Classical Mechanics | Lecture 1

(September 26, 2011) Leonard Susskind gives a brief introduction to the mathematics behind physics including the addition and multiplication of vectors as well as velocity and acceleration in terms of particles.
This course is the beginning of a six course sequence that explores the theoretical foundations of modern physics. Topics in the series include classical mechanics, quantum mechanics, theories of relativity, electromagnetism, cosmology, and black holes.
Stanford University
www.stanford.edu/
Stanford Continuing Studies
continuingstudies.stanford.edu/
Stanford University Channel on KZbin:
/ stanford

[@moralester]

711,000 people viewed this and learned at least a little bit in a very short time. It was a free class taught by an extremely educated man. Imagine the world we would live in if we had this kind of access to every class

[@tvaddict7846]

Notes about lecture: conservation law conserved quantaty allowable laws of physics, allowable rules 25:40 non-allowable law (in classical physics) can't retrodict the past (opposite of predict) non reversable if reversed, unpredictive (don't know this or that comes next) 29:20 predictive one way, not retrodivtive other way not reversable, "I" don't call it irreversable 30:10 classical physics doesn't allow probability conflicts with the rules of classical mechanics quantum mechanics are not deterministic ambiguity in knowledge of initial condition, so from this statistics in classical mechanics despite deterministic 33:30 how precise do you know the initial condition, this determins how far you can predict the future, example three day weather forcast other way around, if you know how far you want to predict, then you can determine how exact you need to know the initial condition 35:50 allowable, if every state has one incoming and one outgoing arrow next example: point particle(s) moving in space 37:30 first some preliminary mathematics vectors, coordinate systems coordinate system: describing space quantitatively space with three dimensions/coordinates but we are perfectly free to think of systems higher dimensioned or lower dimensioned 38:10 we are interested in describing the basic pricipals, so we don't have to restrict ourselves to specific examples a particle can move in one dimension, it can move in five dimensions, but for now we use three dimensions 39:30 three coordinates, doesn't matter where we put the origin, but it's easiest to put it at the (? 0 location) the three axis are mutually perpendicular label e.g, x, y, z or x1,x2, x3 40:00 still ambiguity about the rotation of the axis, which direction they go in fixing the origin, we also have to fix the orientation of the x,y,z axis theres a convention, right handed coordinate system, if you pick x and y, still need to decide is z pointing in the blackboard or out of it, we settle at right hand, x thumb, y inex finger, then z middle finger points out of the board towards us this is the right hand rule another convention, for distance we choose units 41:50 point is labled by x,y,z, thats also how we describe a particle 43:10 what is a vector has both length and direction, for example a position of a point, relative to it' origin, magnitude is the distance, and it has a direction don't think of a vector of being located anywhere 43:55 vector is the same, no matter where it is drawn in space, doesn't need to be drawn in space vector labled by bar on top, more precise a little arrow it could e.g. be velocity, it could be acceleration, it could be an electronic field it's got, length/magnitude, and it's gotndirection 47:55 (see formula) length equals square root the sum of squares of its components adding vectors, multiplying vectors by numbers 53:30 VectA+VectB=VectC VectA*VectB=AMagnit.*BMagnitude*cos(winkel feda) "the calculated dot product" the product of two vectors is not a vector, it's a number 1:00:00 we can display the dot product in component form VecA*VecB=Ax*Bx+Ay*By+Az*Bz, you can prove this with a little bit if trigonometry VectA*VectA=AMagnt.*AMagnit. 1:08:40 The velocity is the time derivative of the position Dot means derivative with respect to time (so this does not have to be writtenover and over again) Velocity is x of i dot (x1, x2, x3 for the coordinates) 1:13:50 acceleration is derivative of velocity or second derivative of xi, so it's written x with 2 dots X - position V - velocity a - acceleration r-Vector for radius, positiin vector 1:16:00 Formula of an object falling in gravitational field with constant acceleration, xt=a+bt+ct2 uniformly accelerated particle, that has acceleration 2c 1:18:00 Circular motion x+y achsis, the angle increases linearly feda=omega*t 2Pi/omega=period omega is the angular frequency X=cos(feda), y=sin(feda) derivatives of trigonometric functions velocityX=-omega*sin(omega)t angle between velocity and position? more on velocity, acceleration, calculated ways for this shown

[@seandafny]

U saved my life bro

[@CreativeVery]

Lol. It's "Theta" not "feda".

