All physics explained in 15 minutes (worth remembering)
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- เผยแพร่เมื่อ 14 มิ.ย. 2024
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Five areas of physics worth remembering: Classical mechanics, energy and thermodynamics, electromagnetism, Relativity, and Quantum Mechanics. Classical mechanics - two main concepts worth knowing. The first is Newton’s second law: F= ma: Force equals mass times acceleration. If you apply a force to a fixed mass, it tells you how much acceleration you will get. And knowing acceleration which is the change in velocity, you can make predictions.
The second equation is the law of universal gravitation. it allows us to determine the motion of heavenly bodies. It says that the gravitational attraction between two bodies is the product of their masses divided by the distance between them squared, times a constant, called Newton’s gravitational constant.
Energy is not a vector like force or momentum, but it is just a number. Work is closely related to energy. It is force times distance traveled. Energy for most objects consists of kinetic energy plus potential energy. KE is the energy of motion, It is KE = ½ M V^2 - the more mass you have and/or the more velocity you have, the more energy you have.
Gravitational potential energy is expressed as PE = m g h - mass times the gravitational acceleration times the height. The total energy of an object is both Kinetic energy plus potential energy. Potential energy can take many forms. Gasoline or petrol has chemical potential energy. Important: Energy is always conserved. It is not created or destroyed. It only changes form.
Thermodynamics is the study of work, heat, and energy on a system. We showed energy is how much work you could do. But another form of energy is thermal energy. If a car is moving and you apply the brakes, the kinetic energy of the car gets converted to thermal energy, created by friction of the car’s brakes. Temperature is the average kinetic energy of atoms in a system. Thermal energy is the total kinetic energy of atoms in a system.
Entropy is a measure of disorder, or more accurately, the information required to describe the micro states of a system. The 2nd law of thermodynamics states that entropy of an isolated system can never decrease. Energy at lower entropy can do more work than energy at high entropy. The one way flow of Entropy seems to be the only reason we have a forward flow of time.
Electromagnetism is the study of the interaction between electrically charged particles. The essentials are in Maxwell’s equations. If you have a static object with a charge, it will affect only other charges. If you have a static magnet, it will affect only other magnets. It will not affect charges. But if you have a moving charge, it will affect a magnet. And if you have a moving magnet, it will affect a charge. The constants mu naught and epsilon naught are the permeability and permittivity of free space. These two constants determine the speed of light because they measure the resistance of space to changing electric and magnetic fields.
Special Relativity: Einstein presumed that the speed is the same in any frame of reference. This was one of the postulates.
The second postulate was principle of relativity - the laws of physics are the same for all observes who are moving at the same velocity relative to each other. Einstein showed that the only way these can be true is if time was not fixed, but was relative.
General relativity: Later Einstein showed using the same assumptions, there would be no way to tell if you were in an accelerating reference frame or standing stationary on earth. A flashlight beam will bend in gravity. But since light always takes the shortest path between any two points, this means that space-time itself is bending.
Quantum mechanics: Three principles are important. First by Max Planck, says that energy is not continuous, but is quantized. The amount of energy equals the frequency of the radiation times Planck's constant. Using this, Einstein later showed that a photon is both a wave and a particle.
The second is the Heisenberg's uncertainty principle: you cannot know both a particle’s exact position and it’s exact momentum at the same time. For a particle with mass, this means if you know exactly where a particle is, you don’t know how fast going. If you know exactly how fast it’s going, you don’t know where it is.
#allphysics
#arvinash
Schrodinger's equation: prior to measurement, quantum systems are in superposed states. This means that their properties can only be expressed as a wave function. A wave function simplified, is a set of probabilities. So in a hydrogen atom, you can’t know where to find the electron in advance. All you can know is the probability of where you might find it, if you measured it. Prior to measurement, all quantum systems are waves of probabilities. This is not a limitation of our measuring devices. It is a limitation of reality.
