Classical Mechanics | Lecture 2

[@joabrosenberg2961]

Aristotle's laws of motion; Aristotle's law is irreversible 13:00; Newton's law 17:00; momentum 31:00; phase space 33:00; Newton Oscillator is reversible 37:30; Conservation laws 52:00; Newton's 3 laws 55:00; Conservation of momentum 1:02:00; Energy conservation 1:07:00; Harmonic Oscillator 1:33:30

[@mastershooter64]

thank you mate

[@AlexTrusk91]

The quality of this video may be bad, but its still great content from a good campus. Im glad you put it online regardless of the sound quality. Stanford does its part in giving everyone in the world informative, yet enjoyable, ways to enhance capeabilities to unterstand and form the world. Please accept a humble "thank you very much".

[@bradyp671]

53:35 Annotations: "Different orbits of different radii correspond to different tentacles." Physics is full of beautiful surprises.

[@georgetim1990]

Dammit, you beat me to the tentacles bit.

[@BruceWayne-dh5hy]

"..correspond to different energies". Just imagine an electron revolving around the nucleus on discrete Energy states--that energy is what is meant here.

[@PankajBhambhani64]

I heard it as "testicles".

[@EdSmiley]

I've often reflected on the fact that p stands for "pomentum" and B for the "bagnetic field" sounds like a physicist had a cold some time.

[@sayanjitb]

@MrComrade wow, new information 👍

[@joeboxter3635]

He's a yankee! More precisely a nu yoker. Lol.

[@KeePassDownload]

Thanks for putting subtitles, made it easier to follow along.

[@rajsinghbani9766]

I love how he is so casual with his knowledge

[@of8155]

Yes bro

[@essamhassan7943]

عظيم الشكر للعالم الجليل على هذه المحاضرة الاكثر من رائعة

[@yourlocalclosetedgaybestie3165]

53:53 *Different orbits of different radii corresponds to different tentacles* I love the guy who added the subtitles lmao

[@SUONIndustry]

Professor Suskind is the first to know the shape of string in string theory.

[@meetghelani5222]

Hilarious scene in the last few seconds of the lecture and a great lecture as always in general, thank you stanford and professor leonard susskind for this!!!1

[@gauravbhokare]

Lucid, crisp and clear ! simplicity is perfection !

[@pragalbhawasthi1618]

Thank you professor. All these lectures are helping me a lot.

[@of8155]

Yes

[@pocok5000]

There is a very misleading error in the subtitles at 19:12. The correct sentence is: The laws of physics are that there exist inertial frames.

[@pol...]

+Dávid Kertész Same in minute 28:49 where he says "they don't satisfy..." and the subtitle says that "they both satisfy..."

[@jsh31425]

Here's something odd: In the book The Theoretical Minimum, which is based on these lectures and follows them very closely, Susskind makes the opposite point: he shows that Aristotle's law *is* reversible (p. 62)! It seems a much more clear argument than the argument presented in this lecture that they are not. In this lecture, he seems to be mixing in the issue of sensitivity to initial conditions with this question of reversibility, in a way that I found very confusing. Anyway, to quote his own book: "The conclusion is clear: If Aristotle’s equations of motion are deterministic into the future, they are also deterministic into the past. The problem with Aristotle’s equations is not that they are inconsistent; they are just the wrong equations."

[@guyfromkerala3577]

I think what's written in the book is the right way.

[@relaxnation1773]

here he aslo says that aristotles law is reversible, if you had infinite precision when you mesure stuff, but you dont so they are nit reversible in that sense.

[@markholmescellphone6136]

he also assumed an interpretation of aristotles logic 4:21 4:53 . plus hes just giving historical progression. obviously there is an evolution on paridigm of force sparked by aristotle for following mathematicians. it was A lecture. not his book. the recording of this was.the only bad one. quality wise. the mit course is also dope.

[@olivernorth7418]

Isn't the claim about the sign of acceleration being independent of time also wrong? If I watch a film of an accelerating car in reverse, I'll see it slow down.

[@ralfg9194]

I also stumbled across this point. If you look at the exponential function, you can of course trace the course of the equation back into the past. The reasoning seems to be that at a finite precision, all trajectories run into an endpoint below the discrimination threshold and are therefore indistinguishable. The reasoning seems flawed to me, as it could be applied to alls systems that evolve into a fixed endpoint. The argumentation book seems to me to be the correct one here.