[@ANOLAMCA122]

Susskind dinleyen türkler var duygulandım :D

[@iahmmei1849]

holy ish dude i cant believe u took the time

[@yagmuraljaerhan9804]

Ayıp ettin

[@bobrericha]

I love this man. The way he explains things, the way he talks, the way he thinks, the way he moves, his wisdom. Having watched many of his lectures, I feel a deep friendship without ever having met him in person. Thank you so much, Lenny.

[@YasoHisham]

How are u doing now, 3 years later

[@mtmind6560]

@@YasoHisham They got married.

[@sisypheanexistence8955]

​@@mtmind6560a beautiful relationship blossomed after such hard Dick riding

[@math.physics]

I remember watching videos like these before college, which definitely kindled a passion for physics and math deep inside me. Then I also started reading advanced books, which were not even part of the course syllabus, for example the famous series of books published by Lifshitz and Landau. Among other things, I published the step-by-step solutions to many of the classical physics problems in the first book "Mechanics" in an online course on Udemy (called: "Multivariable Calculus and Classical Physics problems"), which deals with the mathematics and physics of rigid bodies, non-inertial systems, and much more. This is to say that videos like these can be very helpful in inspiring youngsters to appreciate physics.

[@mpay2874]

The Udemy course you mentioned is not showing up. Is that still available ?

[@math.physics]

@@mpay2874 Oh I see, now it has a different name, it's called "Multivariable Calculus and Classical Physics problems", I decided to merge two courses into a single one, due to the strong connection between the two. So, yes, it is still available.

[@aayushpandey6725]

I'm in final year of my high-school and I'm slowly starting to love physics. Thinking about studying physics in undergraduate. So, spending my time watching these lectures.

[@Akshaygupta13]

49:05 Yes professor, your lectures are like the music that one want to hear over and over again. ❤️

[@jcnotnot8120]

First 16 minutes is the most succinct and persuasive explanation for conservation of energy I’ve sat through. A lot of people tend to explain it through tautologies.

[@Darkownage2]

Thanks Stanford. These lectures really get you interested into science and just the aspect of being in a university itself.

[@nandha0150]

Extremely thanks for providing such quality content for free of cost and enabling it to be accessible from everywhere. #LovefromIndia

[@ThePhysicsConnection]

Nandha Kumar yes this is one of the great things about our world today

[@of8155]

❤️

[@joabrosenberg2961]

Coin and dice configurations and laws of motion, conservation; infinite configuration space 22:00; non allowable laws, reversibility 26:00; vectors 37:30; particle position and motion and acceleration 1:05:30; 2 examples: motion on a line, circular motion 1:15:00;

[@PianoImprov.rjgc1991]

Indeed your lectures are amazing everytime we hear them.

[@mileswetherington5628]

Native English speaker and I literally just learned the word 'retrodict' (opposite of predict) from Lenny. The perks of this class are boundless.

[@whannabi]

Not a native speaker and I learned die and retrodict too

[@saikatislam1221]

hello brother

[@halilibrahimcetin9448]

You are the definition of people who are awesome, Professor Leonard Susskind. LONG LIVE Leonard Susskind. We need you like how we need water to live.

[@BadAssBradders]

100%

[@supern0is349]

jesus this is incredible it's like watching the hulk trying teach someone how to lift a 10lb dumbell

[@ryanyoon6772]

Super N0iS3 😂 lol bro

[@randomblueguy]

@Andrew Walter III Kaamo 'D La Simmetrie what the fuck

[@Joepage69]

@@ForeverStill_Fan1 and physics.

[@sadunfdo2888]

@@Joepage69 Don't use phone then. Be a Priest. Without Physics you are still trieng to use Pigeons as mail man.

[@Joepage69]

@@sadunfdo2888 physics is very much the unknown that was my point it changes all the time

[@christophersoelistyo1905]

53:30 That little slip from his Quantum Mechanics lectures

[@lgcookie1933]

Christopher Soelistyo I know this is a super old comment but HAHA I saw that.

[@ThePhysicsConnection]

These lectures have changed my life! Watching this feels nostalgic!

