Matt Haley's Physics Site

For most people, a fair amount of work will be required; at least 5 hours study time per week should be considered essential and 10 still reasonable for difficult topics or for when your instructor is covering ground quickly. Some of you will have already had some physics training in high school, which can be a blessing or a curse--don't make the mistake of thinking that your former physics instruction will make up for lack of studying past the first quarter of the semester!

Now, as you may soon discover, the process of learning physics is not always the smoothest of rides, and in spite of pro-educational slogans you may have been exposed to, such as "Physics is Phun," keep in mind that doing physics or other difficult work is not always phun. Think of learning physics as similar to learning a musical instrument. Initially, nothing has the potential to make you feel dumber and more incompetent. That's a perfectly normal response to rigorous subject matter, and even in my studies now there's some degree of the feeling of not understanding things as fast as I would hope. Your goal, though, is to slowly rise above the trees to where you can see the forest, and this takes a while for physics or for any other high-level discipline. Try not to get discouraged when you are stuck, since this at least means you are conscientiously testing yourself. There is also a fair amount of help available to you in the form of staffed coaching tables on the 5th floor of RLM during normal daytime hours, your professor's office hours, and me.

I think the reason 303K is often found trying by students is that, unlike most other college courses, physics is not just about learning the material, it also involves thinking critically about problem solving. "Haven't I done that in math classes before?" you might ask. Yes to some extent, but even in a class like calculus, finding the volume of a paraboloid, integrating by the method of partial fractions, or finding derivatives via the chain rule all essentially boil down to remembering a series of steps and following the algorithm. While introductory physics doesn't require any unique genius, it does take problem solving to the next level by getting you to apply what you know to new problems that you've never seen before. Problem solving of this kind is a very satisfying (and marketable) skill, so work hard and you'll get the hang of it!

Tips for the beginning student

1. Trigonometry

Make sure you know trigonometry cold, in particular SOHCAHTOA. If you don't, you will have problems right away, and they won't go away. Luckily, if you've forgotten this subject, it's very easy to relearn quickly, so do that.

2. The importance of algebra

     The importance of doing problems algebraically in physics cannot be overstated. What I mean by this is simple: your equations should be almost entirely comprised of letters (variables, that is), and you should only use your calculator once your equation looks like "x = ...", where x is the thing you're solving for and "..." are variables. There may be some rare exceptions to this rule, but in general this is the way to go.
     Let me give you an example of why algebra is a better and even an easier way of solving problems than using numbers. Consider example 5.10 in your Serway Jewett 6th edition textbook on p.130. Don't worry, you don't really need to understand this subject matter to follow along with these comments, so keep reading! You'll notice that values for the hanging and sliding masses are NOT given as numbers, nor is the angle of the incline. Thus, in solving for certain properties of this system, you have no choice but to do this problem with algebra--however, many of the questions you'll be doing for homework give explicit values for the physical parameters, so the answers you'll end up with will be numbers. Does that mean you should do the problem differently when you are given numbers? NO!!! You should always proceed in the manner shown in 5.10 and do everything with algebra. Why? Several reasons:

1. The more calculations you input into your calculator, the greater the chances are that you will make an error typing something in. Having your final answer in the form "x = ..." means you will only have to do ONE calculation, which improves your odds of not making a mistake. Also, more calculations can introduce rounding errors if you don't keep all the digits, and these errors can add up so that your final answer might be considered wrong by UT Homework Services even though you did the problem right.

2. It's hard to find mistakes when you use numbers. Let's say you used numbers at several steps leading up to finding the acceleration in eq.(5). Then instead of ending up with

you'd end up with something like, say,

Now, if you made a mistake somewhere, which is quite likely since you're still a novice, the latter of these answers isn't going to give you much of a clue as to where you went wrong--it's just a bunch of numbers. You also can't trace back your steps very easily the way you can with a series of algebraic equations if all you've written down are numbers. Deciphering your mistake from a pile of numbers can be very tedious and often results in you having to work the problem all over again from scratch--no fun!

3. The algebraic method often allows you to easily correct mistakes. Let's say you work out this problem incorrectly using algebra and obtain

In Chapter 1 you learn about dimensional analysis, a handy tool for fixing mistakes in your formulas (which by the way is still extremely useful in advanced physics.) Notice in the above equation that we have a g2 in the numerator. This can't be right since every term in the numerator (or denominator) must have the same units and sinθ is unitless. Also, since acceleration has the units of force over mass from Newton's 2nd law, we can see that terms in the numerator need the units of force, or mg. Thus, the g2 must be wrong. Knowing that, it can't be too hard to go back and find where you went wrong in your algebraic steps.