[@ijonilisha]

I just fuckin love this guy...I used to watch these series to have a better understanding of my high school Physics...and now that I'm in Med School and do the same shit all over again, Susskind is just a treat :)

[@shahidshuvo8191]

I am doing same..

[@flamurbedrolli802]

He is a BOSS . They dont call him a rebel of physics just like that . He proved Hawking wrong once

[@jsh31425]

Note: the orbits in phase space that Susskind draws for simple harmonic motion should be moving *clockwise*, not counter-clockwise, as he suggests. (If he had drawn momentum as the x-axis and position as the y-axis, they would have been counter-clockwise.)

[@1eV]

does it make any actual difference?

[@adarsh659]

@@1eV ofcourse not

[@mmaannaann]

The portion where Prof.Susskind mentions that Aristotle's law are not reversible didn't seem very satisfying. Indeed the Aristotelian 'force' is actually momentum(=mv) of the particle. In a closed system, if we know the momentum as well as the initial position of the particle, doesn't the Aristotelian law actually become generally reversible? I guess this is infact the very basis of Lagrangian and Hamiltonian formulations.

[@WaddiaS]

Momentum is conserved over time.Taking that as a postulate, if Aristotlean force is just momentum, how will it allow us to predict past and future of the particle's motion? It won't. At least not in both past and future directions. So Susskind is right.

[@CapitaineBleuten]

Aristotle's force is something you can apply to an object to set it in motion. In that sense, it is a force and not momentum...

[@LeavingCertMaths]

He is the first person I have come across who says that Newton's first law is really just a special case of Newton's second law (set a = 0), so Newton's first law is essentially redundant.

[@Urdatorn]

KeysToMaths1 Set F = 0, not a! a = dv/dt, which is what you want to be 0.

[@winston_best_tank2277]

This is actually not uncommon - in the sense you can find books "deriving" first law from second law

[@DrDress]

1:17:00 Energy conservation

[@AlMQTB]

The lectures are pure gold! Sorry... subtitles here play a twin role: with the existing quality of sound, spontaneous look at the subtitles either helps or just completely ruins the brain from time to time...

[@PasinduPereralink]

Thanks for the guy who asked why reversibility is important

[@atrumluminarium]

He takes a break from the lesson and what seems to be the Schrödinger equation suddenly appears on the board... What the hell happened during the break?!

[@chrisryan6464]

These lectures are put on the internet for the public, but are not normal class hours from Stanford. it.s a programme some universities do, called further education if I am not wrong. The people participating to these lectures aren.t just students, if any at all, they come from all walks of life and professions, therefore when you see other wild equations appearing on the board after a break it means they might have discussed something with the professor, or he just got bored and started doing other physics stuff..

[@jcnotnot8120]

The equation was both there and not there until you looked at it.

[@stephengibert4722]

Take a few more breaks and maybe we get the TOE?

[@vaishnav_mallya]

@@jcnotnot8120 Lol

[@of8155]

@@vaishnav_mallya ha ha

[@firstevidentenigma]

For instance, at about 20:38, he's going over what mass is, and the caption says x. Keep in mind that he is from new york, gang. You can also see that he was talking about mass when a few seconds later he says "force divided by acceleration," which is indeed mass in F = ma. So, don't believe everything you read in the captions, everyone.

[@netrapture]

At 06:42 "We can solve this equation very easily and p plus delta, the two graphs, right over" [here] is actually "We can solve this equation very easily for x at t plus delta, let's do that , right over" [here]

[@OfficialEnman]

He takes a lunch break and suddenly a wild Schrodinger Equation appears. What did I miss?

[@dontquestionmyname5490]

a lot

[@ironmantis25]

Quick throw a Pokeball at it

[@vaishnav_mallya]

@@ironmantis25 hahaha

[@pavlenikacevic4976]

1:23:40 ''it's a law of physics that it's true, you cannot derive it from anything else'' well, not quite, it's because rot(F)=0. That doesn't work in the magnetic field, for example. And you can derive that curl of fields he used is 0 (you must know general relativity to prove for gravitational field though, but it's still provable, it's not just a law of physics we can do nothing about)

[@kshitijgarg4970]

but isnt it always true from a math point that such a function will exist? i mean if i have fx, fy and fz, cant i always reproduce the function V irrespective of whether f is a force functon or not?

