Lecture 2 | Modern Physics: Classical Mechanics (Stanford)

[jc0501871]

F(t) = ma

F(x) = mv

Am I right?

[edwardmeade]

Derivative of jerk is jounce. (Thank you Mr. Clark, my HS Physics teacher.)

[MrBrew4321]

83,459 people just got smarter 273 people are smart... 9 people have something wrong with them.

[paigerocks884]

in the beginning he totally works out F=mv and then he says this is a false law.that doesnt make sense.

[Dreadnought9T]

@paigerocks884 F=ma not v. Momentum is mass x velocity.

[Matthewkindpend]

@paigerocks884 Yes, he's demonstrating mathematical logic, I believe. He's giving you an instant where you can see that the math is flawless, but the physical law is nevertheless flawed. Aristotle's mechanics were actually along those lines, I believe.

[lawanbrown16]

you can think of the derivative as the change in velocity, thats how it relates to Newtons equations.

[AVIDSATANIST]

this dudes so over it



[nirdeshreddy92]

great video

[ganravichandran]

It is very easy to follow him.

[silencedidgood]

At 50 minutes he just completely demystifies partial derivative. Check it out!

[007MrYang]

Im 17 and I've never done differential equations, but I love physics!

[SalsaTiger83]

@007MrYang try khanacademy here on youtube

[007MrYang]

@SalsaTiger83 Thanks

[MrDepressionist]

@007MrYang ME TOO!!!

[xSeiZmikx]

Don't you love it how the smartest people in the world always look like hobo's :) No disrespect prof, love you.

[itsmancini]

I don't see how knowing a single x co-ordinate is enough to determine f. Unless it is just an assumed property. Wouldn't you have to know two positions and the time between them to calculate dx/dt, which is needed to calculate f?

[mcgilson007]

@itsmancini He left out the fact that there is another equation (rule) that links the x coord to the force, F. Only when combining F=ma and the force law, F=f(x), can you determine future states of the particle. He could have used Newton's law of gravitation, where F_grav = (G * m1 * m2)/r_12. Because we assume the Earth is fixed all one must know to get the force due to gravity is the distance of the particle from the Earth's center of mass. Thus x determines F. x => F(x) => a

[dabrownone]

@mcgilson007 He mentions the force law later, but it was kind of in passing. That could have been clearer



[JLXOutlaw]

@mcgilson007 GOOD WILL HUNTING RIGHT HERE PEOPLE!

[achintyagopal1486]

does anyone know why kinetic energy is T and momentum is p

[WhySoBass]

@achintyagopal1486 I'm guessing it's just a variable. It doesn't matter what the letter is as much as the definition. If i under your question which i hope.. loll. i didn't finsh the video.

[achintyagopal1486]

@WhySoBass what do you mean, "if i under your question which i hope

[WhySoBass]

@achintyagopal1486 Understand* your question.

[achintyagopal1486]

is it weird for a fourteen year old to know math up to differential equations?

[ripperduck]

When he says that force is causing the motion of a mass, does he actually mean that its energy? It seems to me that energy which is the phenomena which causes a mass to move and therefore create a velocity. 

[Liaomiao]

Hmm, I've got a little bit of maths under my belt (calc 1-3, linear algebra, diff equations) but I dont have any knowledge in physics. The physical concepts explained here seem to jump around from place to place. Anyone else with very little experience in physics having the same problem or is it just me?

Great set of lectures anyway.

[ZenPajamas]

@Liaomiao You should have a look at university physics 1, and university physics 2. They cover the fundamentals clearly. This is not for you, yet.

[WhySoBass]

@ZenPajamas I'm gunna have to try that one too, understanding this math with geometry skills not such a good thing? i get lost sometimes.

[SmokeWeedEveryHour]

I could watch this for days on end.

[SenorMorgenStern]

I haven't seen the calculus of variation for a while. Great exposition and pedagogy Dr. Susskind--I'm very grateful for the simply incredible lecture!

[italouruguayricano]

I am looking for non inertial reference frames , rigid bodies, rotational motion and euler angles. I am going over prof. Susskind's videos any one know which videos cover that?

