The best introductory mechanics textbook

[adjurovich]

So I’m a high school student and I am planing to participate in higher-category physics competitions in my country. However, I think that my theoretical understanding of the basics isn’t clear enough yet - by basics I mean classical / Newtonian mechanics. I am the type of person that learns by proving something and frequently asking why something works and looking answers. That’s why I really love proofs in math. However in high school physics textbooks in my country, proofs are rarely talked about, and it doesn’t work for my brain understand stuff because the books says it’s correct - it feels like memorizing. I know some basic calculus and I am looking forward to learn more about it before taking a new textbook. Which mechanics textbook do you recommend for self-studying that talks about things in details (does a lot of proofs).

 

[symbolipoint]

I know some basic calculus and I am looking forward to learn more about it before taking a new textbook. Which mechanics textbook do you recommend for self-studying that talks about things in details (does a lot of proofs).

Physics (Mechanics, Kinematics, other ) USES Mathematics but is not itself Mathematics. Do not expect proofs. Definitely expect derivations.

 

[adjurovich]

Physics (Mechanics, Kinematics, other ) USES Mathematics but is not itself Mathematics. Do not expect proofs. Definitely expect derivations.

I will ask the question I ask over and over again. How do you actually understand physics if you don’t understand why things work the way they do? I am probably a little too much used at mathematics at the moment so I am used to learning by proving and profound deriving. I feel like understanding how things work isn’t really enough. For example, if I say: tension is the force that appears in rope when it’s under some stress and acts by pulling bodies that are attached to it. Do I really understand it? I can describe how it acts and draw the vectors but can I explain why? No. I just feel like I only “remember” the way it ”works”

 

[Frabjous]

I will ask the question I ask over and over again. How do you actually understand physics if you don’t understand why things work the way they do? I am probably a little too much used at mathematics at the moment so I am used to learning by proving and profound deriving. I feel like understanding how things work isn’t really enough. For example, if I say: tension is the force that appears in rope when it’s under some stress and acts by pulling bodies that are attached to it. Do I really understand it? I can describe how it acts and draw the vectors but can I explain why? No. I just feel like I only “remember” the way it ”works”

Fine. You need to learn about stress and strain.
That’s not right either. You need to learn about microstructure.
That’s not right either. You need to learn about molecular potentials.
That’s not right either . You need to learn about quantum mechanics.
That’s not right either. You need to learn …
Why can sometimes be an excuse not to learn things.

 

[adjurovich]

Fine. You need to learn about stress and strain.
That’s not right either. You need to learn about microstructure.
That’s not right either. You need to learn about molecular potentials.
That’s not right either . You need to learn about quantum mechanics.
That’s not right either. You need to learn …
Why can sometimes be an excuse not to learn things.

So you think I should stick to this simple definition (and other definitions I find in textbook), because I could delve too deep by asking why question?

 

[Frabjous]

The point is that there are many levels, all of which are “consistent”. While going to a different level can provide insight, this frequently comes with a loss of computational ability.

 

[Dragon27]

stick to this simple definition

why question

I'm not sure what does 'why' have to do with definitions. You can ask why some force appears and acts in some way, but you can't ask 'why' to a definition, it's just a definition. That just how we define tension, and then we try and see what we can derive from the definition. Or maybe you mean that you want to know why this definition is useful, but math books suffer from lack of motivation (and count on you to figure that out for yourself) too.

 

[gleem]

I am the type of person that learns by proving something and frequently asking why something works and looking answers.

In math, you start with definitions and postulates you must accept to proceed. and oh, by the way, memorize them.

I feel like understanding how things work isn’t really enough.

If understanding is not enough then what is left?

In math, you start by setting rules. In physics, you make special note of observation of the way things are and establish laws or principles that you use to understand relationships. Newton'sHis first law defines uniform motion. His second law defines force. His third law introduces reaction. Together they are the springboard that you use to explain and thus understand motion.

Use the definitions and laws to give order and thus understanding to your intuitive/naive concepts of physics, that is your everyday experience with the physical world.