[@pavlenikacevic4976]

The problem is that sometimes F won't be equal to a gradient of any function (V). For example (in two dimensions for simplicity), take F(force field) = -y*i + x*j, where i and j are unit vectors. Then, you want to find V(x, y) such as partial derivative of V with respect to x (w.r.t. x) equals -y and partial derivative of V w.r.t. y equals x. You won't be able to find any V for which that is true. And that's because 2d analogue of curl of F that I gave you doesn't equal 0, it equals 2 (in the other words, the field is rotating with angular velocity curl/2 = 1. Whenever you have rotating fields, you won't be able to find V)

[@kshitijgarg4970]

right. thanks much.

[@baetoven]

Feynman Lectures Vol 2, Chapter 2 is a great read regarding this. Great catch. Just adding stuff for others. Basically, when curl is zero, what Susskind says is true.

[@camilodominguez4678]

we are living in such a strange world nowadays that this guys sneezing and coughing that often freaked me out

[@abdomohamed8665]

Same man! You should cover your ears XD

[@TheVincent0268]

all the sounds of the person(s) setting next to the microphone are annoying

[@netrapture]

At 06:12 the caption says "Let's not make the limit, let's just write it this way" and what Susskind actually says is "Let's not TAKE the limit, let's just write it this way"

[@yichuli9896]

"T" representing kinetic energy comes from "travail méchanique" (mechanical work)

[@torresfan1143]

Professor Susskind on savage beast mode at the end

[@bsatyam]

Gods like Susskind shouldn't have to worry about money. They should be allowed to use whatever resources to advance the knowledge of humanity. It's a sad world we live in.

[@ucanihl]

Regarding the question about importance of reversible nature of physical laws, I think it's because the set of all reversible laws is a tiny subset of the set of all possible deterministic laws, which could be seen by analyzing the graphs presented in the Lecture 1.

[@dreamsxcaster]

I'm not usually into phisics but all these conservation laws and the way they are proved impress more like properties of the model; they are our way of thinking and viewing reality ( but a good one).

[@fjolsvit]

The bit about acceleration being the same when time is reverse was revealing. His finite element approach to developing the Euler Lagrange equation was also enlightening.

[@rkbshiva]

Can someone tell what does he exactly come to say at 1:23:20? Thanks in advance.

[@kshitijgarg4970]

i think hes wrong there. Clearly such a function exists.

[@netrapture]

There's a subtitle/caption error at 02:15 where the caption says "He thought that velocity was a natural consequence, of course" when Susskind is actually saying "He thought that velocity was a natural consequence of FORCE".

[@WorldBurial]

Both are used. It depends a bit on the context but in Lagrangian mechanics T and V are usually used for kinetic and potential energy respectively.

[@krishnendusarath7110]

40:06 i didnt understand the eqn of X .where the t0 is coming from ?

[@nishanjayaram7448]

KRISHNENDU SARATH it’s a second order differential equation, and hence it must have 2 constants. The most general solution to that equation would be Asint + Bcost. Now by basic trigonometry you can see that you can reduce that to Dcos(t-t0), where D=(A^2 + B^2), and tan(t0)=A/B

[@LoquaciousApe]

That's actually often pointed out when classical mechanics is discussed, be it in textbooks or lectures.

[@kamranalam0110]

Are these lectures for bsc or msc?

[@georgeluther2469]

41:40 actually there's a complex solution, x = e^(it)

[@ehabmalkawi194]

He is a great physics teacher... I would also recommend a new channel for solving somewhat advanced problems in classical mechanics with thorough discussion... kzbin.info/www/bejne/pZe3naaDqcl1b5o

[@MrAnanyo]

From 12:52 to 14:50, Prof. Susskind says how Aristotle's law cannot be used to predict the past. I didn't get what he said. Can anyone please explain? Can somebody also tell me what he means by "reversible" and "irreversible"?

[@tobywhite1100]

See lecture I at about 27:00-35:00. In classical mechanics, we have to be able to "predict" (= calculate) all past & future states of a closed system from the state information at any given time. That's reversibility (= conservation of information). Aristotle's law is not reversible because, for example, every rolling ball grinds to a halt after a while. Once it's stopped there's no way we can calculate how fast it was going before.

[@muqker]

Toby White But the way he explained it, the particle would not in fact reach the 0 position ever. So there is no "loss of information". I am not convinced he correctly showed that Aristotle's low would be irreversible for that case.