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For those that want more in depth information on some of the subjects I talked about in this video, here are some detailed videos I made:
1) Newton's Law of universal gravitation: th-cam.com/video/MApnf7L4g44/w-d-xo.html -
2) Entropy: th-cam.com/video/T6CxT4AESCQ/w-d-xo.html
3) Electromagnetism and the speed of light: th-cam.com/video/FSEJ4YLXtt8/w-d-xo.html
4) Special Relativity: th-cam.com/video/ZAf7FXih-Jc/w-d-xo.html
5) Einstein's General Relativity: th-cam.com/video/tzQC3uYL67U/w-d-xo.html
6) Quantum mechanics basics: th-cam.com/video/fP2TAw7NnVU/w-d-xo.html
7) Extra Credit: 4 fundamental forces of nature: th-cam.com/video/669QUJrF4u0/w-d-xo.html
Arvin Ash Thank you Arvin, you rock!
So a weighing machine shows us our mass??
@@impracticalwill2771 No it shows us the weight which is force times mass. If you take that machine to the moon, it would show a different number.
@@ArvinAsh ooo thanks 😀
th-cam.com/channels/RF3J0ALbtztpYya4lEdr7w.html
Well if your going to teach physics you gotta start from the beginning, it’s a warm summer evening in Ancient Greece
I know where this is from🤣
Big bang theory
WOW...WISH TO BE THERE
Hahaha sheldon cooper ❤️
LMAO
I like how he explains the speed of light at the speed of light.
c is the symbol for lightspeed.
.5c= 149,896.2km/s
For americans.
149896.2km/s= 93,141.18mi/s
1c= 299,792.5km/s
For the US .
299,792.5km/s= 299,792,500mi/s
I feel like I should add reference examples but its like crazy fast..
.5c = 440,495 .45 mach if that helps
And didn’t age a bit while doing it
lol exactly
why this is so funny?
It’s insane that the same subject I hated and was forced to learn in school is the same subject I am up at midnight binge-watching for fun 🤩
Same here! 😊
Same here.
Infact I am thinking whether I can restart my learning from the scratch after many years of being a commerce student and professional!
Some things you have to grow up to and experience life to get to. And Sometimes You have to smoke bunch of cannabis to Want to learn about physics😂👍
@@unknowngba aiiiyoooo meee too
are you will to open a textbook book and solve basic kinematics problems?
I'm late to this party but I wanted to let you know that your explanation of relativity and the graphic of the two trains has helped more of my physics students than any thing else I have come across. Simple. Elegant and accessible. Thanks for the great videos.
Glad it helped.
Bro 456 likes and just 1 reply (now2) that too from the channel itself 😂
5 yrs of engineering and I still don't really get entropy
i heard that taking off the word "disorder" would make things easier to understand, and it did.
Energy can only do things when theres different concentrations in different areas, for example a cold spot and a warm spot. You can use this to do whatever you want, make kinetic movement with an engine or catalyze a chemical reaction. But entropy and inneficiency means that the energy will become useless once it mixes. The cold and hot spots will become just warm, and there will be no way to use that energy to make pressure differences or anything else because in order for _anything_ to happen, there must be a flow of energy, from high to low or low to high. But when it is all average, there stops being high or low.
Another way to describe it is to stir a cup of water. There is energy in that glass, shown by the water's movement. But with entropy, the water stops swirling. The real life problem is that this is the state the universe is in. For the cup, you can just stir it to give it more energy, but you can't just give more energy to the universe.
Nobody does.
Entropy is information gained
When your final Physics exam is in 15 mins and you barely studied anything:
I joined a quiz bee contest and this is what Im watching 2 hours before the contest as a review lmao
@@irahngio I'm guessing that your quiz is done, how did it go?
هههههه
Thats nothing to be proud of
@@andrii5054 sorry mom...
This is exceptionally explained. I was also a student of physics and can somewhat understand the complexities involved. I only wish that he should have taken half an hour instead of 15 minutes. Hats off to you Sir and thanks.
4 years of engineering and i have to say he got most of the useful stuff for anyone in here.
It's always nostalgic seeing how easy some of those equations look at first glance XD
Physics is not about remembering ,
Physics is about Concept
- Walter Lewin
Well sometimes our Physics teachers are not good or are just boring when teaching concepts in physics.