 

[gmax137]

Which mechanics textbook do you recommend for self-studying that talks about things in details (does a lot of proofs).

Maybe we have different ideas on what "proof" means. In my view, there are few (if any) "proofs" in physics. Physics is an empirical study: we create models and test them against what happens in the real world.

 

[adjurovich]

Thanks to all previous answers about my personal misunderstanding of the matter. However I’d like to know which textbook explains mechanics in a very detailed manner?

 

[symbolipoint]

Thanks to all previous answers about my personal misunderstanding of the matter. However I’d like to know which textbook explains mechanics in a very detailed manner?

Depends on your level of advancement. Early in your Physics study? Possible choice is any of the commonly used Physics books for beginner undergraduate science students, such author combinations as "Sears & Zemansky"; and "Halliday & Resnick".

 

[adjurovich]

In math, you start with definitions and postulates you must accept to proceed. and oh, by the way, memorize them.


If understanding is not enough then what is left?

In math, you start by setting rules. In physics, you make special note of observation of the way things are and establish laws or principles that you use to understand relationships. Newton'sHis first law defines uniform motion. His second law defines force. His third law introduces reaction. Together they are the springboard that you use to explain and thus understand motion.

Use the definitions and laws to give order and thus understanding to your intuitive/naive concepts of physics, that is your everyday experience with the physical world.

I totally agree. But I usually tend to overcomplicate things because I delve to much into details too early. It’s probably some sort of annoying curiosity that doesn’t allow me to admit I understood something if I can’t explain it on an atomic level. By doing that I get really confused and get the impression that I understand nothing. It’s still much more of a personal problem I’m trying to overcome

 

[Baluncore]

You must control your OCD. Your search for the lower basement is a distraction, it will prevent you from reaching the higher floors.

 

[adjurovich]

You must control your OCD. Your search for the lower basement is a distraction, it will prevent you from reaching the higher floors.

I think it’s quite the opposite. Tell me about anything on non-fundamental level and my brain will understanding it. The more abstract the easier it is for me. It’s fine for me to “accept” the fact that electron will go through both slits if not observed, but it’s counter intuitive for me that reaction-pair of friction will cause motion. My brain constantly tries to understand things into non-fundamental level. When I say fundamental I mean Newtonian and visible to the naked eye. This seems to be so wrong but works for me for some reason? Studying kinetic theory of gases seemed to be really intuitive, thermodynamics too but still I never feel confident about the most basic relative motion or Newton’s laws (even though I feel confident about laws of conservation).

 

[marcusl]

In that case, I suggest Landau and Lifshitz.

 

[Frabjous]

In that case, I suggest Landau and Lifshitz.

For a high schooler who knows basic calculus?

I would suggest Morin or Kleppner /Kolenkow or a standard 1st year calculus based text(Serway, Sears and Zemansky, Halliday and Resnick, Young Freedman)

 

[Vanadium 50]

Honestly, I think your attitude "I can only learn things one way" will seriously hamper your studies. Your priority should be to change that, not trying to rush ahead on content. If for no other reason that there really aren't any books that do it "your way".

 

[marcusl]

For a high schooler who knows basic calculus?

I would suggest Morin or Kleppner /Kolenkow or a standard 1st year calculus based text(Serway, Sears and Zemansky, Halliday and Resnick, Young Freedman)

The OP already rejected Sears and Zemansky and Halliday and Resnick (see posts #12, 14) and wants a deeper mathematical treatment. L&L show that conservation laws follow from underlying mathematical symmetries and proceed to equations of motion. I don't know of any true intro book with that approach. The OP will perhaps be motivated to learn the required math beyond basic calculus in order to understand mechanics at their desired level. Or they'll discover that the standard progression, starting with calculus-based intro books, is actually a good way to learn physics.

 

[adjurovich]

Honestly, I think your attitude "I can only learn things one way" will seriously hamper your studies. Your priority should be to change that, not trying to rush ahead on content. If for no other reason that there really aren't any books that do it "your way".

