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

Stanford Continuing Studies

Stanford University Channel on YouTube:

[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

[tvaddict]

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
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

[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.

[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.

[Akshaygupta]

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

[jcnotnot]

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.

[mileswetherington]

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

[joabrosenberg]

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;

[Darkownage]

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

[halilibrahimcetin]

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.

[nandha]

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

[rationalsceptic]

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

[christophersoelistyo]

53:30  That little slip from his Quantum Mechanics lectures

[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

[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.

[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.

[DrDress]

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

[JLongTom]

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

[supernis]

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

[Red-bbqj]

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