Thanks

[Escaladist]

is this a graduate or undergrad course?

[StanfordUniversity]

@Escaladist It's a course from the Stanford Continuing Studies Program.

[x89codered89x]

@Escaladist THe content in this course would typically be seen in as undergraduate.

[x89codered89x]

@Escaladist THe content in this course would typically be seen in an undergraduate course.

[bbsonjohn]

@Escaladist This is an awesome course

[BenBen2351]

Something i don't get : he says aristote's is a one dimensional space because it only needs x.

Following its logic, I would (humbly) describe it as a 2 dimensional one : you need the position, and the force that moves things around. And since F=mv, that means you need x and v. X alone doesn't tell you what force is being applied to it (no matter how you describe it). dx/dt tells you, but that means you need a "pair" of x.

That's two dimensional to me...

Anyone ?

[superok4luv2u]

@BenBen2351 with on exception you forgot that f it istelf is f(x) it's depentant only on x so if you know x then you know f

[TheOvermaster]

@BenBen2351 we are taking the force law as a given

[joeglimmix]

aristotle=epic fail

[QuantumMaths]

@joeglimmix

His ideas regarding physics were incorrect to be sure, but be careful for such stringent criticisms of past scientists. Most people could be forgiven for mistakenly thinking that velocity requires consistent application of a force. His famous (incorrect) thesis that heavier bodies fall faster was likely derived via the movement of objects through *liquid* media, which do indeed produce this effect (it was actually a creative idea, but a misguided one).

[HunterDX77M]

These are overall very good videos, though I wish they were subtitled like the MIT ones so that I could understand what the students are asking. Its really difficult to hear them.

[mmongia2009]

Really Interesting, mind-boggling last 30 mins !!!! :D

[DigitizedSelf]

Meh, it's dumbed down, inconcrete and largely unformal but very pedagogical and with an alternative angle to classical mechanics - interesting, but hopefully they have a book that complements the lectures/fills the gaps.

[QuaternionEM]

@DigitizedSelf

Looking at your favorite videos makes me think

that you shouldn't even be here...and for you to

comment is ridiculous.

Go watch a clip on pseudo-science and leave

the math to us.

[DigitizedSelf]

@QuaternionEM You're probably right about the first part - I've just started doing my thesis about conformal super-symmetrical Yang Mills theories (theoretical particle physics in case you're wondering), so I guess this IS a bit of a waste of time... but it's okay to watch while eating or cleaning ;-). My comment of course was made in comparison to when I had classical mechanics myself and not my current level.

Way to be judgemental btw - what do you do for a living?

[QuaternionEM]

@DigitizedSelf

Yang Mills...yeah...THAT's the ticket!

Tell me some original awesome math details about your thesis.

What specifically is the conformal part?

[DigitizedSelf]

@QuaternionEM Now actually that's a good question - actually I've had about super-symmetry and Yang-Mills theory in my courses but not the conformal part (in the beginning there's quite some theory to read up on). To the best of my knowledge "conformal" implies preservation of angles under scalings of the energy which in turn means that the coupling constants are independent of the energy... since this adds additional symmetries to the Lagrangian density it also alters the commutation relations

[DigitizedSelf]

@DigitizedSelf defining the theory; a new operator in these relations is the dilation operator, although I have to admit I'm not yet entirely certain what it does and why.

...you still didn't answer my question though; what do you do for a living? ...and how come you think that it allows you to be condescending to people and decide what they are allowed to comment on? Your profile says you're 45 - if that's the case you really ought to know better :-/.

[QuaternionEM]

@DigitizedSelf

Isn't the dilation operator just 1/(sqrt(1-v²/c²)) ?

Also, isn't conformal mapping just the mapping of one complex

function to another?

Lets talk basic complex math. You should be a whizz at that...

Also, in answer to your question, I rub baby-oil on supermodels for $200/hr.