[@TheBBoyKish]

To understand it, you can just imagine the way it would be in reality, if you let go of some mass on a string at some location x0 then you can check at some other position it's velocity and from this information you will be able to tell where you started from (because of the total energy). However in this case no matter where you start, the point mass will try to go to zero the same way. To express is mathematically. If you start at two different positions, for every epsilon there will be a t(time), when the difference of x will be smaller then this epsilon. Which means it can be made as small as you want. This way starting from two different position you can choose t such that no matter the original differences the difference at t will be as small as you want it to be, hence you lose information. Hope this helped

[@takanara7]

The point is that in a truly closed system you could predict the past from Newtonian mechanics *even if* you didn't have perfectly accurate measurements. The mass would continue to oscillate on the spring forever. Obviously the real world is governed by quantum mechanics, which doesn't allow for perfect prediction of the past.

[@MrGoatflakes]

Because no matter where we started, eventually the system will come to rest at the origin. Therefore we can't tell how far the spring was pulled back in the past.

[@behnamasid]

46:02 , back when coughing was a normal thing

[@asdfghj6222]

at 51:00 Prof. Susskind says if you take a movie and run it backward nothing will happen to the acceleration. I am not able to understand this, doesn't the body decelerate on reversing time?

[@Chris-gy3eh]

He means that the acceleration will be exactly reversed, and will follow the same equations. Whereas with Aristotle's equation the object would behave differently if you were to watch it backwards in time.

[@asdfghj6222]

thanks for clearing my doubt

[@dihan6130]

Why the acceleration will be reversed? I think it would be the same, isn't it?

[@dsa3df3]

It is the same I think. If you drop a ball, it will go faster and faster downwards as it accelerates. In reverse it will go up fast at first, and slow down. So same downwards acceleration in both cases.

[@fjolsvit]

At 35:56 a question is asked. It is very important, and not addressed well. Newtonian Mechanics and Analytical Dynamics are subtlety distinct. The former assumes a coupling between position and time, a priori, the latter asserts that coupling as an additional condition a posteriori. Very few physicist appear to appreciate that distinction. That is the original sin of quantum mechanical epistemology. To paraphrase Schroedinger, we are talking about phase space, not real space.

[@xsli2876]

on 51:04, I cannot understand about running the acceleration movie backward, same.

[@xsli2876]

I found this youtube video very helpful on reversibility of physics laws. kzbin.info/www/bejne/ZnvZoZVjmJKLnLs

[@xlr1271]

He says that the force law for the spring is -kx. He is assuming the force law of the spring for Newtonian Mechanics and forcing it on Aristotle's Mechanics. Wouldn't the force law for the spring be proportional to the square of the position for Aristotle? Then the resulting trajectory would be the same as derived from Newtonian mechanics.

[@rn12543]

The force law for the spring (Hooke's Law) is experimental. It is not derived from any equations of motion so it wont change with respect to any equations of motion which we use as our theory is based on experimental knowledge and not vice-versa.

[@hannaedwards5197]

I think i know where you are coming from in the sense that Aristoteles appears to have "defined" what he called force as mv . But therefore we would need to know what he exactly said or wrote or thought .

[@repsilat]

Why a spring, though? Imagine a different system: a ball rolling up a round hill with juust enough energy to reach the top. In Newtonian mechanics this system is *exactly* as irreversible as the spring-like system Susskind sets up for Aristotlean mechanics -- a stationary ball at the top of a hill could have been at the top forever, or it could been rolled up to the top from any direction at any time in the past. It's clear enough, then, that the reversibility is a property of the combination of the physical laws *and* the system of forces set up, and Susskind provides no argument in this lecture for the use of the ideal spring system as a litmus test rather than something like the "round hill" (or even stable frictional systems.) If we can ignore the hill system in Newtonian mechanics for not being reversible, we might "let Aristotle off the Hooke" in a similar manner by criticising the choice of the spring system/equation.

[@netrapture]

by that logic every theory of mechanics is irreversible so you haven't let Aristotle off the hook.

[@netrapture]

@Rahul Narula - Correct - as Susskind says at the very beginning of Lecture 1, the laws for particular systems, like say a mass on a spring (F=-kx), are independent of the general framework of mechanics (e.g F=ma or F=mv)

[@paulnewton3556]

19:36 ...or do/dt =0 .... not happening but you could drive a bus through his maths .... but he’s amazing

[@dexterdev]

In the theoretical minimum book he says that Aristotle's laws of motion is reversible. And it is off course reversible although he says the opposite in this video. By reversibility what should I understand? If I can get the initial value (let t=0 ) (provided I have an infinite precision and accurate device) from any point from time instant t1 > 0, I am happy to call the process reversible. That indeed means I can predict the past not just future. Please comment on this if I am wrong.

