Tips on understanding concepts on a deeper level?
December 4, 2009 8:45 AM   Subscribe

How can I better approach learning intro physics?

I'm a post-bac premed and college-level (non-calculus) physics is kicking my ass. I know that physics isn't about mechanically plugging numbers into formulas, but how do I achieve a deeper conceptual understanding? I read the textbook thoroughly, chug through the homework, and I'll think I get the topic, but if faced with a problem that's twisted a bit differently (e.g. killer exam questions), I'm at a loss. I have no idea how to apply what I know to unfamiliar problems, which means I didn't really get it at all. I rarely have that "a-ha" moment of clarity. My professor is horrible, and tutors seem to focus on problem-solving instead of teaching me how to *think* about physics. (And this is only mechanics/kinematics right now; I predict if the trend continues, I'll be totally screwed in electromagnetism.)

The final is 2 weeks away and 45% of the final grade, so I still have one last chance...

I know what I'm looking for sounds a bit vague, but I'd appreciate any advice on how to learn something that's abstract, and thinking about concepts from different angles, as well as how to stay motivated and even psyched about learning. I'm kind of down on physics right now, and filled with this sense of dread/fervent wish I were Isaac Newton, which doesn't help.
posted by amillionbillion to Education (23 answers total) 16 users marked this as a favorite
 
Have you tried looking up the same topic in different text books? Sometimes another way of presenting stuff makes it click. Can you get hold of a copy of Feynman's Lectures on Physics? You don't need the whole set, but the basics principles of physics are explained excellently.
posted by swordfishtrombones at 8:49 AM on December 4, 2009


The Feynman Lectures on Physics
posted by Comrade_robot at 8:53 AM on December 4, 2009


Response by poster: I've looked through the Feynman Lectures, but the explanations rely too much on math that for me is difficult and gets in the way. (It's been years since I took calculus.)
posted by amillionbillion at 8:57 AM on December 4, 2009


I suggest getting something like this.
posted by sickinthehead at 9:01 AM on December 4, 2009


Many universities offer courses in conceptual physics, sometimes called "Physical for Liberal Arts Majors", or which are sometimes just the lowest numbered physics course in the catalog. A textbook for that type of course may be helpful to you. I took a course in conceptual physics before I took calculus-based physics, and I found it immensely helpful in my later studies.
posted by jingzuo at 9:10 AM on December 4, 2009


Best answer: So you're essentially where I was about one year ago. I finished my premed postbac in July (interview this weekend-- wish me luck!) but had some early trouble with the more conceptual physics and chemistry stuff (hated math & had all the other trademarks of a recovering humanities major). The best way to really understand how physics works is to develop an intuitive feel for the mathematical relationships behind your models.

For instance, let's look at a classic physics problem, that of the block sliding down an inclined plane. Think about all the forces in play in terms of their Newtonian pairs: the force of gravity on the block & the normal pushing back up, the frictional force of the two surfaces sliding against one another, &c. Now, change each of these values slightly, one at a time, and look at how the relationships change. What happens when the block's mass doubles? is halved? What happens when the incline increases? decreases? What happens on our moon? on Ganymede? on Neptune? It might help to program the relationships into a spreadsheet and take note of how they change when altered-- which relationships are direct? Which are inverse-square?

Most of these relationships are fairly simple, but if you learn to get a good feeling for how they interact now, you'll be in a much better position when you get to more advanced kinetics or E&M. I second the Feynman lectures suggestion, though I don't think you have time to really get into that until after your final.

Anyway, best of luck with the final and the rest of your postbac. Don't let your nonenthusiasm for any of the basic sciences get in the way of your ultimate goal: patient care. Don't hesitate to MeMail me about anything else post-bac related.
posted by The White Hat at 9:15 AM on December 4, 2009 [1 favorite]


Actually, for intro physics, a lot of taking exams really is just mechanically plugging numbers into formulas. To study for the test you should have a cram sheet that lists all of the relevant formulas. There really aren't all that many. For example:

F=ma
a=v2/r
P=mv
F*dt=m*dv=dP

Figuring out which formula or formulas are relevant to the problem is 90% of finding the solution. When you read the problem write down all of the variables from the problem that are stated. Write down the variable that you are trying to find. Then you scan your cram sheet for the formula that contains most of the things you either know or want to find. It is an exercise in pattern matching.

