Expert: Daniel Mazur - 8/9/2010

Question
QUESTION: Hi daniel,

We have had enough conversation on the topic of rotation. But one thing I again wanted to confirm is that can we derive the entire concept of rotational dynamics from the newton's laws?

I ask this because I read this again in another mechanics book. Can the "definitions" of torque and angular momentum be extended back to the newton's laws and derived as manifestations of newton's laws or are they the starting points themselves, representing completely independent facts of nature?


Many books say the same thing, that we can derive it all from the newton's laws. And this is what confuses me again and again.

Thanks,
Shikhin

ANSWER: Hi,

yes, we CAN derive all those terms from a bunch of definitions and Newton's laws. I recall it's been over a year, since we've had the long discussion on this topic and I believe I repeatedly said "yes, it can be derived from Newton's laws". It this wasn't so, it wouldn't be taught at schools so unequivocally. There are textbooks (I studied from some, but not in English, sorry), which explicitly do the derivation of rigid body and all pertinent definitions that follow (torque, moment of inertia,...) for the reader. But it is considered so basic by all authorities that it has dropped out of all modern textbooks and an inquisitive being such as yourself needs to look for old textbooks or the original (Newton's, Leibnitz's, ...) articles.

I wish you that you don't spend your whole life with this problem.

Daniel

---------- FOLLOW-UP ----------

QUESTION: Hi Daniel,

Of course I'm not planning to spend an entire life on this problem!! But it just won't let me relax until I SEE the derivations and how these definitions come about.

That's how I am. Can't help it.

You mentioned, some textbooks which explicitly derive it all. But as they aren't in english, it would be redundant.
Any other resource or book you can think of? In english ofcourse?

Also, in another seperate question I have asked you, you mentioned the use of lagrangian mechanics for a similar problem.

Can the derivations be done without lagrangian mechanics? What about the non-english books you mentioned, did they do it with or without lagrangian mech.?

Thanks,
Shikhin

ANSWER: Hi,

I perfectly understand your drive to understand, I merely expressed my wish that you sate your thirst for knowledge soon. It slows your progress down, you must feel that. I personally think you need a tutor to discuss this with, as information can be transferred much, much faster face to face with a blackboard (whiteboard, paper ...) at hand. I have written as much as I could here at AllExperts, given the topic as much time I thought useful, now I think I am at an end of what I can do for you in this. Unfortunately, I do not know a useful resource in English for your particular request - had I known it, I would have suggested it up front. I would like to help you, but I'm at my limit.

Regarding the balls connected by springs and the infinite-k limit, I think there is no better concept than the Lagrangean formalism. In fact those equations are just a certain way of writing the usual equations of motion, but the formalism gives you a few extra tricks to tackle and solve the problems. I would strongly discourage you from trying to use anything else, you'll waste more time. I should add that without understanding this, you can hardly make much use of quantum mechanics either, for the Classical and Quantum Mechanics are built up in a parallel. In other words, the Classical Mechanics (with its Lagrangean, Poisson's brackets, Hamiltonian, d'Alembert variational principle,...) is a stepping stone, without which one cannot access modern physics. One piece of good news is that almost all textbooks on Classical Mechanics are good and there are many out there. It's only your pick (I suggest to browse some in a University library), if you like ones more academic or more towards problem-solving.

Good luck!
Daniel



---------- FOLLOW-UP ----------

QUESTION: Hi daniel,

Currently I am doing an intro. to mechanics by kleppner and kolenkow.
Though I was planning to start with Quantum mech. and electrodynamics after this, for which I have books by the author D.J. Griffiths.

Should I instead start off with classical mech(lagrangian mech) by I.N.Herstein, before tackling Quantum mech and electrodynamics.

The book on lagrangian mech. I mentioned above, looks pretty lengthy and involved, looks like it'll take ages to finsih it off, and moreover, it's all new stuff and new formalism and concepts.

Should I then carry on with Q.M and Electrodynamics side by side along with the classical mech book by I.N. Herstein?

And do I really need a private teahcer? I mean not just for the above problems but in general, for my undergrad. study? Because all thej prof.s at my Engineering college, look incompetent to me. They are all very much into applied science and stuff, as expected since the Institute is an Engineering and I.T. Institute.

Also, I wanted to appear for this very prestigious scholarship here in India called KVPY (www.kvpy.org.in)
For that I first need to submit an original science project to be eligible. They say they are looking for creativity and innovativeness and the candidates ability to explore.

Can you suggest anything on which I can make a theoretical project?

Thanks,
Shikhin

Answer
Hi Shikhin,

it is not surprising to me that the book of Classical Mechanics (CM) is lengthy and involved. Nevertheless, this is what it takes to tackle all but the simplest problems in classical physics. I haven't found your book by I.N.Herstein on Amazon at all, but I think this one http://www.amazon.com/Classical-Mechanics-2nd-H-C-Corben/dp/0486680630/ref=sr_1_ is cheap and would do perfectly fine, because it has exercises at the end of each chapter. If you want problems with solutions, you will need something pricier like this http://www.amazon.com/Introduction-Classical-Mechanics-Problems-Solutions/dp/052 .

A private teacher or an older student as a tutor, it is essential to answer your questions. I cannot do it in this long distance manner, it is very inefficient. I think that if you can learn CM from a book without the need to ask anyone a single question, then you don't need a tutor. Otherwise you probably do, and no matter how difficult it is to get one, you just won't progress without one.

Original science projects, especially in theoretical physics, are just out of the scope of the help I can provide. In my experience this must (!) be done in a close collaboration with a professor, so that he/she gives you something that they want to work on and they mentor you along the way. In theoretical physics (TP) you may be able to come up with something without assistance and in principle you could even solve an eligible problem - the experimental physics students need the professors and their equipment simply to do measurements, so they simply cannot do without a supervisor like that. In TP, it is in principle more open and you could apply and work without guidance, but you must be extremely good and do it from A to Z all by yourself. I cannot help with it and think that without an advisory from an able professor, there is a microscopic chance of success - because those applicants, who HAVE an advisor, are likely to make a much better impression than a free-lance self-learner. All I can deduce from the organization of the stipend is that money comes according to the category (Bc., M.S., Ph.D. etc.) in which you are enrolled, and that that you should be better at physics and maths than most physics students in your category to have a fighting chance.

I am not much help this time I guess, but this is reality.
Good luck.
Daniel