[@Zyphare]

I was confused at that one too. In the book,Susskind describes the force as a function of time and then proved that force to be reversible and deterministic. He also does this in the lecture at around 7:00 too. Later in the lecture, he proves that a force that is a function of position is not reversible as it is not deterministic into the past. This is where the lecture differs from the book.

[@danielhoven570]

If Tywin Lannister tought physics...

[@StaticBlaster]

i understand everything he's talking about because i've taken physics 1 before and calculus 1 and 2 before. i actually have taken more than this up to physics 3 i.e. optics/light, quantum mechanics and particle physics/intro to cosmology and ordinary differential equations and linear algebra.

[@iam_mausam]

whats the order to take advance physics course for self learners

[@StaticBlaster]

​ @iam_mausam For self-study here is the correct order from the most elementary foundational topics to the most advanced if you want to study string theory: good luck in your studies by the way. So, without further ado, here is the list of courses to take: 1. Calculus 1 (Differentiation) 2. Calculus 2 (Integration/Series) 3. Ordinary Differential Equations/Physics I and II. 4. Calculus III (vector calculus) 5. Discrete Math/Proof Writing 6. Linear Algebra/Physics III 7. Probability and Statistics 8. Partial Differential Equations (the whole subject) 9. Set Theory 10. Number Theory 11. Algebraic Topology 11.5 (I forgot this one) = Complex Analysis 12. Real Analysis 13. Abstract Algebra I 14. Abstract Algebra II 15. Group Theory 16. Lie Algebras/Lie Groups 17. Ring Theory 18. Tensors Analysis 19. Fourier Series/Fourier Analysis 20. Harmonic Analysis 21. Differential Geometry 22. Special Relativity 23. General Relativity 24. Quantum Mechanics I 25. Quantum Mechanics II 26. Quantum Mechanics III 27. Quantum Field Theory I 28. Quantum Field Theory II 29. Quantum Electrodynamics I and II 30. Quantum Chromodynamics 31. Differential Topology 32. Knot Theory/Manifolds/Fiber Bundles 33. Noncommutative geometry 34. Supersymmetry and Supergravity 35. String Theory/M-theory

[@iam_mausam]

@@StaticBlaster thanks a lot mate!

[@StaticBlaster]

@@iam_mausam You're welcome. I know it's a lot to study but string theorists have at least 8 years of education under their belt.

[@sergeydenisov15]

Great lecture but there are some minor things. F.e., when drawing the harmonic oscillator trajectory in the phase space, there is a little mistake made: It cannot go counterclockwise, only clockwise (when the momentum is positive, x is growing etc).

[@AdenKhalil]

It depends on the initial conditionals. You can throw it towards the equilibrium point with an initial velocity

[@AdenKhalil]

And count positively the momentum when you go towards the equilibrium point.

[@sergeydenisov15]

@@AdenKhalil now please think about what you have written (and try to plot it)

[@sergeydenisov15]

@@AdenKhalil how could on throw some thing towards something - with the velocity pointing to the OPOSITE direction?

[@netrapture]

At 06:57 "times p" -> "at time t"

[@netrapture]

There's a subtitle/caption error at 05:58 where the caption says "X dot is x times t + delta" when he actually says "X dot is x at time t+delta"

[@rationalsceptic7634]

Lectures should not be like reading a detailed Book....they should be about clarifying concepts with examples...in,that,he reminds me of his great Pal,the mighty Richard Feynman...he was awesome at clarifying complex and deep ideas 💡 😀

[@amphysics5650]

Do you allow downloading videos?

[@david52875]

Because he divides by delta twice, one to get velocity, then again to get acceleration. (a/b)/b = a/b^2

[@rohitraj4275]

How to access ur notes?

[@guestguest9603]

Not sure why he would say that in one dimension any function can always be written as the derivative of another function. What about the case when F(x) = sin(x^2) whose integral cannot be expressed as elementary functions?

[@ucanihl]

A non-elementary function is still a function. You can compute it using numeric methods for integration for instance. A function is simply a mapping, it doesn't have to be computable at all.

[@suhrapbazarow8841]

prof prof , u na different level ,i see no mistakes in his lectures

[@merlinthegreat100]

For the differential equation of harmonic motion, the exponential function works if it is e^(ix) ... Why is that?

[@BrianParsons-or1lv]

Magnificent thank you

[@pankajagarwal5358]

the reaction force NEVER acts on the same object as the force that causes the reaction. The initial Action, and the opposing Reaction occur on two different objects. Then how the book placed on a table remains at rest

[@pmcate2]

@53:36 "Different orbits of different radii correspond to different tentacles" 🤣

[@oscarobioha595]

Hmmm these students are asking very good questions

[@steffensolgren7503]

Why did he divide by delta squared, at 26:20?