Walter Lewin is DA BOSS
@@gaudencioalejandre118 then find other ways to learn such concepts. i was curious how helicopters worked and the videos i watched didnt throughly explain gyroscopic precession so i spent hours learning what just one concept was so i could understand the rest lmao
Fire determination
I think you should stop quoting Walter Lewin. He is a stain on the physics community now.
Here we go boys. I'm about to become a physicist.
Pfft 😂😂😂
Right here withcha
Me too. Lmao
😑😑😑😑😑😑😑😑😑😑😑😑😑😑😑😑😑😑 (-_-)(-_-)(-_-)
(-_-)
👕
👖
Good luck
Arvins videos should be mandatory learning for fundamental physics courses taught in our educational institutions. They are similar to the mechanical universe series video courses and describe various principals of physics with astonishing simplification and clarity. Bravo Arvin.
First day of 2022 and I’m sitting here with a Blunt digging deep into this. Quantum Mechanics has peak my interest heavy. Thanks for the content ! Science is life.
Me too!!
As a physics PhD student, I gotta say, your videos are some of the best I’ve seen at explaining physical phenomena. Thank you for making these to have more people interested in physics, everyone should appreciate the beauty of this subject.
Thanks, I appreciate that. All the best in your pursuit. The world needs more physicists!
@@ArvinAsh I am 14 and I wanna to do something with physic but I don't really now what jobs are with physic
I bet this guy isn’t actually a PhD student
Big Ole k
@@Black-vt5vb ask your physics teacher.
Still a very underrated channel.
☹️☹️
I feel I have a reasonable chance of understanding Arvin. Even the really hard stuff.
Hey guys if you like space videos then do visit my channel once pls 🙏 🙏🙏 🙏😊
@@EXOPLANETnews I have space but I don't have time...
It has space for improvement but t needs time... If Arvin removes his materialistic bias...
I never truly understood the difference between weight and mass until I heard your explanation. Thank you.
If someone asks for your weight tells them it about 800 Newtons oh you mean mass 81 kilograms. 😆
you explained physics in 15mins better than my professors did the whole year !!! total support
Me: I feel like I know everything
Exam: “*gets 0 score*”
*surprised pikachu face*
Because you get nervous in exam room🤔
Getting marks is not important what did you learnt is important
@@botyashgamer6082 i couldn’t have said it better myself.
@@botyashgamer6082 You're right, I myself prefer understanding things first rather than just applying all kinds of equations and formulas that I don't fully understand why they are like that or where do they come from.
Duuuuude. For years and years I never understood why time slows down when you move faster. Your diagram with the two flashlight beams completely cleared it up! Subscribed.
You can't sense the difference by moving normally, it's like a fraction of a second
Same, i finally understand it now
And you most likely have misinterpreted it, because it was explained very badly and easy for someone to misunderstand the concept.
@@ericstout7336 You dont.
Time doesn't slow down for you when you're moving fast, your "proper time" is always the same. Your time just appear to be moving slower from the perspective of a second observer outside your inertial reference frame.
Edit: Then if you change directions and accelerate back towards the second observer, their clock will be moving a lot faster from your perspective. When you finally complete your journey and return to the same frame as the second observer, they will have aged a lot more than you.
The chillest, most informative, coolest TH-cam channel!
Really good when one once had more detailed knowledge but it faded. This brings back a framework of context. Reflecting on it, I then begin to piece the details into place. Love it!
Thank you so much for your insight and for how you rendered these deep and hard concepts palatable!
Newton: “Okay let’s just use this small apple as an example of one Newton for this demonstration on my theory”
Physicists hundreds of years later: 1 Newton = one small apple
Is tgat true, 1 apple = 1 Newton? It confuses people outside physics fan you know😅
Fatima Al-Amri it’s close since an apple weights around 70-100 grams F = ma, = 0.1 x 9.8 = 0.98N round up = 1N so yeah its 1N obviously not all apples are 1N but they average out to be 1N
@@cattyom3 no sadly not, that would be incredibly funny! A Newton is 'simply' 1 k*g*m*s^-2 (F=ma, so the units for mass and accelerations multiplied), so one newton is simply the force on an object accelerating at one m/s^2 (one meter per second per second) that weighs one kg. This makes it so that you don't need a constant in his second law which is ofcourse very handy.
