mean, I agree, but that doesn't change that it's useful :P

Python is good. Mathematica is much better if you are going to need to do integrals, especially symbolically.

even mathematica ain't the best lol

If I was allowed to follow my aesthetics in programming, everything I wrote would either be Haskell or Rust :P

But do note that Python is so user friendly that it makes it likely that you would develop bad habits

granted it's a matter of what exactly @nickbros123 wants to do

@ACuriousMind I'm having a lot of fun with Rust right now.

Haskell's fun too.

if he's thinking of using programming for scientific research, python is a very good starting point

I mean, depends on the research!

true

I have used GNUplot for plotting; it is very nice for rough plotting that you just want done and you don't care about beauty

Whereas if I want to publish, I'm gonna plot in LaTeX TikZ

Fortran is supremely nice to use and good.

@SirCumference I don't know really, for the stuff I'm learning now in physics as a 1st yr student, pen n paper are more than enough.

But later on, I suppose one needs to use a computer to do calculations

@naturallyInconsistent "It would be nice to have a Rust-style enum here" is something I think in my (non-Rust) job almost daily

@nickbros123 pls tell me the function. I will plot a graph for you

@nickbros123 Ask your seniors what programming language is being taught as part of the mandatory curriculum, and learn that in advance.

@nickbros123 reason I recommended python is because it's generally useful for a lot of different things, including calculations

@ACuriousMind Exactly! So nice.

but at the end of the day once you learn one language, you have the mindset to learn others far more quickly

I think distribution function has solution which exponential decay on both sides

I used to be an old skool C bro. It was so natural to meow. But it is very silly to insist on it now.

@nickbros123 It's not so much for "calculations" - most of the programming I did at uni was a) to control devices in the lab or b) in courses explicitly focused on numerical simulation/computation

Modern idiomatic C++ is also really nice to play with.

granted, you can do a lot more when you learn to program than just performing computations. e.g. you could create computer applications or change parts of a website for personal use

it's generally just a very handy thing to know

@naturallyInconsistent it's python in my place. We have a 1 credit course next semester on it

you could get through the entire bachelor's and master's degree without learning how to program if you had a lab partner who could for the few mandatory labs :P

@nickbros123 Then yes, please learn that.

@nickbros123 I took a 1 credit course in python and found it very helpful

@SirCumference I know some very very basic stuff to do on python, like taking ur date of birth and telling on which day you were born hehe

@naturallyInconsistent With C/C++ I'm mostly frustrated by the absence of a standardized package/build system

manually mucking around with header files and make files is so much not fun

I would suggest to learn how to 1) plot functions of 1 variable 2) plot one vector of numerical data 3) basic linear regression 4) numerically integrate 5) numerically differentiate.

@ACuriousMind Rust made myow life soooooo much better in this.

@naturallyInconsistent well, it's good to get used to the language as a whole before that

@ACuriousMind I have a course on numerical analysis as a math minor, in a year's time

like taking a course or reading the documentation

But ROOT's C++ interpreter is such a genius piece of work. Badly documented, though; you have to know how to coax the information out.

@SirCumference If he can already work with the language enough to talk about day you were born, then he should know just about enough to start on these.

I have made too many simulations for physics and mathematics. For complex numbers, functions, vector fields , scalar fields. And many 1D , 2D and 3D motion in physics.

@naturallyInconsistent i mean that's a start, but it's hard to say how much he knows based on just that info

e.g. regarding functions or classes

@ACuriousMind The prof might be looking to diminish the class size

@ACuriousMind that's pretty hilarious

I can do only basic stuff as I said, some simple loops like checking prime number, making lists of primes in an interval, Armstrong numbers, reversing lists, ordering a random list, some other stuff

@naturallyInconsistent nah, they actually seemed happy how many people showed up - they just had failed to properly communicate their expectations in advance

and you really had to know C because the first exercise was like "implement the distributed Monte-Carlo algorithm from the lecture in C using this multithreading library"

@nickbros123 This is already rather useful, more than one might think it would be.

@ACuriousMind That is just horrible teaching if that is the first thing. But this is a graduate module that is not the first computing module, isn't it?

yes, it was an advanced course

@naturallyInconsistent hmm, what I know in python is this stuff, running loops, working with strings, lists; I haven't had the time to learn about the important libraries and using them so that's where I am right now. Electrodynamics took all of my time

@ACuriousMind Then I would point out that if you are doing multithreaded stuff and you use C, then you ought to die.

@nickbros123 I know; hence why I said you should learn to use those. Step by step, no need to rush. Anything you learn on your own free time is, after all, on your own pace.

@naturallyInconsistent you're not wrong but it was an interesting experience ;P

lol

There's an exponetial map for affine connections, but is there an exponential map for higher affine connections

Or would that spoil the bijectivity of the exponential map

Higher in the sense of being connections on the k-th jt bundle

Nothing wrong with doing MT with C as long as you don't allow your threads to share memory (ye even for read-only purposes, just to be on the safe side, copy it allll)

Joe Armstrong very cleverly distinguished parallel programming from concurrent programming

Hi @Amit . How are you?

Can't be better

Heyllo

@Amit Why . Is there any problem?

No it's my favorite response

Can't be better by definition lol

@Amit Oookay.. :-)

Good to know

Yesterday discussion with you helped me a lot.