[DigitizedSelf]

@QuaternionEM No, what you wrote there isn't even an operator and carries a suspicious similarity to the Lorentz factor used in the Lorentz transformations of special relativity... also, while it is true that conformal mapping exists as a map between complex functions, then even in that simple case it needs to conserve angles. In the case of conformal field theory it implies an additional symmetry of the lagrangian which in turn leads to the fields being massless, making the coupling constants

[DigitizedSelf]

@DigitizedSelf fixed (or at least not running).

Oh, and nice one about the job - it's either 1) a lie to somehow make me jealous and not tell me what you actually do (most likely) or 2) You're real profession which I'd imagine being the most unfulfilling job in the world (no wonder you feel the need to put others down). In both cases I'd say you aren't really qualified to feeling superior :-/.

About the complex math: Go grab a text book or at least make your comments more concise...

[DigitizedSelf]

@DigitizedSelf *questions more concise.

[QuaternionEM]

@DigitizedSelf

Dude,

Relax...that is the Lorentz factor.

I just wanted to see if you're for real or not.

Good answers.

Tell me more.

My degree is a MSEE, but I love pure physics.

So you really think I'm lying about the super-model job?

That hurts, man.

[DigitizedSelf]

@QuaternionEM Yeah, actually it struck me it might have been a test but wasn't quite sure :-/. ...and sorry if I seemed annoyed but I'm getting a bit tired of ppl without competences questioning mine which most often happens on YT (on the other hand I should have realized that there's way too many trolls for postulates to be trusted on here).

MSEE in what field?

You still have to specify the "tell me more" further though - unsure if you're asking about my thesis, QFT or...? (and what lvl?)

[QuaternionEM]

@DigitizedSelf I'm noticing that one of the biggest differnces between physics and EE is the nomenclature. Have you ever read "Classical Dynamics" by Thornton? I have a copy. I'm wondering if it's considered a good text or not. Here's a good question: What, mathematically, are the higher dimensions of string theory? Are they similar to electro- magnetic dimension or are they actual spatial dimensions. What equations describe them? Thanks.

[DigitizedSelf]

@QuaternionEM Hm, don't know the book by thornton, but try to look up some reviews (or just ratings 'n' comments on Amazon if nothing else's available... might give you an idea).

The higher dimensions of super string theory are just spatial dimensions and I'm fairly certain that they are basically just an analytical continuation of the three spatial ones we know (i.e. instead of integrating over a 3D space its a 10D etc). I'm not really that into string theory though :-/.

[DigitizedSelf]

@DigitizedSelf I'm unsure why a minimum of 10 dimensions are required though, but it is my impression that its related to internal symmetry of the theory (in what way however I don't know). Sooo, having basically said I know almost nothing about string theory here's another revelation: What are the dimensions of electromagnetism? (haven't ever heard of dimensions specific to EM...)

[QuaternionEM]

@DigitizedSelf PG?....is that you? (That's a joke. PG is a hacker friend of mine.) Anyhow, yeah.....I hate trolls who come on here pretending to be physics students...I've busted a couple of them. MSEE = Master of Science in Electrical Engineering My knowledge of physics extends to about classical dynamics and introductory QM. My degree was equal parts Digital Signal Processing, RF analog electronics, EM field theory and applied math.

[Oecleus]

I don't understand anything he did in the beginning. It sounded like he just made up an equation then manipulated the terms and talked about it. Did anyone learn anything from what he did or am I not alone in not learning shit?

[mascoteponto]

At about 7:30, doesn't he make a mistake? If he's deriving with respect to time, it should be:

mj = (dF/dx)*a + (d²F/dxdt)*v

[QuaternionEM]

@mascoteponto

I figured it out.

It took me about 1/2 hour, but Dr Susskind

is right again. The d²F/dxdt term can be written as

d/dx(dF/dt) = d/dx(dF/dx*dx/dt) = d²F/dx² * v + dF/dx * d/dt(dx/dx)

but dx/dx = 1 and d/dt(1) = 0

So we get exactly what he said.

