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HOW TO STUDY PHYSICS
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The following guidelines are adapted from "How to Study Physics" by David R. Hubin and Charles Riddell.
It's important to recognize that physics is a problem-solving discipline. The course places stress on major themes and principles, and one major goal is that you, the student, will be able to apply these principles to understand and solve problems. You should focus on this fact, that in a physics course, you are expected to solve problems.
An overview of your course can help you organize your efforts and increase your efficiency. To understand and retain data or formulas, you should see the underlying principles and connecting themes. It is almost inevitable that you will sometimes forget a formula, and an understanding of the underlying principle can help you generate the formula for yourself.
Take these steps to getting an overview early in the term so that all subsequent material can be integrated into your overview:
1. Examine the course outline (syllabus) carefully.
2. Preview the textbook:
a. Read the introduction and table of contents.
b. Read any notes to the student (or teacher) that are included and the preface.
c. Check the course outline to see what chapters are assigned and which are omitted.
It's important that you be well prepared for class in order to use its potential fully for integrating the course material. To prepare for the class, you should do the following:
Prior to each class:
1. Check the course outline or reading assignment to see what will be covered.
Prepare by briefly previewing the sections of the textbook that apply to the subjects to be covered. This preview will improve your ability to follow the class, for you will have seen the new terminology and will recognize signposts that will help integrate the classes into an overall picture.
2. Read the introduction and the summary of the relevant chapter and look at the section headings and subheadings. Try to formulate questions in your mind about the subjects to be covered. This question-formulating helps you manipulate and therefore better understand the material.
3. Examine the drawings and pictures. Try to determine what principles they illustrate.
4. Make notes of new words, new units of measure, statements of general laws, and other new concepts.
5. Right before the beginning of class, check your notes from the last class. Reading your notes will prepare you to listen to the new physics class as part of an integrated course and will help you to see the broad development of themes.
1. Come to the class on time. Because of the level of difficulty physics should take
precedence over other activities.
2. Take good notes. It's helpful to draw up a set of abbreviations and use them consistently in taking notes. Keep a list of them for later reference. Leave ample margins for later comments and for questions or write on only one side so that you can use the opposite side for comments and questions (see After Class, below).
3. When you copy drawings, completeness is worth more than careful artwork. You should not only copy what is on the board but also record important points that the instructor makes orally about the diagram.
4. If you get behind in your note-taking, leave a space in your notes and go on. You
can fill in your notes later with the help of a classmate or your textbook.
5. Be familiar with all the resources available to help you with your study.
1. After class as soon as possible, review and edit your notes. You need not rewrite
them. Rather, you should look for important ideas and relationships among major
topics. Summarize these in the margin or on the opposite side if you've taken notes
only on one side, and at this time you may want to add an outline to your notes.
Also, this would be a good time to integrate notes from your textbook into your
lecture notes; then you will have one set of integrated notes to study by.
2. As you review your notes, certain questions may come to mind. Leave space for
recording questions, and then either ask the teacher or even better, try to answer
these questions for yourself with your classmates and with the help of the text and other available resources.
Reading the text and solving homework problems is a cycle: Questions lead to answers that lead back to more questions. An entire chapter will often be devoted to the consequences of a single basic principle. You should look for these basic principles.
These Laws of Nature give order to the physicists' view of the universe. Moreover, nearly all of the problems that you will be faced with in a physics course can be analyzed by means of one or more of these laws.
When looking for relationships among topics, you may note that in many instances a specific problem is first analyzed in great detail. Then the setting of the problem is generalized into more abstract results. When such generalizations are made, you should refer back to the case that was previously cited and make sure that you understand how the general theory applies to the specific problem. Then see if you can think of other problems to which that general principle applies. Some suggestions for your physics reading:
1. Make use of the preview that you did prior to the class. Again, quickly look at the major points of the chapter. Think back to the points stressed in class and any questions you might have written down.
2. Read the homework problems first. If specific homework problems have not yet been assigned, select several and look these over. Critically assess what principles seem to be most significant in the assigned chapter. Based upon your brief review of the class and your examination of the problems, try to generate questions in your mind that you want the chapter to answer.
3. Read actively with questions in mind. A passive approach to reading physics wastes your time. Read with a pencil and paper beside the book to jot down questions and notes. If you find that you are not reading actively, once again take a look at the problems and the lecture notes. Read to learn, not to cover material.