[@alanplateadocastro831]

acceleration is the rate of change of velocity with respect to time, but velocity itself is the rate of change of position also with respect to time if you work it out yourself you'd see that delta appears twice in the denominator and thus you can write it as delta squared

[@steffensolgren7503]

@@alanplateadocastro831 oooh. He is taking the double derivative. Thanks

[@danielfisher6401]

I still didnt understand why the Aristotle theorem was irreversable? why its irreversable if all particles return to their origin?

[@manideepsridhara2831]

Daniel Fisher lets say there are two particles, one at 2 and other at 3 after infinite length of time both end up at 0. Now if we want to move In reverse we don’t know where to go (2 or 3?)

[@mudavathsanthoshkumarmudav9845]

Can I have ur not book sir any one plz help me

[@Poemand]

شكرا ❤❤كل تحياتي من جزائر 🇩🇿

[@johnniefujita]

mass is how much resistance a particle will display to change its momentum. I think that schools relate too much mass to volumetric bodies. In a sense that the most important concept of inertia sounds kind of residual, when it is the true essence of mass.

[@francescos7361]

Thanks prof. Susskind for sharing your studies with us, as engineer I understand this studies.

[@AdrikMax]

He sais if you can have an infinite ammount of accuracy (which means counting each coordinate to infinity) you have reversabillity. You can't do that practically. So you take limits.If you take the limit of x as t goes to +infinity, you get zero. Every dt, as the function hovers over the x axis, gives us a certain dx which is practically zero when you compare to infinity.

[@allrounder2367]

Sir, you haven't discussed the transformation of vectors.

[@robertprince1900]

He is wrong about (dt)^2; it doesn't work like that. You can't say time is -1and it goes positive for that reason it is shortened form of a second derivative. It works because a change of a change is still plus 1.(50.480

[@아루루-q5r]

He said relationship between potential energy and force is law of physics and can't be derived from anything... then does it mean potential energy is just discovered and it has the meaning like that???

[@이말러]

wonderful!

[@itsalh5793]

1:17:22 anyone knows why the X double dot ?

[@dhritishmanhazarika3894]

simple differentiation

[@2c4everybody]

X is position. X dot is shorthand notation for the derivative of X, ie the velocity. X double dot is the derivative of X dot, hence the acceleration.

[@rokasha40]

So i watched only lecture 1&2 yet, I wanted to learn how come Kinetic Energy is 1/2 mv² and not some other constant times mv² (units still would workout right??) but what i have gotten from this video is that i can prove the formula where KE = 1/2 mv² by assuming conservation of total energy and i can prove the conservation of total energy by assuming KE = 1/2 mv² so it's kind of a chicken and egg story, so what exactly came first someone kindly tell me...

[@roksanazinchenko4145]

Roksana Zinchenko1 second ago Dear STANFORD, thank you so much for all the lectures you post. My deepest gratitude and respect for your generosity and passion for knowledge. Nowadays, almost everything is monetized generosity is truly rare.

[@drthrean]

Precision of measure is not of relevance here. Reversability of a law cannot be determined by the precision we measure outcomes. Even if that would be valid, same would hold for newtonian laws. Both xdotdot = -x and xdot = -x (his examples for aristoteles and newtonian laws of motion) have unique solutions that depend only on initial conditions.

[@drewkavi6327]

how can you retrodict with newton equations

[@ahmadalmaghraby7792]

Why when he deal with the derivative he doesn't write the limit ?

[@ahmadalmaghraby7792]

But as I know the derivative is a whole part itself it can't be treated like this , because it's a limit and we deal with the limit when we say derivative not with the function itself

[@waynemeher117]

You could write in the limit but you would get the same answer so he just leaves it out for the sake of simplicity, sort of like a short hand .

[@justtolivecomment]

all the coughing makes it a great Halloween watch in 2020

[@valtih1978]

Why does he identify F with x? He says that dx/dt = p/m tells us how x changes but dp/dt = F/m tells us how p changes and the system eveloves. But, in order the system to evolve, change of p should determine the change of x and new value of x should affect p new value. So, x must be identified with forsce. But, I do not understand why F this is the case? Why is F identified with x (rather than p, for instance)? Is it because x = cos t and F = -W^2 x in harmonic oscillations?