QED

[mascoteponto]

Sorry, I think you made a mistake. The term I meant to put there is not d²F/dxdt, but rather (d²F/dxdt)*v. You can easily see my answer is right by dimensional analysis: I'm sure we agree that his first term, (dF/dx)*a, is correct. Well, that is (force/distance)*(distance/tim­e²) = force/time². His next term has different units, thus being wrong. It is (force/distance²)*(distance/ti­me) = force/(distance*time). My correction, on the other hand, has the right dimensions. :)

[QuaternionEM]

From Dr Susskind's formula mj = (dF/dx)*a + (d²F/dx²)*v²

1st term --> (N/m)*(m/s²) = N/s²

2nd term --> (N/m²)*(m²/s²) = N/s²

Your units from mj = (dF/dx)*a + (d²F/dxdt)*v

1st term --> (N/m)*(m/s²) = N/s²

2nd term --> (N/(m*s))*(m/s) = N/s²

Yours works also but it still has a time derivative which we seek to eliminate

to obtain an ODE rather than a PDE.

[mascoteponto]

@QuaternionEM

No, his second term doesn't have velocity squared. :P

By the way, I'm not criticizing him, just pointing out what I think is a honest mistake on his part. I'd love have a tenth of his knowledge. :)

[QuaternionEM]

@mascoteponto

Yes, his second term does have the velocity squared.

Here it is in black and white at 8:05.

Just own your mistake and quit crying.

[mascoteponto]

@QuaternionEM

You are absolutely correct. Every time I looked at it, I put it on the 7:30 mark, at which the expression was still incomplete. My apologies. =P

[TheBubu983]

I cant get past 5:37

[roboflop314159]

I understand that (F is a function of X) counts for the assumption that by knowing the position of any particle in the system you are supposed to know the force on any particle because of Newtons action and reaction principle that determines the force (by the masses) on one particle by the relative position of the other particles in the system. So for any given values of the masses of the objects you can compute the Force on any from position of all particles.

[roboflop314159]

This can be said and imagined for the force of gravity. In Newtons universe movement or v tells you nothing about F for it doesn't account for a force on an object or vice versa as it is the case for Aristotle's assumption.

[roboflop314159]

F depends on a CHANGE in "v" for a "m"-massed particle or in other words on "a". Furthermore in Newton mechanics the movement of a particle doesn't change its mass and so doesn't interfere with its inertia or its exerted force of gravity for it's non-relativistic. Hope that was more helpful than confusing. Hope more so that I'm not confused and in severe need of help myself.

[superfahd]

Heres something thats confusing me. How do we assume that F is a function of X. For Aristotle's law it might make sense cuz V is a function of X and T (and T is initially 0). This isnt so for Newton's law.

Any ideas?

[ibreakkidslegs]

we simply suppose that is the case

[BevanRamsden]

@superfahd We are looking at the special case where it is X, it could be a function of something else.

[Psychosmurf547]

F can be a function of x since there exist such forces. One of them is the harmonic oscillator for which the force law is F= -kx

[JovialJuggler]

please calculate the schmuck

[Chaosynthesis]

Where is the sixth course on Modern Physics? Was it not uploaded on Youtube?

[ishwarrior]

If you're having trouble finding one of the lectures, click the "more info" button in the description box to the right of the video and follow the link under where it says "complete playlist for the course."

[BarbaraPloyer333]

I'm fourteen and trying to learn a bit about classical mechanics and the Theory of Relativity (both Special and General) on my own. I want to know more about physics, science, math and the world!!!

Anybody have any tips on how to learn this through sole internet lectures and perhaps a few books (can anyone name a few good books)?

Any help---please??

You all seem to know a lot more than I do.. and I feel a bit clueless.

Help?

[BumX10]

Definitely look up Cassiopeia Project. They have lots of excellent videos on science... and I'm only 16 but I'm trying to do the same as you so don't feel so clueless -- you're off to a good start!

[BarbaraPloyer333]

Thanks for the advice... I'll try Cassiopoeia Project, then!

[bwfarmerjr]

Search google for the following:

"classical mechanics" inurl:edu filetype:pdf

Try to get the book and follow along with the syllabus. If you get lucky, you may come across a course that posts homework exercises and practice tests.