4. Stop periodically and pointedly recall the material that you have read. It is a good idea to repeat material aloud and especially to add notes from the textbook into the margins of your class notes.
5. During your reading you will notice sections, equations, or ideas that apply directly to assigned problems. After you have read such a section, stop and analyze its application to a homework problem. The interplay of reading and problem solving is part of the cycle of question --> answer --> question. It helps you gain insights that are not possible by reading alone, even careful reading alone. Passive reading is simply following the chain of thought in the text. Active reading also involves exploring the possibilities of what is being read. By actively combining the questions that are inherent in problem solving with your reading, you enhance both your concentration while reading and your ability to recall and to apply the material.
You may now be like many students a novice problem solver. The goal of this section is to help you become an expert problem solver. Effective, expert problem solving involves answering five questions:
- What's the problem about?
- What am I asked to find?
- What information am I to use? What principles apply?
- What do I know about similar situations?
- How can I go about applying the information to solve the problem?
- Does my solution make sense?
You, the expert, will decide, "this is an energy problem," or, "this is a Newton 2 problem." A novice is more likely to decide, "this is a pulley problem," or, "this is a baseball problem." The novice concentrates on the surface features of the problem while you concentrate on the underlying principle. You, an expert problem solver, will answer these questions, play around (briefly) with the problem, and make drawings and sketches (either in your mind, or even better, on paper) before writing down formulas and plugging in numbers. A novice problem solver, on the other hand, will try to write down equations and plug in numbers as soon as possible. A novice will make many more mistakes than you will when you become an expert.
In a physics course it's important to remember a couple of things about physicists and physics professors:
- A physicist seeks those problems that can be modeled or represented by a picture or diagram. Almost any problem you encounter in a physics course can be described with a drawing. Such a drawing often contains or suggests the solution to the problem.
- A physicist seeks to find unifying principles that can be expressed mathematically and that can be applied to broad classes of physical situations. Your physics textbook contains many specific formulas, but you must understand the broader Laws of Nature in order to grasp the general overview of physics. This broad understanding is vital if you are to solve problems that may include several different principles and that may use several different formulas. Virtually all specific formulas in physics are combinations of basic laws.
General outline of how to approach a physics problem:
1. Read the problem. Look up the meanings of any terms that you do not know. Answer for yourself the question, "What's this about?" Make sure you understand what is being asked, what the question is. It is very helpful if you restate the problem in your own words or if you tell a friend what the problem is about.
2. Make a drawing of the problem. Even a poor drawing can be helpful, but for a truly good drawing include the following:
a. Give a title that identifies the quantity you are seeking in the problem or that describes the problem.
b. Label the drawing, including the parameters or variables on which the solution depends and that are given in the problem. Write down the given values of these parameters on the drawing.
c. Label any unknown parameters that must be calculated along the way or obtained from the text in order to find the desired solution.
d. Always give the units of measure for all quantities in the problem. If the drawing is a graph, be sure to give both the units and the scale of the axes.
e. Include on the drawing information that is assumed and not given in the problem (such as g, the value of the acceleration due to gravity), and whether air resistance and friction are neglected.
3. Establish which general principle relates the given parameters to the quantity that you are seeking. Usually your picture will suggest the correct techniques and formulas. At times it may be necessary to obtain further information from your textbook or notes before the proper formulas can be chosen. It often happens that further information is needed when the problem has a solution that must be calculated indirectly from the given information. If further information is needed or if intermediate quantities must be computed, it is here that they are often identified.
4. Draw a second picture that identifies the coordinate system and origin that will be used in relating the data to the equations. In some situations this second picture may be a graph, free body diagram, or vector diagram rather than a picture of a physical situation.
5. Even an expert will often use the concrete method of working a problem. In this method you do the calculation using the given values from the start, so that the algebra gives numerical values at each intermediate step on the way to the final solution. The disadvantage of this method is that because of the large number of numerical calculations involved, mistakes are likely, and so you should take special care with significant figures. However this method has the advantage that you can see, at every step of the way, how the problem is progressing. It also is more direct and often makes it easier to locate a mistake if you do make one.
6. As an expert, you will more and more use the formal method of working a problem. In this method, you calculate the solution by doing as much as possible without using specific numbers. In other words, do as much of the algebra as you can before substituting the specific given values of the data. In long and complicated problems terms may cancel or expressions simplify. Our advice: gain experience in problem solving by substituting the numbers when you start physics, but gradually adopt the formal approach as you become more confident; many people adopt a compromise approach where they substitute some values but retain others as symbols (for example, "g" for the acceleration due to gravity).