@@mcbutt6149 you know I just started getting into these physics vids and this comment proved the physic major stereotype of rounding 🤣🤣 "0.98,round up, equals 1"...."pi essentially equals 3"
I fig Newton equals 3 small figs !
Key takeaway from this video:
I weigh about 712 apples.
Ah yes america
Key takeaway comment for your stalker and FBI agent
[ star-spangled banner plays in a distance ]
I Weight 637 apples lol
this video is absolutely not for science students cause they know it , if they didnt then they are not science students
You're one of few people who can give me a headache and still make me smile and like your videos.
Good job, Bald Ape! I really enjoy these lectures. This was just below my level, as a physician, but others are just above, so you hit me just right.
He is expressing all phenomena better than my professor.
J D lol. here comes the gatekeeper.
What a condescending prick you are. As a comment on the generally failed classroom format, it’s valid enough.
Hey guys if you like space videos then do visit my channel once pls 🙏 🙏🙏 🙏🥺
@J D so, you figured out electrical charge without experiments or being taught?
In Quantum Mechanics it is called interpreting...
I’m an art student who slept through almost all of those classes, failed miserably on both math and physics in high school, yet somehow youtube is making me fascinated by them rn.
Because it's a different environment in school. Learning because you are forced to learn is way different from learning when you want to.
@@waikard267 Yes, but I also disagree at the same time. Clearly people are interested in science regardless. People like learning about the comprehensible side, like how energy cannot be destroyed nor created, or how photosynthesis works in plants. They dont want to know the equations, the prerequisites, or doing the exam. It can be boring. Science is interesting to many, but not many wants to put the effort into it.
@@waikard267 lol no. People with natural curiosity about nature will always go for stem courses.
Arts isn't essential for your making sure your species survives. It's just there to diversify what already exists in terms of "culture". Sooo not so bright people like that because it's dumb and easy to understand.
It's simple as that . Take any science student and throw them in an arts class and they'll still score more than your arts students. Throw an arts student in an science class . They'll fail miserable.
Regardless of your environment
@@SumitYadav-ik2df if only all Indians can walk the talk and make South Asia a better region. Your argument whatsoever holds no substance. Just that typical brag one would expect from an Indian. I was dumbstruck by your shallow cleverness. Did you score 100% for JEE and whatnot or something 😮
@@marinaaguas9219 haha why bother arguing with that typical Indian? Not just supporting the disgusting Israhell, but also proud with their castee stuff. God.
An inarguably noble project, and nicely done! Cheers.
As professional in subject and being skeptical about 15 mins of physics want to say big thank to author - good job.
Excellent. This is the most important thing we have: science and knowledge, not money
Money is apart of economics isn't it? That's important in a different realm of society.
@@andromedaiscoming185 money is not bad, is necessary in the world that we live. The problem is when money is the goal of life, is a big mistake because generally is opposite to knowledge
@@emiliomencia7429 ok yes money doesn't equal emotional well being, I agree. Lack of money though can be very painful because society is built on it. if you can't contribute to society you don't make money, if you don't make money you don't eat or have a place to live then you have to rely on charity or government help or you just become homeless on the street. That's society. Before money it was land and cattle and gold and silver. Gotta have something that's worth something. If not you have to go into the woods and grow vegetables and fruit trees and build a house from logs and build a chimney to keep warm and kill animals for fur and protein. That's ok but you'll be outside of society.
Science and Money compliment one another. Without money science won't be developed further, and without science generating money isn't truly imaginable in this day and age.
@@andromedaiscoming185 freud would say would wise
If any Indian students are seeing this , then remembered and learn this whole video line by line because whatever in this video says this is a summary of class 11th and 12 th physics in India...by understanding this video properly can lead u to feel easy to understand class 11 and 12 th physics.
After board exam 20-21 cancelation I'm watching this 😅😅
@@amarjeetyadav8302 me too 😎
you guys learn thermodynamics and relativity in 11/12th class?