Sometimes you will need to combine two formulas to include all of the knowns. Then you just solve for the desired variable. If one of the quantities needed to solve the problem is not immediately obvious, then you know that that is probably the "trick" part of the problem. Draw a picture or use some other formula to derive the missing variable first, then proceed to the final formula to solve for the desired variable.
posted by JackFlash at 9:19 AM on December 4, 2009


I hate the titles, but the "Dummies" series is usually pretty good at explaining things - you might want to browse Physics for Dummies and see how it helps.

BTW, did you know that Newton invented calculus so that he could describe physics? You might want to get a conceptual understanding of calculus (e.g. a derivative is the slope of a line, which could be a curved line, at any point on that line) -- perhaps that would help you understand physics a bit better. There's another book for that -- I think just the first three chapters might help (it explains integration, differentiation, and the limit theorem in pretty straightforward terms).

Good luck to you! The first time I tried to learn geometry, I didn't "get" that I was supposed to use logic to derive proofs -- I thought I was supposed to memorize them. That didn't work too well :). (I was being taught by a guy who had a master's degree in religion -- I don't think he knew any more geometry than I did :)). I went to a public high school next year with a real math teacher, and once he explained that geometry proofs were about logic, I was good to go. I ended up getting a BS in electrical engineering -- I often wonder what direction my life would have gone if I hadn't gotten over that hump :).
posted by elmay at 9:20 AM on December 4, 2009


You want the Levin lectures. They were so helpful and my course was so inadequate that I quit showing up but still set the final's curve.
posted by glibhamdreck at 9:31 AM on December 4, 2009


Spend a some time with a friend who is an engineer or physicist on a walk. Ask them to point out things in every day life that demonstrate the principles that are having trouble with. Ask him/her to describe why that is happening. After a few of these types of experiences you'll start to get that intuitive understanding you are looking for.

I had a similar problem (no intuition) with thermal-fluids. Once I saw more real-life examples, I became better at understanding on an intuitive level what I was seeing. Applying the equations became much easier once I could imagine what was going on in real life.
posted by chiefthe at 9:49 AM on December 4, 2009 [1 favorite]


The Feynman lectures are great -- if you already have some sense of the material and want to see it from a different perspective. For a first run-through they don't do it for most people. Connecting the ideas to the math is really tricky, and the plug-n-chug approach doesn't really help you to approach new problems effectively.

I think Paul Hewitt's Conceptual Physics book is a good first place to read about the concepts without trying to make the math connections. There are also materials out there that focus on getting beyond the plug-n-chug approach and connecting concepts to math. None of these are really tailored to individual study, but they might be worth a try:
Tutorials in Introductory Physics
Ranking Task Exercises in Physics
Physics Active Learning Guide
The other thing I'd suggest at this point is to think about how you are categorizing the problems you are given. Deciding how to approach problems based on surface features -- 'ramp problem' 'roller coaster problem' can get you into trouble. Try to decide what underlying physical principal is involved as a starting point: Newton's second' or energy, for example.
posted by Killick at 9:54 AM on December 4, 2009


Expanding on JackFlash... Even if you can't remember the formula, sometimes you can use the "units" given in the problem to help figure out how to calculate the answer.
very simple example: Given that a car is traveling at 50 mph how long does it take to go 13 miles?
you have miles/hour and miles and need to get hours; the only way to get hours from the given units is to divide miles by miles/hour.
It might help to add general units to the list of equations:
e.g.
F=ma=mass*distance/time2
posted by crenquis at 10:09 AM on December 4, 2009


I find Excel is wonderful in "feeling" mechanics. Set up the equations to plot a graph of say position as a fuunction of time with constants you can adjust then see what happens to your graph when you change gravity, frictional coefficients, initial velocity or whatever. This approach allows you to do quick "experiments" to feel out the major effects without doing a lot of distracting and trivial algebra.

