Six Not So Easy Pieces

MagicMarker

I've started reading this after finishing 'Six Easy Pieces', but I'm having a bit of trouble from the get go.

I understand Feynman assumed that students had basic knowledge of the subject when he gave these lectures, but, I've never been to a physics class in my life, and it's been about 10 years since I've been to a math class. So I don't understand the equations that are consuming the pages at all, and I'm wondering how much I'm supposed to actually know already?

Even if there was an index in the book of what all the symbols mean I could maybe figure it out, but no such luck.

Are there any websites that could explain simple equations for a simpleton like myself?

Enkidu

You're basically meant to know a bit of linear algebra (vectors + matrices), some calculus and geometry.

Why don't you ask questions here OP, I'm sure people would be happy to help? A lot of the symbols will be context dependent.

Enkidu

My previous message doesn't give you much, so I'll just give you a guide to some of the stuff you'll see in Chapter 1 about vectors, from 1-1 and 1-2.

The first equations is something that looks like this:

m (d^2/dt^2)x = F_x (I'm using ^ for superscript and _ for subscript.

First the (d^2/dt^2). x is basically your position on the x axis in some frame. In English, if we pick some point and call it the origin, x refers to how far to the left or right of the origin you are.

(d/dt)x, is the time derivative of x. This tells you how quickly your value of x is changing. In other words your velocity in the x direction.

Then (d^2/dt^2)x is the time derivative of the velocity, or how quickly your velocity is changing. In other words the acceleration in the x direction.

m is mass.

Finally F_x is the force in the x direction. This force can be anything, gravity, electromagnetism, e.t.c.

So the equation m (d^2/dt^2)x = F_x is saying that your acceleration in the x-direction is determined by the force in the x-direction. Basically the insight here (by Newton) is that Force only affects our acceleration not our velocity directly.

The other two equations are just this equation in the other two directions.

The remainder of 1-2 is spent trying to show that these equations hold true in every frame. As I mentioned above, x is a measure of how far to the left and right of the origin you are, however what if we'd picked a different origin? The point is you'd want equations like m (d^2/dt^2)x = F_x to still be true, otherwise physics would depend on our choice of origin. Feynman then shows this is not the case, the choice of origin doesn't matter.

Hope this helps OP, if this isn't what you want or you feel my manner of explanation sounds condescending please say so.

MagicMarker

Hi,

Thanks so much for taking the time to respond in such detail! It does help a lot, but I have to ask what is probably a stupid question.

In the case of....

m (d^2/dt^2)x = F_x

I understand 'm' is Mass and presumably F is Force, what does 'd' & 'dt' mean?

sponsoredwalk

They are the operators indicating that you're taking a derivative.

I'm not going to lie to you, if you didn't know that you wont finish that book.

I tried reading that over a year ago knowing nothing about math and
pretty much being contemptuous of it & failed miserably

I know the 6 easy pieces gives you the illusion you can hack the rest of the lectures knowing nothing about math but you can't.

An example is the one you asked about, on page 2 of the book,
here (click search inside another edition of this book)
in equation (1.1) at the bottom,

[latex] m \frac{d^2x}{dt^2} \ = F_x [/latex]
[latex] m \frac{d^2y}{dt^2} \ = F_y [/latex]
[latex] m \frac{d^2z}{dt^2} \ = F_z [/latex]


comes from trigonometry & the breaking up of a Force vector into
components.

[latex] m \frac{d^2x}{dt^2} \ = Fcos \theta \ = \ F_x [/latex]

and when he takes the derivative of the person in the x' = (x - a) position
you need to understand why the [latex] \frac{da}{dt}[/latex] disappears.
It is an important issue for the point he makes a few lines down &
if you understand the mathematical reason why it all clicks instantly!
You'll realise why

[latex] m \frac{d^2x}{dt^2} \ = F_x = F_{x'} \ = \ m \frac{d^2x'}{dt^2} \ [/latex]

is just saying force is the same to different people.

6 Easy pieces is the first 6 Feynman lectures, the vectors lecture in 6 not-so-easy pieces is actually the 9th lecture of the Feynman lectures &
so you've skipped the 8th lecture on derivatives & integrals which would give you a hint about calculus - but by no means explain it!!!

If you really have an interest in reading the Feynman lectures I could
give you the perfect crash course so that you've got enough math &
physics under your belt so that you could hack the whole first 2 parts of
the Feynman lectures instead.

1: www.khanacademy.org
Do all of the math videos up to the end of calculus,
(well, just the algebra, trig, pre-calculus & then calculus)
These didn't take me too long seeing as I immersed myself in them.
I used these a year ago when I couldn't add fractions & hated math.
These videos got me to math so much - I wont stop talking
about how good these are if you start me

2: http://en.wikipedia.org/wiki/The_Mechanical_Universe

These lectures are like a crash course in physics the way the above math
videos are for calculus. They are all free online in the link provided
and on google video.

I think these are so much better than
the Feynman lectures for a beginner!

There is so much visual aid, so much history, so much working out of
math equations in an understandable way, so many good explanations,
these go from the basics up to quantum mechanics, relativity, everything!
These videos changed my life even more than the math videos did,
just unbelievable to see how interesting math is when you know nothing
about it & the way it's applied to the real world makes so much
sense when it's taught properly.

I would like to recommend to you to watch these first, like I did, knowing
no math! however, if I'd watched (or even known about) the above math videos
and done them first I would have appreciated these videos 5 million times
more! In short, do the math first - them videos above are nothing like
the math you did in school, it's made interesting & understandable.

The only problem with these phys lectures is that they don't go deep
enough to solve problems. When you finish them & are in love with physics
you can go to the Feynman lectures & fill in the gaps in an honest way!

Check out my messages in the useful physics links & the math useful links
sections to get access to about 30 more resources if you ever get stuck
anywhere

Anyway, if you don't want to learn the math but are interested in Feynman
and liked 6 easy pieces I would say to you, against all of the better advice
I gave above , to just watch the 52 part physics videos without
learning all of the math. You'll get more passion for, & appreciation of,
physics by watching those videos than struggling through the Feynman
stuff due to math problems. You can just soak up the logic & development
of all of the physics concepts & watch the math parts trying to understand
without taxing youself too hard. If you choose this unwise course of
learning why physics is so beautiful I bet that by the end you'll want to
learn the math It's a matter of saving 26 hours of time & appreciating it
all the first time round than rewatching all these things.

MagicMarker

Thanks a mill for that, great help!

I've actually seen those lectures linked to before but I can't see any links to the episodes on that wiki page?

sponsoredwalk

Ahh!!! They used to allow these to be streamed from the site.

That is the Alfred P. Sloan foundation for you, appear to be
very philantropous but always strive to cut with the money.

Type in the title names on google & they should come up on both
google & youtube.