@@I_Am_The_Pataphysicist yeah in 11 but why ?
lol most of this is 10th or 9th grade stuff
Thank you so much Arvin! I enjoy your videos so much!! 🙏
Years of physics and never understood why time slows down but this video made me finally understand it
8 years of physics lesson in just 17 minutes
This is all just basic stuff
Yep it all changes when you actually have to solve problems.
@Science Revolution my brain hurty
@Science Revolution Cheeseburgers~👉🍔
@Science Revolution they are not replying u just because there are some limitations to Ur theory
As follows :-
1)the electrons or protons repel each other but they get weaker by increase in distance b/w them as they result in being constant.
2)the electrons in mass are capable of repulsion force created other wise it will just of few distance on particles level.
3)charges cannot be free for much time as they need an anti-charge for their neutralisation or to form molecules and intermolecular forces.
These are my thinking about your result but it would be excellent to make a bound of charge(which will neutralise and then a mass force created by mass electronic repulsive force b/w them with
It will be artificial force created by mankind
If there are limitation to my limitations please let me know
Arvin, You do NOT know how thankful I am for this video. I've always been interested in physics since my childhood, but gave it up later as a rather foolish act of rebellion against the forceful insistence of my parents that I become a doctor. (They themselves are both doctors and I am from an Indian family, so you can imagine what pressure I was in) Anyhow, since the education system in our country is structured such that all science graduates must go on to become doctors, I gave up the sciences, and having done so, I pursued Law at University. These details about my life, youth and interests will no doubt bore you, but the reason I state these is that as a practicing lawyer who never had this interesting of a science teacher as you clearly demonstrate yourself to be at any period of my school life, I feel forever indebted and grateful to you from the bottom of my heart for so artfully piquing my long lost interest in science once again, to the point where I have now decided to expand my knowledge in the sciences in the duration of these rather unexpected days of pandemic where I am mostly at home with little to no clients in my practice. Thanks a lot once again!
I'm delighted to hear that! It's never too late to learn about things you have a passion for.
@@ArvinAsh Thank you, and please keep continuing the great work
This is fantastic. Seriously, thank you for making this video!
Thank you, and cool video! I’m definitely going to watch this more than once because, I’m new to most this stuff.
Always gets me hyped when he says "...that's coming up right now!". Well played Mr. Arvin, well played.
Mark Steven no u
Author: “Your weight is a force, not a mass”
Me:
Great lectures sir Arvin Ash! I am grateful for your knowledge-sharing!
What superb condensation of all the topics in physics explained in such a clear way!! ❤️
Ha! Watching this video increased the entropy in my brain....I think. lol
No, it lowered the entropy in your brain and increased the entropy in the rest of the universe as a consequence.
How dare you steal our entropy
@@YawnGod Are you sure? I thought that increased entropy= more information required to describe the system. Increasing the amount of information in your brain would require more information to describe all the information in your brain. Isn't that how the Paradox of Maxwell's demon was solved, the entropy increased in the demon's brain? Then again i could be all wrong. lol
Picture this: high entropy (or high disorder) states are like a mess you cant extract much from it. If you acquire information by any means, like rearranging your neuron connections, you are decreasing its entropy (or it disorder).
You’re right, you can’t decrease entropy.
Literally summarized all my interests. Thanks for the video m8!
Incredible Video! Thank you!
Really a video worth watching. Whenever I feel really negative about physics being attacked always by the odds in "classrooms " and "exams", this video heals me! Though I watch, I can't understand all of them,hope to understand in the near future!
Physics makes me happy! Seeing the connections of the universe is just amazing!
I swear you are a hero and a savior to students world wide. thank you for helping a new generation of future physicists and others, find joy in the topic youre passionate about
I watched a dozen videos dozens of times on time dilation.. from your very simple explanation I think I finally get it a little.
Outstanding graphics! The Professor we all wish we had.. A pleasure to watch Arvin.. The ONLY regret I Have is that there's nothing controversial to debate in the comments..Thanks.
Don't worry I'm about to make several videos where there will be plenty of controversy. lol.