[@MrGoatflakes]

I think Professor Susskind messed up a bit. Because of the limitations of KZbin comments I will use *bold* for vectors _ to indicate a subscript and ^ to indicate a superscript or taking something to a power. He should have I think said *F* = m (d^2 *r* / d t^2) and not *F* = m ( d^2 x / d t^2) That would just be the x component of the force, and is more properly written F_x = m ( d^2 x / d t^2)

[@TalooshDaBoss]

Can someone tell me how exactly he found x at 12:00

[@airsphere]

He solve the differential equation, x'(t) = - (k/m)x(t), x'(t)/x(t) = - (k/m), you integrate each side and you obtain ln(x(t)) = - (k/m)t + a => x(t) = exp(- (k/m)t+a), x(t)= exp(a).exp(-(k/m)t), A = exp(a). finally, x(t) = A.exp(- (k/m)t)

[@TalooshDaBoss]

+RTool airsphere Thanks for the explanation, I understand now. I have never took the differential equations course before so I am bad at this. I still don't understand why exp(a)=A

[@airsphere]

+TALOOSH You juste put exp(a) equal to A to simplify. you can keep exp(a) if you want, it is the same thing ;)

[@TalooshDaBoss]

+RTool airsphere Thanks for that. I just wish susskind could have explained how to solve the equation correctly on the board so I wouldn't get too frustrated to move on. I hate it when that happens and I forcefully watch the rest of the lecture in a sad mood. People like you in the comments really help me out :)

[@sciencego8929]

50:43 .. It is not t^2 it is the second derivitive !!!!

[@shadmanshakib5568]

1:23:45 Didn't get it

[@kyanos-3909]

Why there sometime appears “e”?

[@jumpman2672]

Gonna tell my kids this is god explaining how he made the world.

[@drthrean]

he tells us at least 4 times that x(t)=e^(-at) will eventually come to a rest zero and therefore Aristoteles laws are not reversible. That's wrong for every initial conditions besides x0=0: a trajectory never reaches zero either or it was zero from the start. And in both cases we can compute exactly the location of the trajectory a given dt before.

[@danielblumowski34]

I don't quite get why the existence of V(x) is a law

[@matusfrisik3887]

Person who wrote or edited subtitles for this video didn't make a very good job. So many errors.

[@averyhaferman3474]

so.. if we watch all these lectures do we earn our degree?

[@karlruv8332]

Why should the spring be a good measure of force...?

[@karlruv8332]

The only way I can test the equivalence of masses is through the equivalence of forces needed to shift them. In other words, F=ma is still tautological.

[@karlruv8332]

Finally, Susskind assumes the equivalence between weight and mass, which I find doesn't sit to well with me...

[@jameskaczmarczyk8563]

Karl Ruv No, the way you test equivalence of masses is by using a scale. All measurements in physics are relative to a common standard.

[@dexterding1080]

Shouldn't the general solution to X'' = -X be X(t) = C1 cosX + C2 sinX instead of just C cosX

[@balasujithpotineni8184]

Simplify it. You get c=sqrt(c1^2 +c2^2)

[@Sans_K5]

great❤

[@goldfishno20]

Hi guys, some questions here. Any help would be very much appreciated. (fyi I am a super noob here btw, so please be patient....). I) I dont think a system dictated by a law dx/dt=v=-x (a simplified version of the discussed Aristotele's law) is a bad system in the context of predictability... At the end of the day, x=exp(-t) has a unique solution for all t. Also, the law of the system can alternatively be expressed as a=x, and when the time is flipped (ie, -v=-x), the law (a=x) remains the same, so the law works just fine in both time directions. Combined, the system thus can be fully traced both forwards and backwards in time under the law a=x. I don't see any problem with this law.... Nevertheless, I think bad laws do exist, so...the question is what are the sufficient and necessary conditions to generate a law that doesn't have a predictability + an example? II) It seems to me he implies that any law of motion that can be expressed in the form of newtonian law of motion, mx''(t)=f(x(t)), is always a good physical law. Is this true. I highly doubt it... III) It also seems he implies that knowing only how the momentum (or velocity) and the location relates to one another, i.e. knowing p = f(x), is sufficient to fully describe how the system evolve through time. Is this really correct? Cheers,

[@NeutroniumIon]

The problem is that unless you have infinite accuracy, at some point the particle will inevitably appear to be at the point x=0, which would not allow us to determine the initial condition and thus the entire past. So while in theory we might be able to measure the very small displacement at large values of t, in practice, when the particle gets too close to the origin, we cannot measure any displacement from the origin, and hence cannot solve the equation to determine a law of motion.