7. Criticize your solution: Ask yourself, "Does it make sense?" Compare your solution to any available examples or to previous problems you have done. Often you can check yourself by doing an approximate calculation. Many times a calculation error will result in an answer that is obviously wrong. Be sure to check the units of your solution to see that they are appropriate. This examination will develop your physical intuition about the correctness of solutions, and this intuition will be very valuable for later problems and on exams.
An important thing to remember in working physics problems is that by showing all of your work you can much more easily locate and correct mistakes. You will also find it easier to read the problems when you prepare for exams if you show all your work.
8. When tested, you will have to do problems under a strict time limitation. Therefore, when you are finished with a homework problem, practice doing it again faster, in order to build up your speed and your confidence. When you have completed a problem, you should be able, at some later time, to read the solution and to understand it without referring to the text. You should therefore write up the problem so as to include a description of what is wanted, the principle you have applied, and the steps you have taken. If, when you read your own answer to the problem, you come to a step that you do not understand, then you have either omitted a step that is necessary to the logical development of the solution, or you need to put down more extensive notes in your write-up to remind you of the reasons for each step. It takes more time to write careful and complete solutions to homework problems. Writing down what you are doing and thinking slows you down, but more important it makes you behave more like an expert. You will be well paid back by the assurance that you are not overlooking essential information. These careful write-ups will provide excellent review material for exam preparation.
If you have followed an active approach to study similar to the one suggested here, your preparation for exams will not be overly difficult. If you haven't been very active in studying, your preparation will be somewhat harder, but the same principles still apply. Always remember: Physics courses, and therefore physics tests, involve problem solving. Hence, your approach to studying for exams should stress problem solving.
Here are some principles:
1. Prior to the exam, follow the three steps below. These steps should give you a reasonably good idea of what has been stressed and on what you can expect to be tested.
a. Review your notes and recheck the course outline. Your goal at this point is to make sure you know what has been emphasized.
b. Reread your solutions to the homework problems. Remember that these solutions, if complete, will note underlying principles or laws.
c. Review the assigned chapters. Once again, your purpose in this early stage of test preparation is to make sure you know what topics or principles have been emphasized
.
2. From this rapid overview, generate a list of themes, principles, and types of problems that you expect to be covered.
3. Review actively. Don't be satisfied with simple recognition of a principle. Aim for actual knowledge that you will be able to recall and to use in a test situation. Try to look at all the possible ways that a principle can be applied.
4. Effective test preparation involves an interaction among homework problems, the classes, your notes and the text. Review actively, including self-tests in which you create your own problems which involve a combination of principles. You need to be sure that you can work problems without referring to your notes or to the textbook. Practice doing problems using both the concrete and the formal approaches, to see which you are more comfortable with.
5. Remember that tests will include a variety of different problems. You want to look back on an exam and say, "I know how to do friction problems so well, that even though they were asked in a weird way, I could recognize them and solve them."
Weekly Flow Chart for Studying Physics
http://dgende.homestead.com/index.html
http://www.oberlin.edu/physics/dstyer/StudyTips.html
See below.
Study Tips for Introductory Physics Students
Compiled and edited by Dan Styer,
Oberlin College Physics
Department;
http://www.oberlin.edu/physics/dstyer/StudyTips.html ;
last updated 21 May 1997.
This World Wide Web page gives tips that Oberlin College Physics faculty have found useful for their students, particularly for students in introductory physics courses. If you have suggestions, please inform the compiler.
Following these tips and suggestions will take more time and effort than does a casual reading of the text, but they will pay off in a savings of time when you do the problems, in a better understanding of physics, and in increased confidence on exams.
General tips
Keep up with the course. Once you fall behind it is very difficult to catch up. If you ignore this advice and do fall behind (it happens to the best of us sometimes), and if you cannot manufacture the time to do a thorough job of catching up, then skim the passed-over course material for its most important points and move on to a thorough study of the current course material. Attempting a thorough study of last week's material usually results in being one week behind for the entire semester.