At 3:19 (for those who are actually studying from this video) the distance is taken from the centres not the boundaries of the objects! Probably it was a editing glitch but nice explanation! Loved it❤️❤️
Yep, missed it during editing. we fixed this in future videos. Of course, if the celestial objects are very far apart, like the sun to the earth, adding the radius wouldn't make much of a difference.
To be extra clear: It's all about the center of mass.
Excellent video Arvin! Bravo!
Your video was inspiring.Very exciting, thank you for a well done presentation with great material. Thanks , Howard
I wish I had a teacher like Arvin. Thanks again, I wish to meet you in person someday.
I have a Master's in Physics and I'm a civil engineer. Always nice to have refreshers.
Man you deserve respect . Respect from every human on earth . Salute 🙏🏽
THis was pretty epic. I love where he is coming from with this. His heart is in a great place.
It’s summer. I don’t know why I find myself watching this stuff.
May be its so cool
Because it’s around you year round
Cicolas Nage absolutely agree
Its much fun when you decide to learn things by ur own not when you feel like you have to
@@cicolas_nage YES! VERY TRUTHFUL.
Arvin you are the clearest physics instructor on TH-cam - you deserve millions of views.
This was so incredibly informative and easy to follow.
In this day and age, I wonder how I managed to stay fully concentrated at a 17 minute video.
Absolutely beautiful
It is an amazing and unique brief lecture of Physics Laws. Love!
If only all teachers could explain like this I would deffo not be bored
This needs to be recommended to action filmakers..lol😂
feels gratifying when you already know the basics of the subjects mentioned :)
Great video! Thank you
*He is explaining stuff that professors and teachers have failed to explain over the years, again and again*
Lemme explain why....It's all in the brain, when u are in ur class listening to ur teacher, U may be bored or distracted by ur friends AND on top of that, like be honest, When u are in ur class, the thing that's in ur mind is "I have to study well so that I can get good marks" NOT "I need to gain knowledge for the long run".....But here, U clicked on the video just purely because of gaining knowledge, Like there is no pressure of test being done so ur stress gets reduced, Lesser the stress,Better the brain functions....Hence u understand stuff better in YT videos compared to say ur class
@@sanathkumar6526 or they are not explain it simple enough.
When teachers discuss, it's boring XD. They act just like robots pretending they understand the material in a deep way. It's lucky if you find someone who's passionately talking about the subject and teaching it with fascination.
you need more subs man. I'll be starting my physics journey in university 5 months from now and you explain all sorts of phenomena so simply so we can understand it better and faster. thank you
14:10 - Say my name.
Wow, first time it made sense to me that time is in fact relative... great job in explaining it!
Why this channel is so underrated. He is explaining so nicely
whoa. i really should use TH-cam back when i was studying.
Excellently presented such a vast body of knowledge in a nutshell ! Good work ! Thanks ...
its 1:42am and i have to go to work at 7:00am, but thats a good video bro
I'm very much impressed by the way of your simple explanation of complex topics !
The best speech so far of the general concept of physics, thank you!
Astounding. I think every individual with any interest in science should watch this video once a year, starting at age 10. Initially, this will serve as a sort of baffling introduction; later, as a review and something tying everything together. Congratulations on this.
Thanks for this video, great job !!
Because of the efforts of you men the quality of my life is profoundly enhanced. When I graduated high school I didn’t understand algebra. I was so incredibly weak in mathematics for most of my life. TH-cam did something for me that college lectures never could. I don’t know what it is but I just learn from TH-cam. Thank you.
Your explanatory description for the general relativity theory is phenomenal! It solved a long time confusion for me. Thank you!
Love this video. Because he says things so simply that I should probably understand. But my simple brain has to watch it a few times and it still explodes.
Liked and subbed
This taught me so much! Thanks!
Answer Gravy: This isn’t part of the question, but if you’ve taken intro physics, you’ve probably seen the equations for kinetic energy, momentum, and acceleration in a uniform gravitational field (like the one you’re experiencing right now). But unless you’re actually a physicist, you’ve probably never been freaked out by seeing a Lagrangian work. This gravy is full of calculus and intro physics.