[andrew11235]

Thanks for the idea. I'm learning this stuff completely for fun. I'm starting with classical mechanics, then special relativity, then general relativity, and finally quantum mechanics (I already understand the fundamentals of these, but I lack in-depth, complete understanding).

[BarbaraPloyer333]

Thanks!

[RonT222]

There is a book on "Relativity" published for the sole purpose of educating individuals, like you, in the Theory of Relativity without the archaic insight in the complex mathematics (I got it at Barnes N' Noble for less than $10). Another book of interest is "A Brief History of Time", by Stephen Hawkings (also, an even simpler version called "A Briefer History of Time"). Plus, it doesn't hurt to build up your logic and simple proof-based concepts of geometry with Euclid's "Elements".

[bushyblowfish]

Are you kidding me? The maths isn't 'arcane' - it's necessary. Do you think you've really understood general relativity if you haven't actually written down the tensors? No. You've learnt enough to be able to impress/confuse people who probably weren't interested anyway.

And Euclid for learning physics? I fail to see what possible use this could be.

[RonT222]

Yes, the math is necessary for a full understanding of Special Relativity & General Relativity, but tell me is it at all possible for a 14 year old (like the person's comment I responded to) to completely understand Tensor Operations, Tensor Analysis, and Tensor Calculus without a background encompassing Vector Analysis or Multi-variable Calculus? This book (Relativity: The Special and General Theory) is for a conceptual overview (one I used when I was 14 yrs. old) of Einstein's theories.

[RonT222]

Also, Euclid's "Elements" helps dawn the logical process of the mind for more complex proofs (proofs are helpful in the realm of theoretical physics) and gives an understanding of basic geometry to better understand curved geometry and differential geometry. I also used this when I was younger... so when someone says Special Relativity and General Relativity does not follow Euclidean geometry, you want to know what the really means (particularly the "exclusion" of Euclid's 5th postulate).

[bushyblowfish]

Come on. This is nuts. Have you really read the whole of the elements or have you read the first few pages and the blurb on the back? If you can honestly explain how learning constructions for things like the quadrature of a lune are going to help you understand relativity then you're a greater man than I.

It seems to me that learning the maths, you pick up the skills as you go along.

PS: This will be my last reply to your nonsensical babbling.

[bushyblowfish]

No. It's not. That's why they have to go and learn all the maths alongside the physics.

[Psychosmurf547]

@BarbaraPloyer333 Don't forget to learn calculus too. It's EXTREMELY important. I mastered it at your age and it's nowhere near as hard as it seems. Just look up some pdfs on google.

[BarbaraPloyer333]

Thanks for the advice!

[fielsjd]

@Psychosmurf547

You mastered calculus at age 14? All of it? Does the phrase, "to master calculus," even have a real meaning?

[Psychosmurf547]

@fielsjd Yes. Yes. And yes. I guess if you're able to use it really well you can say you've mastered it.

[fielsjd]

@Psychosmurf547

It's very impressive that you have mastered all of calculus. Maybe you could spare a few minutes to help me out: I'm looking for a decent proof of the proposition that all non-trivial zeros of the zeta function have real part 1/2.

I understand that you might not be able to prove the whole thing in 500 characters, or you might not feel like it, but if you could just outline a proof or give me some hints I would be very appreciative.

[Psychosmurf547]

@fielsjd If I was smart enough to find that proof (which I really wish I was) I wouldn't be stupid enough to put it on Youtube. I would get it peer reviewed and published so I can get all the rewards that are out there for it.

[Psychosmurf547]

@Psychosmurf547 But, then again, I've never tried before. Hmm... you've sparked my interest in this.

[fielsjd]

@Psychosmurf547

I thought you would have already figured it out, considering that you have mastered all of calculus.

[Psychosmurf547]

@fielsjd Yeah, but that doesn't mean I've settled every mathematical problem known to man.

[noreaction1]

@Psychosmurf547

how about if you have succesfully defended your dissertation for a field in calculus against a board of people with doctorates in calculus then you can say you've mastered your field of calculus...then being awarded a Ph.D in calculus

[eedahl]

If you want a Ph.D in calculus, you're about 150 years late.