[@rationalsceptic7634]

One of the World's leading Physicists and Teachers, showing how to teach Science

[@MrKinaidos]

Thank you Leonard and Stanford for this. The extras and insights mean a lot. You could lean this stuff from a Dover reprint, but learning it on a trajectory towards Scrodinger and company really helps one focus on what counts. I have been able to make quantum work for a long time, but I find myself returning to the roots over and over again to regain a sense of what I'm actually doing. I think lecture series like this are invaluable for contributing towards a future in which a significant subset of us understand what the world we can make claims about actually us.

[@maniacidus]

Mike from Breaking Bad

[@toplobster5374]

Now , I can't unsee😂

[@IAyala1010]

Put your pencil away Walt. I’m not having a lecture with you.

[@Optimumprime728]

@@IAyala1010💀💀☠️

[@JLongTom]

46:00 When a world-leading theoretical physicist struggles to draw a vector in three dimensions, there's hope for us all.

[@user-zk1wf7le2t]

it's normal. My grandfather Ph.D in his 80 can't even draw a 2d vector lol

[@mmartin5816]

JLongTom Lenny in perfectly imperfect!

[@jeffrey8770]

Даниель Крузе (But u didnt say what area your grandfather specialised in, lol.

[@ruskodudesko9679]

not in art ^

[@ThePhysicsConnection]

JLongTom haha

[@DrDress]

I clicked classical mechanics and I'm watching graph theory. This is gonna be good!

[@GGyinyie]

Thank you stanford university for making this free to everyone, i decided to study physics however had (in germany) to decide between chemistry and physics as a school subject, i chose chemistry inorder to at least have some fundamental knowledge about it. Now i figured out that german university have their lectures uploaded however only on private servers which are unacessable to anyone whos not in their university. Thanks for giving me the chance to learn the basics to prepare for university

[@WorldBurial]

I really like the book as a companion to these lectures. It gave me deeper insight in some physics concepts that I used to just "take for granted" otherwise. The exercises also help for that matter and I can't wait for a quantum mechanics sequel and the rest of the series.

[@afifakimih8823]

He is always extraordinary..he always find the simplest version of explaination!!if anyone don't understand him,he never understand physics.

[@n3r0z3r0]

Last 15 minutes, describing of circular motion, was awesome! Everything become clear!

[@ozdergekko]

Finally I found someone who is going to teach me the concepts in math I need to understand my big love, astrophysics, a little better. That it's such a famous physicist, the better. I'm somewhat proud I still remember and understand most of what he talked about in this lecture although I graduated from high school 38 years ago although I never really needed this since then.

[@tomstalley3179]

listen to startalk if you love astrophysics!

[@JRush374]

ozdergecko the Closer to Truth channel has a lot of good conversations about cosmology and astronomy stuff.

[@puspita282]

@@tomstalley3179 can you comment the link of the channel? or is he a person?

[@tomstalley3179]

Puspita Das just search ‘startalk’ kn KZbin, it’s Neil degrasse Tyson’s channel

[@spunts144]

Wow. That cleared up a lot for me. I'm looking forward to the next lecture.

[@neonblack211]

I've never seen a video on classical mechanics that quite starts like this, informative

[@MANOJTIWARI-ni8jr]

Highly insightful lectures I ever came across, thank you sir for your work

[@Red-bb6qj]

Just 10 minutes in, I already have a feeling I'd learn more once I finish watching this vid than 10 hours in class...

[@davidbennett3046]

Professor Susskind, thank you for these videos. Theoretical Minimum Classes suit me to a tee. I really like them.

[@AT-27182]

49:09 Such a good analogy. And yes, Prof. Susskind, your lectures are like good music. Bravo maestro and thank you.

[@rickperez8975]

This was hilarious

[@aravindhvasu195]

For those, who are starting this course..... It's very slow and a bit dull, But it's THE best. He won't show you experiments and stuff , but all your common questions and misunderstanding will be addressed in this course. Really it's the best.

[@GustavoMartinez-tx5cr]

This is amazing. Big Thanks to Stanford and to L. Susskind.

[@monnsideol]

Leonardo,your lectures ARE music to our ears

[@notagain3732]

Once again im glad to find a lecture from stanford to help me learn more

[@Tinydude10]

This is fantastic, thanks to Stanford and professor Susskind :)

[@user-wd7yu1eo2f]

oh its unbelievable... Thank you so much to Standford and this gentle man

[@GregoryEvansRacing]

These videos are absolutely fantastic. Leonard Susskind is amazing!