Your life will always be richer for reading some Feynman regardless of whether it helps you in the class.
posted by Fiery Jack at 10:14 AM on December 4, 2009


Tiger Woods is using Get A Grip on Physics.
posted by anniecat at 10:16 AM on December 4, 2009 [1 favorite]


JackFlash and crenquis have it.
posted by notned at 10:35 AM on December 4, 2009


My favorite:
Physics for Future Presidents

The lectures that the book is based on are also available as a free podcast in the iTunes store
posted by limited slip at 11:01 AM on December 4, 2009


Best answer: I came in to recommend Walter Lewin's lectures, linked above.

I see the same disconnect you're describing all the time. I think the difficulty of applying the subject matter leads people to focus on plug & chug solution methods. I really try to advocate for stepping back and taking the time to ask "why?", and using your imagination and physical intuition to envision what's going to happen in a given situation -- you do, after all, live in the physical world, and you can usually "see" a solution even if you can't describe it mathematically -- yet.

And for me, that's the point. The math isn't the answer, it's a description of the answer, using the best language we've got for accurately describing the world. The real answer is the physical objects bouncing around.

You can develop physical intuition doing really easy, stupid experiments, e.g. grab a box of rubber bands and shoot them off at different angles to find the best one for distance. You can't do this for everything, but once you start seeing the connection between some of the equations and the physical reality they're describing, the rest should start to become readable in the same spirit.
posted by range at 11:42 AM on December 4, 2009 [1 favorite]


Best answer: Thinking Physics is great for this.
posted by Pants! at 12:42 PM on December 4, 2009


Develop your intuition by guessing at the answer: Are we talking millimetres or kilometres? Seconds or minutes? When you reach something less intuitively familiar than mechanics, take some time to find out sensible and non-sensible answers. When your guess is completely different to the answer that you can confirm is correct, work out why - the counter-intuitive bits are the bits where you learn.

Try micro-thought experiments, take things to extremes: if it was a vertical slope, how would it work? What if it was on the moon? If the two masses were the same? If one was an elephant and the other a fly?

Look for symmetries.

Depending on your thinking style, you might have different ways of engaging with the material (you might be a graph drawer, for instance).

The key is to give yourself the two tracks to the answer - knowing (or being able to derive) the formula and plugging in the numbers, and being able to reach an answer and think "that's about right" or "that's crazy, something along the way has gone horribly wrong!".
posted by Wrinkled Stumpskin at 1:11 PM on December 4, 2009 [1 favorite]


Seconding videos - those MIT videos look terrific.

Check your library for videos, especially Conceptual Physics or The Mechanical Universe. You can watch The Mechanical Universe at the Annenberg/CPB site. They also have programs for teachers, which might be helpful to you as well: Science in Focus: Force and Motion (there's one on energy, too).

There's also this online Amusement Park Physics interactive exhibit thingy.

Look for free software. I was playing around with a KDE disc last weekend and discovered that it had Step, a physics simulator. You can also find science-related software (some free, some not) at Apple downloads.

If you have time, call around to thrift stores and friends-of-the-library sales to see if they accept and resell textbooks. I have about a dozen physics textbooks I picked up for a buck each at library booksales. It's a cheap way to check out the same concept in other textbooks, as swordfishtrombones suggested.

Again, if you have the time, you might try reading about the history of physics, which can really help you understand what the scientists were trying to understand. Maybe Great scientific experiments: twenty experiments that changed our view of the world?

Finally, if you have the funds, you might see whether you could pay a tutor to help you really understand this stuff. (I'm assuming the tutors you mentioned are not people you're paying directly. If they are, let them know you really want help understanding, and if they can't help you with that, keep looking around to find someone who can.)

Good luck!
posted by kristi at 2:35 PM on December 4, 2009 [1 favorite]


tutors seem to focus on problem-solving instead of teaching me how to *think* about physics. (And this is only mechanics/kinematics right now...