[noreaction1]

no, that's too general

[eedahl]

If you study mathematics or physics you're pretty much expected to know differential calculus by heart by your second or third year. At least at most places. It's really not a field of study anymore. I guess differential geometry, functional analysis, operator algebra, ... is the natural continuation today but I'm not certain.

[eedahl]

Did I say field of study? I meant field of research.

[TheElMarsh]

well, I guess you could talk about Analysis as being "calculus"

[eedahl]

I've always thought of calculus as being the slightly more naïve one-variable together with the multi-variable/vector case (of which the one-variable calculus seems just a special case dealing only with functions on R). Calculus is then the subset of analysis not too concerned with topological questions and more formal aspects. Still you certainly have books on 'Advanced Calculus' which tend to be introductory expositions on differential forms.

[noreaction1]

@Psychosmurf547

when you've done that then I can refer to you as a master of this thing

[TheDrakeequation521]

I think to some people that mastering calculus just means understanding the chain rule, the product rule and the quotient rule and that it helps one to follow along in the logic of Susskind's lecture.

[blairguitar]

megodzillaudead.... Mathematics is the language of physics.

[keggerous]

Man i wanna go back to highschool and actually do good, so i could take advantage of the opertunities out in the world. like learning from ppl like this!

[accord3702a]

Well, you can!! Like they say, 'just do it'...

[aradioactivedonut]

@keggerous Yes i'm sure that you will get one of the pioneers of string theory as a high school teacher.

[keggerous]

@aradioactivedonut u have bad reading comprehension skills

[aradioactivedonut]

@keggerous I rest my case.

[keggerous]

@aradioactivedonut what case is that? that u cant read properly? cuz i've known that sense u left me that retarded comment about a physicist working at a high school . . . where exactly did u get that idea? i certainly didnt write that . . . .

[toddolavi]

yeah, but think of how much they will be paid for being there..

[Kizilagac]

Too much unnecessary talk!

[almukahal]

Why does he spend over 10 minutes on F = mv, which is a wrong law. I do not see the point of it.

[adkinsjr]

It's an incremental demonstration of why we have a 2-dimensional phase space in classical mechanics. If the laws of physics were based on f-mv then the phase space would be 1-space.

[megodzillaudead]

I couldn't agree more! This is clearly for mathematicians and not physicists.

[mysitupon]

I love watching physicists do sloppy math:

You just cancel out dx in (dF/dx)(dx/dt) to get dF/dt.

Also he used the chain rule in the calculation of jerk, but you should be clear about what is a function of what.

Interesting lectures.

[MrBradGraham]

i dont get why u have 2 thumbs down. i agree lol

[mathinvestor]

To be a decent physicist requires mathematical skill and insight. I found the discussion of f=mv insightful.

[TheElMarsh]

IN classical physics, F = Mv would be a valid physical law, since it is deterministic. It's only wrong because we know from observation and experiment that forces follow F = Ma

[mexico0106]

isn't f=mv stands for the equation to calculate the momentum and f=ma is the calculation of the force apply on a object

[sephiroth317]

@mexico0106 no f=mv is not a formula. you're thinking of p (momentum) = mv. don't have a clue why letters really matter -__- they're all variables anyhow

[SpazzzDog]

That's about as meaningful as saying Newtonian mechanics would be indeterministic if experiment confirmed it was indeterministic.

[thenaughtymangareth]

these are a great set of videos! haven't done maths in a while so i've had to go out and buy 'calculas for dummies' to keep up...........

[ArianeQube]

This guy explains analytical mechanics in a clearer way than I have ever heard from a professor or read in any textbook. Just perfect ;)

[StrugatskyBrothers]

I know, right? It's awesome.

[ImTheOneTrueLordO]

Wow, he reminds me of the white wizard on lord of the rings. This class rules!

[meichenl]

FYI, in answer to Susskind's mention of the derivative of jerk, the fourth, fifth, and sixth time derivatives of position are called "snap", "crackle, and "pop"

[justwaving]

Superb! Thankyou