The “action”, S\left(\vec{x}(t)
ight), is a function of the path a system takes, \vec{x}(t)=(x_1(t),x_2(t),x_3(t))=(x(t),y(t),z(t)). More specifically, it’s the integral of the Lagrangian between any two given times:
S\left(\vec{x}(t)
ight)=\int_{t_1}^{t_2}\mathcal{L}\left(\vec{x}(t),\dot{\vec{x}}(t)
ight)dt
where t1 and t2 are the start and stop times, \vec{x} is a path, \dot{\vec{x}} is the time derivative (velocity) of that path, and \mathcal{L} is some given function of \vec{x} and \dot{\vec{x}}. If you want to chose a path that extremizes (either minimizes or maximizes) S, then you can do it by solving the Euler-Lagrange equations:
\frac{\partial\mathcal{L}}{\partial x_i}=\frac{d}{dt}\frac{\partial\mathcal{L}}{\partial \dot{x}_i}
This is called the Euler-Lagrange equations (plural) because this is actually several equations. Each different variable (x1=x, x2=y, x3=z) tells you something different. In regular ol’ calculus, if you want to find the value of x that extremizes a function f(x), you solve \frac{df}{dx}=0 for the value x. Using the Euler-Lagrange equations is philosophically similar: to find the path that extremizes S, you solve \frac{\partial\mathcal{L}}{\partial x_i}=\frac{d}{dt}\frac{\partial\mathcal{L}}{\partial \dot{x}_i} for the path \vec{x}(t).
The Lagrangian from earlier, for a free-falling object near the surface of the Earth, is:
\mathcal{L}=\frac{1}{2}m\left|\dot{\vec{x}}(t)
ight|^2-mgz(t)=\frac{1}{2}m\left[\left(\dot{x}(t)
ight)^2+\left(\dot{y}(t)
ight)^2+\left(\dot{z}(t)
ight)^2
ight]-mgz(t)
For z:
\begin{array}{l}\frac{\partial\mathcal{L}}{\partial z}=-mg\\[2mm]\frac{\partial\mathcal{L}}{\partial \dot{z}}=m\dot{\vec{z}}(t)\\[2mm]\frac{d}{dt}\frac{\partial\mathcal{L}}{\partial \dot{z}}=m\ddot{\vec{z}}(t)\end{array}
So the E-L equation says:
m\ddot{\vec{z}}(t)=-mg or \ddot{\vec{z}}(t)=-g
In other words, “everything accelerates downward at the same rate”. Doing the same thing for x or y, you get \ddot{\vec{x}}(t)=\ddot{\vec{y}}(t)=0, which says “things don’t accelerate sideways”. Both good things to know.
You wanna be even slicker, note that this Lagrangian is independent of time. That means that \frac{\partial\mathcal{L}}{\partial t}=0. Therefore, applying the chain rule:
\begin{array}{rl}\frac{d\mathcal{L}}{dt}=&\frac{\partial\mathcal{L}}{\partial t}+\sum_i\left(\dot{x}_i\frac{\partial\mathcal{L}}{\partial x_i}+\ddot{x}_i\frac{\partial\mathcal{L}}{\partial \dot{x}_i}
ight)\\[2mm]=&\sum_i\left(\dot{x}_i\frac{\partial\mathcal{L}}{\partial x_i}+\ddot{x}_i\frac{\partial\mathcal{L}}{\partial \dot{x}_i}
ight)\end{array}
But we have the E-L equations! Plugging those in:
\begin{array}{rl}=&\sum_i\left(\dot{x}_i\frac{d}{dt}\frac{\partial\mathcal{L}}{\partial \dot{x}_i}+\ddot{x}_i\frac{\partial\mathcal{L}}{\partial \dot{x}_i}
ight)\\[2mm]=&\sum_i\frac{d}{dt}\left(\dot{x}_i\frac{\partial\mathcal{L}}{\partial \dot{x}_i}
ight)\end{array}
And therefore:
\frac{d}{dt}\left(\sum_i\dot{x}_i\frac{\partial\mathcal{L}}{\partial \dot{x}_i}-\mathcal{L}
ight)=0
This thing in the parentheses is constant (since it never changes in time). In the case of \mathcal{L}=\frac{1}{2}m\left[\left(\dot{x}
ight)^2+\left(\dot{y}
ight)^2+\left(\dot{z}
ight)^2
ight]-mgz we find that this constant thing is:
\begin{array}{rl}&\sum_i\dot{x}_i\frac{\partial\mathcal{L}}{\partial \dot{x}_i}-\mathcal{L}\\[2mm]=&\left[\dot{x}\frac{\partial\mathcal{L}}{\partial \dot{x}}+\dot{y}\frac{\partial\mathcal{L}}{\partial \dot{y}}+\dot{z}\frac{\partial\mathcal{L}}{\partial \dot{z}}