4. Most importantly, finding algebraic formulas for your answers teaches you more. In fact, once you've done problems like this one, you can probably guess the right answer in the future for similar problems (but you should work them out anyway for practice and just to make sure!) The acceleration down the slope will be aided by the gravitational force on m2 and hindered by that on m1, which is why there is a minus sign in the numerator between the two forces. Also, the sinθ is present because only the component of gravity on m2 that is parallel to the slope will contribute to the acceleration. Since both blocks are being pulled, the effective mass of the system is m1 + m2, thus the denominator. If these remarks don't make total sense to you now, come back to them after studying this chapter and think about them some more. Knowing how to look at an equation and see what it means physically is called intuition, one of the most important skills for a science student to have.

3. Problems, problems, problems

The best way to learn physics is unquestionably by doing problems. However, that being said, the next best way to learn physics is by watching someone else do problems. That's what your instructor and I are here for, of course, but if you feel you need more examples, books with fully worked out problems can be a great aid to you. Check out 3000 Solved Problems in Physics, Schaum's Outline of College Physics, or REA's Physics Problem Solvers in particular for boatloads of exercises + solutions. These books are also very helpful when studying for tests.

Why aren't Quantum Mechanics, Relativity, String Theory, etc. on the syllabus?

Sometimes students are disappointed that Physics I only covers the basic "mundane" aspects of physics, most of which has been known for approximately 400 years. Why don't we talk about the cool paradoxes of time-travel, quantum tunneling, zero-point energy, antiparticles, and the like? Firstly, learning the practical stuff first will be most useful to you in your career. To perform heart-surgery or build a bridge, you probably don't need any detailed knowledge about the curvature of spacetime. Secondly, as you probably already know, these topics are very complicated, such that if you picked up a serious textbook about any of them and started reading, you would find many equations that would make no sense to you, like

or any other equation for that matter, and you'd be lucky to find more than a handful of sentences that sounded somewhat like English. First you need to learn the basics, which are still quite interesting, and then work your way up. However, for the impatient or those with nerdy inclinations (engineers had better have these!), there are a number of good books that describe the deepest truths mankind knows about the universe without requiring any in-depth knowledge of math or physics. Books for the layman won't teach you the nuances of advanced subjects or the details of how we know our theories are true, but they're great for satisfying your curiosity and informing you about some philosophical aspects of modern physics. I've listed a few layman books in the favorites section, but for getting started here are some choices for what you should read first to get the big picture of modern physics:

mildly nerdy, i.e. no pocket protectors or chortling required	Hawking, Stephen. A Brief History of Time. This is the classic that kicked off the layman interest in advanced physics. Hawking, aka "the Wheelchair Guy", writes in a very non-intimidating manner to make for relatively (no pun intended) easy reading. This link is to the updated edition of the book, but you could also try the not much different original edition which sells used for 1 cent on Amazon. Another option is the books-on-tape version, although it is unfortunately not narrated by Stephen Hawking.
moderately nerdy, i.e. you may have been curious at one point how the engine of the Starship Enterprise works	Greene, Brian.The Fabric of the Cosmos. The badass string theorist is back after his highly successful book on string theory, The Elegant Universe. That one's good too, but Fabric is wider reaching and thus better for getting your bearings in the world of theoretical physics. The oft leather jacket clad Greene has an engaging personality and has been referred to as "the only physicist with groupies". You might also want to see his PBS special, The Elegant Universe, especially for its many interviews with the still-living gods of physics. This book is harder to read than Brief History, but still definitely within reach of the average college student.
serious nerdage required, i.e. you probably find programming fractals in your spare time an enjoyable diversion	Penrose, Roger. The Road to Reality. After his poorly received book about neuroscience and consciousness, The Emperor's New Mind, Penrose decided to write another book, sticking to what he knows best: physics. Penrose has been a long-time collaborator of Stephen Hawking and is without question a great physicist. This book of his ambitiously attempts to explain real math to the layman in a simple and straightforward manner. I haven't read all of it, but I intend to, and what I've seen so far is very good. Not for the faint of heart!

Moments of Inertia

Students often ask where the moment of inertia formulas in chapter 10, table 10.2 come from. These are all easily derivable from basic calculus. Maybe try to do them yourself, and if you need help, click on the Teletubbies below to ask them for advice. La La will explain the rectangular plate, Dipsy the solid sphere, and Tinky Winky the thin shell. Po's too stupid to explain anything, though. If you find any typos, email them to me and I will savagely beat the perpetrator.

If there are any other topics you would like me to add something about, let me know!