Obviously not everyone excels at everything. Some people like abstraction, some people prefer to study things they can see and they find them very intuitive. We are all very different. I don’t really think you personally enjoyed / found intuitive everything you learnt about in physics? If you did, hands down. I haven’t met a single physics professor yet that found everything intuitive and enjoyable and excelled at it. By the way, where do you see that I’m trying to rush ahead on content?

 

[adjurovich]

The OP already rejected Sears and Zemansky and Halliday and Resnick (see posts #12, 14) and wants a deeper mathematical treatment. L&L show that conservation laws follow from underlying mathematical symmetries and proceed to equations of motion. I don't know of any true intro book with that approach. The OP will perhaps be motivated to learn the required math beyond basic calculus in order to understand mechanics at their desired level. Or they'll discover that the standard progression, starting with calculus-based intro books, is actually a good way to learn physics.

Thanks for an advice, but I don’t think it’s that easy for me (or anyone except some crazy prodigies), to jump to seemingly advanced calculus in a few weeks. Of course I’m intrigued to learn advanced stuff as anyone who likes science is, but I think learning basic calculus two years before it’s taught in high schools where I live is probably a modest jump for now. My personal complaints are some things that are never explained in textbooks (at least high school textbooks). For example it’s said (in high school textbook I use) that tension exerts torque on a pulley which didn’t really make any sense to me. I previously asked about it on this forum. I hope that you get the idea what I am talking about.

 

[Vanadium 50]

By the way, where do you see that I’m trying to rush ahead on content?

You're a high schooler looking at college textbooks.

You've rejected my advice. Fair enough. Let me know how it works out for you.

 

[adjurovich]

You're a high schooler looking at college textbooks.

You've rejected my advice. Fair enough. Let me know how it works out for you.

if I learnt basic calculus by reading some literature and watching tutorials/explanations, why wouldn’t the same work for physics? I learnt logarithms when I was 14 because I was bored and to this day I don’t see anything wrong with it? You can learn anything as long as you have enough prior knowledge of the more basic topics. Yes physics is harder than mathematics in general, but IPhO competitors that are high schoolers indeed know the basic calculus and you cannot find a high school level textbook using calculus on regular basis? Correct me where I’m wrong.

 

[Vanadium 50]

You have my advice. You don't want it. Your choice. But I am not going to argue the point with you - I would only be repeating what I already said.

You might consider whether your position is plausible: "I am so smart I can jump ahead of my grade level, but I can only do this with a textbook that does things my way." You should also consider what it means if this perfect textbook hasn't been written.

 

[adjurovich]

You have my advice. You don't want it. Your choice. But I am not going to argue the point with you - I would only be repeating what I already said.

You might consider whether your position is plausible: "I am so smart I can jump ahead of my grade level, but I can only do this with a textbook that does things my way." You should also consider what it means if this perfect textbook hasn't been written.

I find something about your attitude to be very arrogant. I really want to know why I “don’t want to” go to competitions? As far as I’m concerned they are really beneficial for developing critical thinking and getting used to solving difficult problems. But when it comes to the textbook, yes I am looking for a good textbook because I am not a physicist nor I have physicists as my friends / family members so I can ask them if I get confused about something. However I don’t know why you seem to be annoyed by someone learning something earlier than its imposed to them by their educational system. There are also prodigies: 14-year-olds that can solve college math problems easily? Why don’t you tell them to follow the curriculum?

 

[MidgetDwarf]

Excelling in high school does not equate in excelling in physics.

You repeat things in physics education. Each time at greater generalization and more detail.

Take a look at something like Spivak's Mechanics , then to any intro calculus based physics, and report here if you still will not adjust your expectations. I will wait.

Just work through any intro college based physics. Once you do that, then go deeper...

here are some good books [intro]

Alonso and Finn : Fundamental Univerity Physics [3 volume set]. Very expensive, but doesnt shy from calculus.

Feynman Lectures on Physics.


The 2 book intro series by Shankar.