ight]-\mathcal{L}\\[2mm]=&\left[\dot{x}(m\dot{x})+\dot{y}(m\dot{y})+\dot{z}(m\dot{z})
ight]-\left[\frac{1}{2}m\left[\left(\dot{x}
ight)^2+\left(\dot{y}
ight)^2+\left(\dot{z}
ight)^2
ight]-mgz
ight]\\[2mm]=&\frac{1}{2}m\left[\left(\dot{x}
ight)^2+\left(\dot{y}
ight)^2+\left(\dot{z}
ight)^2
ight]+mgz\end{array}
Astute students of physics 1 will recognize the sum of kinetic energy plus gravitational potential. In other words: this is a derivation of the conservation of energy for free-falling objects. A more general treatment can be done using Noether’s Theorem, which says that every symmetry produces a conserved quantity. For example, a time symmetry (\mathcal{L} doesn’t change in time) leads to conservation of energy and a space symmetry (\mathcal{L} doesn’t change in some direction) leads to conservation of momentum in that direction.
Need to paste that into a TeX editor to read it even though I write TeX code all the time.
Anton Fetzer lol...... I really should have checked that first😂
I recommend using the physics package in LaTeX, it makes writing derivatives sooo much easier
I wish my teachers made physics as clear and as interesting as you just did.
Most physics and math teachers are very poor at teaching. VERY POOR!
so much info packed into articulate, succint presentation...i will enjoy looking for applications in my everyday. thank you, sir.
Excellent as usual Arvin.
Awesome video! I also loved the connectors you used to fluidly transfer from one topic to the other.
What an artful summation of physical reality as we experience it - bravo!
11:17 That is the best visual I've seen that demonstrates the length contraction effect of relativity. Kudos!
Phenomenal. Merry Christmas.
I have engineering physics exam tomorrow. this is my last hope.
How you have did i hope well
How'd you do?
@@mikafizz1022 he hasn’t replied yet so I think he failed
@@mikafizz1022 he hasnt replied so i guess he doesnt want to talk about it.
R.I.P @Mohd. Favas
Wow! Very nice summary. Loved it. Thanks for sharing it.
This is so so great. Thank you so much
That analogy for relativity was great
I'm a physicist myself, but I really love your discriptions and like your approaches to different phenomena. Great video again 👍
Thanks! That means a lot coming from a physicist.
Thanks! That means a lot coming from a physicist.
Thanks! That means a lot coming from a physicist.
Thanks! That means a lot coming from a physicist.
Wow! This channel is so insightful and entertaining. I am a business student but I am intrigued with the genius in the presenter. I am particularly impressed with the simple explanation of the complexities in physics.
Good work, enjoy this lesson Ty.
Sir, you are no bald ape. Do not sell yourself short. :-) you are a gentleman and a scholar. Such eloquent video delivery. Bravo thank you
I really wish I took physics in high school! I wasn’t interested, fast forward 30yrs, I can’t get enough! Thanks for your videos man!
I feel like watching your videos all days, it makes me the happiest person when ever I am watching them. Your way of explaining things is off the roof. Thank you so much 😊
I wonder why you’re not having millions of subscribers 👍🙏
Amazing! I'm gonna share this with my classmates.
His explanation was great I understood concept very well.