[@redfire1508]

Could please activate in the video the option of automatic subtitles, that depends on the administrator, if they do not activate the other people does not get that option. Podrían por favor activar en el vídeo la opción de subtitulos automáticos, eso depende del administrador, si no lo activan a las otras personas no le sale esa opción.

[@jayashreekuila2637]

This guy teaches classical mechanics in one class and can teach string theory in the other, hat's off to you

[@nazishahmad1337]

53:25 That's what happens when you do Quantum mechanics alot

[@emonfromearth]

This made me laugh 😂

[@askhetan]

hahah!

[@gibson362]

Hey do u know what the general eqn was for the six-sided die? I cant figure it out

[@paxtonpoyiposida8901]

Ah my god

[@pinklady7184]

Which is easier, classical mechanics or quantum mechanics? I am only just today starting to study classical mechanics.

[@adinewsahilu5140]

I would like to thank the professor for his nice and interesting lecture he did!!!!!!!!!!!!

[@pranshupandey4703]

Loved the lecture so much.

[@bulentkarakis]

What a great lecture & what a great lecturer.Thx.

[@abhinandanmalhotra8519]

This is the thing with top Institutions... They teach you 'how to think' rather than what to think.

[@Chillyman010]

This is invaluable, i love learning tho I cant afford to go to a big university

[@clairerogerson2153]

In

[@Adolfofficial9]

r u alive now

[@jolanmoussier9267]

Bad for you to not be french

[@tomassanchez6010]

You can apply for financial aid

[@vgdfgvv4381]

@@jolanmoussier9267 what?

[@WorldBurial]

The book is called The theoretical minimum. Authors Susskind and Hrabovsky. The latter added some extra mathematics parts where needed. Electromagnetism is discussed, Hamiltonians, Poisson brackets etc.

[@lgcookie1933]

Susskind: *show a group of people how to draw a simple 2-dimensional graph* Also Susskind: *Assumes that the same group of people can differentiate trigonometric functions*

[@sirius3333]

@@hiruki8 u didn't get the joke lol. Susskind tries to explain simple stuff and skips over relatively advanced stuff ( students know both) but just the way he is going on

[@alegzyi]

@@sirius3333 I think she just explained it further

[@Neomadra]

I have a question: Are there exercises (and solutions) that was made for this lecture? I really like Susskind's lectures but I think one can only learn, if you do exercises. So I'd really like to get access to exercises that fits to this lecture. If anybody can give me some hints, where to find such exercises, I'd be very grateful. :)

[@kris2k]

it always music to my ears , thank you very much

[@thirukumaran3631]

A wondrous lecture in classical mechanics

[@Anklusos]

Put it at 1.25 speed. Saved my life.

[@MrGoatflakes]

+Klanos 2x and 1.5x for me, but I had to go back to the stuff on dot product and proving the law of cosines cause I was playing Factorio and not paying attention. I love the speed feature of KZbin. I feel like I have been robbed of some of my life because I didn't discover it sooner xD

[@srirampard]

+Klanos You, my friend are a fucking genius and I would forever be in your debt!

[@hicham5770]

thank god i went down here before i saw the vid

[@landonazbill122]

Thank you so much!(:

[@exxel1701]

Great suggestion. Thanks.

[@valtih1978]

Thanks for the download option. Pleas provide a link to playlist, eg. Classical Mechanics | Lecture 1

[@tamimyousefi]

53:25 HAHAAHA best thing to write in classical mechanics.

[@aaqidmasoodi]

So In Love With Leonard Suskind.

[@harishli2020]

thank you so much..... I learned many new things about vector's,before which I didn't get even after watching many other videos.....you are awesome...... :)

[@ahmadrezakhazaie6305]

Will he talk about the Hamiltonian mechanics and Legendre transformation later in this course? I am looking for physics underlying Symplectic and Poisson Geometry would appreciate it if you introduce some materials to me.

[@ghostape]

My brain lasted for 55 minutes. Started to watch bits again more to try and understand. Great lecture.

[@lostsoulsco]

He look like mike from breaking bad

[@digggert]

exactly what i thought :D

[@Mahmood42978]

AyoJeffy He IS Mike from Breaking Bad

[@Pantera1001]

nah he looks like mike from better call saul

[@peterreznikov6464]

Admit

[@Spractral]

Was thinking this watching season 5 of community today .. Sounds like him anyways

[@dve845]

1:23:33 Actually, the dot product being zero isn't enough information to draw the velocity vector. The sign of vx tells you what direction the perpendicular vector is pointing in.