Kleppner and Kolenkow: Mechanics [maybe the hardest here]

Then you have your general run of the mill books : Giancolli, H R, Knight, Tippler, Sears, Serway etc

 

[MidgetDwarf]

Watch this video, and then relfect on what you are asking for is unrealistic.

 

[adjurovich]

Watch this video, and then relfect on what you are asking for is unrealistic.

I watched this video earlier today and it’s a really good explanation. I wouldn’t be exaggerating if I said it really changed my understanding of science from philosophical point of view.

 

[adjurovich]

Excelling in high school does not equate in excelling in physics.

You repeat things in physics education. Each time at greater generalization and more detail.

Take a look at something like Spivak's Mechanics , then to any intro calculus based physics, and report here if you still will not adjust your expectations. I will wait.

Just work through any intro college based physics. Once you do that, then go deeper...

here are some good books [intro]

Alonso and Finn : Fundamental Univerity Physics [3 volume set]. Very expensive, but doesnt shy from calculus.

Feynman Lectures on Physics.


The 2 book intro series by Shankar.

Kleppner and Kolenkow: Mechanics [maybe the hardest here]

Then you have your general run of the mill books : Giancolli, H R, Knight, Tippler, Sears, Serway etc

I solved a few calculus based mechanics problems from Irodov’s General Physics textbook. It honestly felt refreshing, but some of the problems I’ve seen there seem to be really hard - at least for me at the moment.

Also, what do you mean by “repeating things in physics education”?

 

[Frabjous]

Also, what do you mean by “repeating things in physics education”?

mechanics: freshman and junior
E&M: freshman and junior
Quantum:sophomore and junior
If you go to grad school, you’ll take them all again

 

[symbolipoint]

f I learnt basic calculus by reading some literature and watching tutorials/explanations, why wouldn’t the same work for physics?

No! Most (of us ) will reject that as it is stated. "Reading some literature" and "watching tutorials,..." are not enough to learn. The learning process is more than just that, and at present I will not describe it; I have tried to in a few other postings in other related topics.

 

[symbolipoint]

There are also prodigies: 14-year-olds that can solve college math problems easily? Why don’t you tell them to follow the curriculum?

edit: response removed in order to plan the response better

improved response:
Maybe you are and maybe you are not a prodigy. You should not expect yourself to be one.
If interested enough in Physics, then you will respond to this interest. The rest is
you put in enough effort to learn, because you are compelled from the inside to do it.

 

[Vanadium 50]

I find something about your attitude to be very arrogant.

Right back atcha.

 

[adjurovich]

Right back atcha.

Fine, but I still didn’t get the explanation why I “don’t want” to go to competitions?

 

[adjurovich]

No! Most (of us ) will reject that as it is stated. "Reading some literature" and "watching tutorials,..." are not enough to learn. The learning process is more than just that, and at present I will not describe it; I have tried to in a few other postings in other related topics.

It doesn’t matter how I learnt it if can take the derivative? I also have as much theoretical background as I need: I understand what it is, how to use it, where to use it and when to use it? Maybe it’s wrong because I didn’t start from the group theory? I still think that’s relatively good for a high school student. The only gap I can think of in my precalculus knowledge are hyperbolic functions because I was so lazy to learn them, but I’ll do that when I find some extra time. But I don’t think mathematics is what this thread is intended for?

 

[MidgetDwarf]

It doesn’t matter how I learnt it if can take the derivative? I also have as much theoretical background as I need: I understand what it is, how to use it, where to use it and when to use it? Maybe it’s wrong because I didn’t start from the group theory? I still think that’s relatively good for a high school student. The only gap I can think of in my precalculus knowledge are hyperbolic functions because I was so lazy to learn them, but I’ll do that when I find some extra time. But I don’t think mathematics is what this thread is intended for?

I will be nice since you are a kid.

But you need an attitude adjustment. Your responses to the majority of users on this thread have been extremely rude.

Your know it all attitude will be a detriment to not only future studies, but life in general.