I think I understand your complaint, but the thing is, without calculus, there isn't much to think about in classical mechanics beyond like "moving stuff keeps moving, till something else pushes or pulls it", "it's harder to throw a heavy thing than a light thing", and "stuff generally bounces off stuff". The plug-and-chug formulas that are bugging you are just formal statements of these three concepts, but, basically, that's all there is to non-calculus mechanics, except maybe you could add "a thing slows down when it rubs on something else" which isn't really a whole new idea, but the way you will learn mechanics, it will be more convenient to handle it as such, because your test questions will have to hand you a magical coefficient to use in these problems.

Maybe you are looking for some sort of deeper concept because these things seem so intuitive, but really, there isn't one. That's it. The Great Achievement of classical mechanics is that with these three ideas and their matching mathematical formalisations, you can make all sorts of reasonably-accurate predictions about the behavior of the natural world at the scales we generally experience in our daily lives.

If you can attach the formulas you learn to these intuitive concepts, then you can start using your intuition about the problem to figure out what to do. A cannon is firing a cannonball...ok, well, the cannonball will keep on flying unless something pulls on it. Wait, gravity pulls on it...then you just fit the motion equations together like a puzzle to get what you want. A tutor will probably drag this line of reasoning into a too-extreme test prep approach: the test question says ignoring air resistance, that's a clue, its a cannonball, that means we should use the range equation. Maybe that is what is frustrating you? Anyway, back to the cannonball, we're thinking ok, when will this cannonball hit the ground? How much time will that take? We know the cannonball's mass, we know its velocity in the up-down direction. We know what acceleration gravity puts on the ball, also conveniently in the up-down direction, so we can solve for how long this will take in time. Now that we know how long the ball will be in the air, we can solve for how far it will get with a reshuffled version of the same motion equations, except in the left-right direction.

I'm not sure if this is useful, but my main point here is that there really is no Big Deep Concept beyond those three pretty intuitive rules, and that unfriendly as they may look, those equations you learn are just very careful statements of the same three rules. Looking at classical mechanics from a History of Science perspective, the amazing thing about it is that "Plug 'N' Chug" can actually be used to make accurate predictions about the world. It doesn't seem crazy now, but it used to seem crazy. And either way, plug-and-chug is actually how you do the problems, its not a cop-out or a dodge of some Mystery.

Even *with* calculus there isn't really anything else to classical mechanics, its just that basic differential and integral calculus is essentially 'how to think about physics' (it turns out to have other useful applications, but IIRC that's why they invented it. Classical mechanics is calculus' killer app).
posted by jeb at 3:37 PM on December 4, 2009 [1 favorite]


Best answer: I'd strongly recommend Conceptual Physics by Paul Hewitt.

It's a textbook and is sometimes used in either highschool or college intro classes. The math is very minimal, and it focuses (as the title suggests) on giving you a thorough conceptual understanding of the material first, before breaking out the equations.

IMO, this is the right way to teach physics. Teaching via equations is only helpful when students either (a) have a good conceptual understanding to begin with, and need to learn how to construct models and make predictions (that's what equations and math in general is in physics: they're predictive models) or (b) have such a thorough and ingrained understanding of mathematics that it makes sense to use math as a sort of analogy to teach the concepts with. Case A is rarely true in an introductory class, and case B is generally only true for very specialized groups of students ('intro physics for math majors').

I've loaned out my (old) copy several times to friends and almost all of them have ended up being much more confident in class as a result of reading it. You'll still need your assigned textbook to pass your class, but it'll at least give you a basis from which to attack a more math-heavy text (and might even make the Feynman Lectures more approachable, although I think you're still a few semesters away from really appreciating them).

Older editions are available for just a few dollars a copy
; I don't think there's really any reason to spring for the newest revision. (Link is to the 2001 ed, here's the 1999 which is even cheaper for better condition copies.) Some versions say "expanded technology," I think this refers to experiments conducted using Texas Instruments programmable calculators, but I'm not positive.
posted by Kadin2048 at 11:16 PM on December 4, 2009 [1 favorite]




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