[@goldfishno20]

If this is really what he meant, doesn't your argument also imply that Leonard would also say newtonian physics is, in some cases, non-reversible? I don't think this is what Leonard said...

[@NeutroniumIon]

That's actually a really good observation and what you're asking leads into a whole different discussion. Briefly: the laws of motion in Newtonian dynamics are reversible (or time-symmetric) because they conserve momentum. You'll notice that in the Aristotle example, momentum is not conserved, purely as a theoretical feature. Yet in the everyday world, ironically this is actually how nature works, but for a very different reason: friction. Friction and other so-called "non conservative" forces *do* induce irreversible and time-asymmetric components to physical laws. The omnipresence of such things is a key observation of thermodynamics. It's essentially the only macroscopic evidence of an "arrow of time". So the answer is that: yes, the overwhelming majority of physical phenomena are irreversible, but this is not any theoretical consequence of Newtonian laws of motion, but rather the second law of thermodynamics and the existence of non conservative forces.

[@goldfishno20]

Ah~~ Thank you very much. (Btw, I am a biologist by trade and haven't got any proper training in physics, so please be patient if I am saying anything wrong and a bit silly). But.... i) I thought conversation of momentum is related to space-translation symmetry, and conservation of energy is related to time-translation symmetry.... but, as far as I know, neither of them tell anything about time-reversibility. Also, isn't that the momentum of a simple harmonic oscillator under the Newtonian law of motion is in fact not even conserved but instead constantly changing with time, both in direction and magnitude? Are you sure this is something to do with momentum conversation? ii) So, in the same way that the motions under the Newtonian law can be fully traced back in time in theory (like, if I know precisely all the motions of all the jiggling particles on the floor, I then in principle should be able to construct the past history in full details), don't you then agree that a particle moving under the law mv=-kx; and hence x= exp(-kt/m), can also be traced back in time fully theoretically? iii) Under this law of motion mv=-kx, the acceleration of the particle follows that a=x(k/m)^2. So, if you reverse the video (i.e., reversing the velocity vector), you will get that -mv=-kx; and still get that a=x(k/m)^2, which is precisely the same as before. So, I would say that not only that the motion of the particle can be fully traced back in time, this law of motion is also in fact time-reversible. Have I got anything wrong here? iii) Say two massive neutrally-charged particles placed symmetrical about the origin at t=0 and move towards each other under the Newtonian law of gravity. At some point in time the two particles will collide and got stuck together at the origin (?). It seems to me that, although the law is time-reversible, the motion of the particles can't be traced back in time even in theory once they collide... Where did I go wrong here? Any explanations? Or is it in fact that they don't stuck together? but how?

[@NeutroniumIon]

goldfishno20 i) You're thinking about the reverse implication (time symmetry implying a conservation law). In that case, yes it is conservation of energy. Conservation of momentum implies time symmetry by the following argument: Changes of momentum within a closed system come from forces within said system. And conservation of momentum implies Newton's third law (it's actually more fundamental than the third law, as alluded to by Susskind). Since momentum changes sign when time is reversed, the total momentum is flipped and each particle in the system has its momentum flipped. At no moment in time does the total momentum change in the reversed system, since it's the same as the original, just with an opposite sign. So momentum is conserved in the reversed system (implying newton's third law). And acceleration+forces do not change sign when time is reversed, so the second law still holds. It follows that the reversed system (reversed movie) satisfies newton's laws and thus describes a "valid" system. All corresponding equations of motion will also be valid. As for the SHO, momentum is conserved when it is posed as a closed system; if you make one end fixed, then the system is not closed (because newton's third law will not hold without considering the reaction force from the particle on the fixed end). If you allow the other end to oscillate, then you have total momentum being conserved. ii) Your math is incorrect. We get acceleration by differentiating both sides of that equation. Doing so, we arrive at ma=kv and a=(k/m)v, which is not preserved under time reversal (velocity becomes negative but acceleration stays the same). iii) Any such scenario where the particles are stuck together would imply some loss in mechanical energy of the system (in our universe, probably via heat). This is not a time-symmetric process, of course, because mechanical energy is not conserved.

[@FliegendeHollaender]

There is no way of acquiring notes, huh?

[@TheNecromancer077]

I love this channel learned alot!

[@halilibrahimcetin9448]

Thats the comment I am looking for😂

[@muslimgiga]

ya f prime of Sine is COSx not -Cosx. Oh well, he is human.