Goooood

(Dont imagine Palpatine)

Are you following a textbook too?

@Amit Yes i am reading. Kleppner kolenkow, symon mechanics , Tylor mechanics and others

Goooooood

Pls see link video imgur.com/a/Tl4qhY6 watching projectile motion by x and y axes separately.

It look motion under gravity free fall motion when we move along x-axis . When watching from y-axis projectile looks just constant velocity motion. As expected by dividing our motion in cartesian components.

I cant now, I have to watch out not to get trampled by a donkey

who will see Mission Impossible Dead Reckoning ?

Surprisingly hard to find free fall experiments

All the google is swamped by the high school physics experiments

@Slereah youtu.be/xdJwG_9kF8s This is a high budget free fall experiment

@Amit Pls see link imgur.com/a/DhExVpE projectile motion as polar coordinates.

I understand how to analyze radial velocity and acceleration. But don't understand how to analyze angular components.

Because angular component should be think of as circle in simulation. But curve of projectile don't follow circles of polar coordinate. What is meaning of magnitude of angular velocity and angular acceleration in this case.

which physics topic was hard to understand for you

Radial i can consider as 1D motion and i can ignore rotation of radial unit vector same as i did in cartesian. But don't know how to analyze angular component of velocity and acceleration. Because trajectory of projectile at any point don't follow polar circle.

for me, it is time dilation, I think

which physics topic was hard to understand for you @Amit @Slereah @ACuriousMind

If you make a transverse wave in a slinky but keep the anchor points the same distance apart the length of the slinky has to stretch. Is there a specific term for the tension this puts on the metal?

I'm wondering how the tension changes as a function of wave amplitude.

It took me a while to understand that there's no limit to how much you can understand about the basic topics. I thought that the Mechanics course is supposed to make you understand CM in the same way Lin algebra gives you a solid basis in Lin algebra, but it's not the same at all

With EM it was worse, at the end of EM I only felt like I can now at least ask coherent questions about what I don't understand lol, forget understanding anything

@Amit I am trying to understand the use of polar , cartesian and tangential-normal coordinate system. Projectile motion is just an example. Afterwards whenever any coordinate system is used in book. I will understand clearly.

Sorry I need to avoid some cows still

if i have a question that's like "i know this outcome is physically impossible so what's going wrong here" -- is this considered a check my work question and, thus, irrelevant to the site? im trying to figure out whether to write up a post of this nature or not

@123 why arent you uploading images to here?

External links can be very dangerous according to some cyber security war chiefs

@Amit These are not images these are videos. I have uploaded video on imgur

You can click my link safely ;-)

You should make your questions at least as simple as to be understandable via images

Imvho

It is a bother to go to the cinema in order to figure out a physics question

@Amit Okay but sometimes situation gets clear on video.

Smell of salty popcorn and all that jazz

Are you sure gif animation isnt supported here?

Circle shows in this is polar grid circle and position vector show radial direction

Let me share you better picture. Which shows every object

can anyone please help

@Relativisticcucumber If the question is not about the derivation it is ok. Ofc, it's a well known trick that some people do to ask a question about a derivation disguised as a conceptual one ;-) but usually one can see through that and if you are honestly not interested mainly in knowing whether your derivation is correct, also show an effort to verify you have no mistakes etc. then I think it's fine. You can even add explicitly "if I have a mistake in the derivation don't correct me, just give a hint"

@Amit I have tried 2 different gif animation it didn't upload. It says only image upload.

please using these identities I am getting different answers

and using analytical approach I am getting different answers'

The circle in my image is the circle of polar grid. You can see angular acceleration with name $a_{ang}$ with magnitude. also angular velocity $V_{\theta}$. At point P the path of projectile don't follow the circle of polar grid. So what is the meaning of angular acceleration and angular velocity here?

@Amit It is said that some Nobel winners still solve CM problems to keep sharp. CM is just as hard as QM

I know angular acceleration magnitude has two parts, which is sum of tangential acceleration $\alpha r$ and coriolis acceleration $2v\omega$.

$a_{\theta} = (\alpha r + 2v\omega) \hat{\theta} $

@RyderRude CM is rigid and QM is hard

I figured out the tension thing.

@Relativisticcucumber .-..—..-…—…—.-

I wish i had taken a intro course in CS :P.

Also some sorts of engineering courses. But alas there exists no more time

@SillyGoose You'll need to give us a bit more ciphertext to give us a chance to break this

@123 Why do you need to know it? Just derive it from $\mathbf{r}=r\hat{\mathbf{r}}$

@123 The site permits GIF anim, but they are limited to 2 MB. Here's an example, from astronomy.stackexchange.com/a/47731/16685

You can even use SVG anims. But you have to host them yourself. And they can only use SMIL animation, not JavaScript. Eg,

@nickbros123 If you need to do a lot of number crunching it's a good idea to learn some Numpy. You can do algebra & symbolic integration using SymPy. And you can do many kinds of plotting with Matplotlib.

Alternatively, you can use SageMath sagemath.org which is based on Python. If you know the basics of Python it doesn't take long to learn enough Sage to do useful stuff. Sage uses Matplotlib for 2D plotting, but it's probably easier to learn how to do plotting in Sage than to learn Matplotlib.

Sage uses three.js for 3D graphics, eg

sagecell.sagemath.org/…