[@darkerthanblackstudios2128]

I had lost my way and my love of physics due to depression. Decided to take a break from my astrophysics studies for a year. I think I will spend the year going through his lectures just to see if I can fall in love with physics again.

[@agrajyadav2951]

if u dont love physics, u literally dont want to understand reality, and that's like death

[@MyJigarpatel]

I am very much interested in mass, acceleration, force, distance and energy. I like this video. He explains in very simple manner.

[@JohnRampton]

Wonderful Lecture, thanks for the laws of motion lecture.

[@dadesway]

Confused? Sloppy? Look at his lecture on 'Demystifying the Higgs Boson' - Of all the lectures this was the clearest overview of all of the great rash of such lectures that came out this year. I find the lectures leave me just enough to think about and sort out myself. I am a big fan.

[@DefendEuropa1488]

this is such awesome content, thank you so so much !

[@friendlystonepeople]

Yes, but perhaps the world is full of people who do not have the same grasp or perspective. Plus, one can never over emphasize the basics. This is what separates great teachers from ordinary ones. I find that a lot of the students brush through the basics and find later that they do not have a deep understanding. The concepts of state/phase space are actually not as simple and are so critical in understanding a lot of the world, it is worth spending some time on. He is a great teacher!

[@ozzyfromspace]

[Paraphrased] "There are some things you only want to experience once, like a book. You don't want to read the same thing over and over again. But there are other things, like music, that you'll want to listen to continually because it just feels good. I hope my lectures are like that... (paraphrased)." Why yes, Professor Susskind, your lectures are a treasure to listen to. Stanford for the win. :)

[@carl14706]

The point of using modulo arithmetic is that you don't even need to assign value 6 on the dice to 0, because 0, 6, 12, etc. are considered the "same" element (they belong to same equivalency class).

[@MindAndLogic]

Well I am a high school student and I am glad that some great universities give a way knowledge for free. I love Walter Lewins Videos he is a great lecturer but they are limited to classical mechanic and electromagnetism. nothing complicated just freshmen's physics.

[@unknownaspect-seba4749]

didn't know mike ermanthraut had the best classical mechanics lecture series on youtube

[@comprehensiveboycomprehens8786]

I really feel like a turkey sandwich right now.

[@ThePhysicsConnection]

Comprehensiveboy Comprehensiveboy haha

[@levi83]

me too

[@pinklady7184]

While watching this video, I feel like eating a wrap with chicken, spices, lettuce, sauces, etc. Add chips (French fries).

[@lazyboi5726]

@@pinklady7184 Chips. Luvley

[@theunusual7631]

me too bud

[@alanism3d]

I agree, Lewins is a great teacher as well, he's awesome.

[@shyamvijay8985]

It's a bit confusing that he uses dice and coins which are in the realm of probabilities to explain deterministic outcomes and states of a classical system

[@mk16ification]

Im watchign this and I thought of the same thing!! I still havent been able to come up with an equation unless you have some sort of condition to evaluate inputs and return the right answer..you find a solution??

[@mantapoke-jf8jp]

For free???

[@milanvarghese]

According to this source, dice was once the plural of die, “but in modern standard English dice is both the singular and the plural: 'throw the dice' could mean a reference to either one or more than one dice.”

[@netrapture]

at 19:03, the laws of evolution for die world are categorized by number and TYPE of cycles, e.g. there might be three cycles: one 1-cycle, one two-cycle and one 3-cycle, like his example but there could also be three 2-cycles, so it is more than just the number of cycles - as he hinted.

[@_titanslayer_]

my like was the 7,000th. feeling very special.. lol Stanford, thanks for sharing these priceless knowlege with the world..

[@Rain.Mippet]

Finally something that isn't boring!!! Hi I'm 15 years old, and thank you internet for quantum mechanics, Now let me learn this first so it makes more sense...

[@Neander104]

5 years later.. How did it go?

[@MikeRoePhonicsMusic]

How I recommend watching these videos: 1 Get some notebook paper. 2 At the top of every sheet, write the KZbin video's web address, KZbin Channel & video name. 3 If Prof. Susskind writes it down, you should also write it. 4 Write a timestamp on the left side of your notes so you can easily get back to a given subject. 5 Pause when needed. 6 Re-watch a section if you're still unclear. 7 Go to Khan Academy if you need to brush up on, or learn new math concepts ( kzbin.info )

[@restitutororbis964]

MikeRoePhonicsMusic Thats exactly what I did, but with another youtube channel named Prof. Leonard, he teaches calc, great teacher btw. Ive filled 3 books worth of calculus, im at calculus 2 rn.

[@serenarife2344]

OneInfiniti MathBoi I watch Professor Leonard.

[@nitotech]

I agree Prof Superman (Leonard) is awesome!

[@Charles-br5ub]

Imagine explaining physics in a simplified way thanks alot

[@potugadu5160]

I have a question: I plan to watch all these lectures by Mr Susskind on classical mechanics, but will I get anything out of these lectures without an accompanying textbook? Thanks.

[@loctran9742]

+potugadu Yeah, I'm in the same situation and I've found something interesting here: ocw.mit.edu/courses/physics/8-09-classical-mechanics-iii-fall-2014/readings/ Hope that helps!

[@potugadu5160]

+loc tran Thanks. Honestly, I prefer not to read a textbook. I am neither looking to pursue a career in physics nor knowledge of physics required for my job; I am just curious about theoretical physics. So, I wanted to know if I can get by with just watching the lectures. I am willing to put pen to the paper, though. I did calculus based physics in high school & for a quarter in college long time back, and I consider my knowledge of physics & calculus still pretty good. BTW, lot of reviews of Landau & Lifshitz on Amazon state that it is not a beginner's book. A book by Georg Joos was recommended instead.

[@loctran9742]

+potugadu Totally right! Landau is horrible even for the ones who study physics =)), it rather be a doc for reviewing when you've already cover all the stuff, I think. If you want to dig (but not too deep) in the physics, Taylor's or Thornton & Marion's would also be a good option. Or you can wait until the Edx have this course. It's well-fitted to those who prefer self-study, especially to study without reading textbook. :)

[@potugadu5160]

loc tran Thanks for recommending Taylor's book. Read reviews that it is a perfect book for self study. An edx/online course on theoretical physic will be great for learning with some structure & discipline, and also to finish the learning/course in fixed amount of time. For me, any study/learning with no deadlines means never completing the study.

[@THEGREATONE420]

+potugadu the best accompanying to this playlist is Susskind's book "Theoretical Minimum: What You Need to Know to Start Physics. and for the playlist on Quantum Mechanics is his other book.

[@subrotochatterjee5788]

13:55 The die could turn into any number of sequences, including REPETITIVE ones, for example.1,4, 5, 5,5, 5. The equation would change accordingly. So, is it deterministic?

[@anything_useful]

Loved the way he forgot and put ket bracket instead of modulus at 50:00

[@IWolfGod]

Best teaching ever.

[@phyaphysicss7055]

Nice video quality. What textbook was used for this course, btw?

[@shoyo_Ishida]

Can someone please tell me that what dose the sir wants to explain in first 40min I mean is it Graph theory or something else

[@andrewnoonan5275]

Time in nature might not actually be the abstract of perceiving it as going back or forward to actual events but instead are actually the observable chronological movements of objects that are speeding up or slowing down "DEPENDING" on the level(amount) of gravity and perhaps G-force that's constricting or not constricting the atoms that gives the "OBSERVABLE CHRONOLOGICAL MOVEMENT" we all see around us

[@abrahamleo3907]

Top notch lecturer♥️

[@TheZombe23]

So then let me ask this, if it is in state zero would it also be at absolute zero for the quantum or is it just going to stay at perfect zero

[@gmwm5419]

You speak a tune with your voice so yes you make notes and numbers sounding like a song 🥰

[@yankumar5280]

thanks for sharing Stanford

[@fadelali330]

Awesome lecture!

[@jattprime2927]

does anyone know when he goes to cross product? I don't understand why we take away the j-component...

[@TonyqTNT]

Can someone explain how a boxer imparts force to an object mass with the execution of his or her punch? Is power exerted by means of kinetic energy or momentum?

[@kingjeremysircornwell7847]

Regulate surface temp to know/control weather patterns.

[@varshneydevansh]

I am loving this

[@Sundayfacts]

Very well explained ❤️❤️🙏

[@LloydSMITH]

Thanks for your work : )

[@primalpiano7580]

Lloyd Smith you have the Coolest channel ever !!

[@loden5677]

Are there worksheets and problem sets which accompany this series of lectures?