Do the reading before attending the lectures. This way way you won't need to take notes on everything the lecturer says, because you will already understand some of the material and you will know that some of it is treated well in your textbook. If you follow this advice, then you can use the lecture for what lecture is good at: asking questions, following the demonstrations, discovering how this week's material fits into the overall structure of the course, and gaining a conceptual understanding of the material under study. At the same time you can use the text for what text is good at: presenting derivations and sample problems, and getting the details right.
Devote a little time to studying physics each day, rather than a large amount of time once a week: this allows the material to sink in.
Make some friends in the course and work through the material in small groups. Use these groups for discussion, problem suggestions, and companionship. Throw ideas into the group's "pot" as well as drawing ideas from it. Do not use your study group as a crutch.
Attend the course's conference sessions to learn informal techniques that are not well-taught through the lecture method.
Do not memorize. In almost all cases, the temptation to memorize indicates a simple a lack of understanding. In the words of Charles Misner: "The equation F = ma is easy to memorize, hard to use, and even more difficult to understand."
Tips regarding reading
Read aggressively. The amount of reading assigned in a physics course will be far less than the amount of reading assigned in a literature or a sociology course, but the reading is much denser and your teacher expects you to read it thoroughly, thoughtfully, and critically. Read with pencil and paper in hand, and follow the algebra yourself. Keep a list of questions and of points that you don't understand.
Take notes in your book. Mark the most important points and record why they are important. The act of deciding what is important is the first step in turning reading from passive page-turning into active, aggressive--and rewarding--penetration. (Some students take notes by highlighting with a yellow marker. This is all right, but don't fall into the trap of highlighting everything in your book!)
Examine the sample problems carefully.
If the reading is too dense, try skimming it once to get an overview of what's going on, then coming back and reading in detail the second time.
The active, aggressive reading advocated here is very time-consuming. Reserve it for the most important parts of your textbook. You might be able to get your teacher to list for you the most important sections, or you might have to decide for yourself.
Tips regarding lectures
Listen aggressively. What you get out of lecture is proportional to what you put into it. If you follow the lecture, think about the material, ask questions, and care about what's going on, then lecture will be an active, productive learning experience for you. If you sit slumped in your seat, then lecture will give you a backache and little more.
Come to lecture armed with questions for your teacher, developed from doing your reading.
Some students are used to rewriting their lecture notes or taping lectures and then listening to them twice. We discourage such practices, not because they are useless, but because they are less profitable than other practices advocated here. (In particular, taping a lecture does not record the all-important blackboard display.)
On the other hand, many students do find it useful to review each lecture by making a simple list of the most important topics, and also a different list of the puzzling aspects that need clarification. This review can be done through your notes or in your memory or with your study group, but it is best done soon after the lecture.
Tips regarding problems
Do the reading and listen to the lectures before attempting the problems.
Do not put off the problems until the night before they are due. In particular, take a stab at the problems before conference sessions, so that you can ask well-formulated questions there.
Read the problem carefully to make sure you understand what is being asked.
Do not rush into solving a problem. Instead, first formulate a strategy for solving the problem. Usually this is as simple as classifying the problem according to its method of solution. Is it a "constant acceleration" problem? A "work-energy" problem? A "Gauss's law" problem?
If you find yourself writing pages of words or working reams of algebra, then you are off on the wrong track. Stop, reread the problem, think, reformulate your strategy, and then start over again from the beginning.
Think of the problems as mystery stories. How would Sherlock Holmes approach this problem?
Don't search through your book for "the right equation". You will not be able to solve your problem by finding an appropriate equation and then plugging numbers into it. No self-respecting college-level teacher would assign such a problem.
If the final answer called for in the question is a number, then you will ultimately have to plug numbers into an equation. But even in such cases it is almost always easier and less error-prone to keep the quantities as symbols until the very end. (For one thing, it is easier to do algebra with the symbol "m" than with the value "2.59 kg".)
Sometimes the problem statement will give you more information than is needed to answer the question. Sometimes it will give you less information than is needed, and ask you not for an answer but for a list of the unknown information required to find an answer. Sometimes the problem will be a short narrative from which you need to extract relevant information. Students often find such problems exasperating, but in fact they develop an important problem-solving skill called building a mathematical model. Problems that arise in the world outside of your textbook usually come with more or less data present than needed to solve the problem. The ability to recognize which data are needed and which are irrelevant is an important practical skill.
Review your problem solutions when they are returned (or when model solutions are handed out). Why did you make the mistakes you did? How could you have avoided them? This review should be quick (after all, you have new material piling up) but five or ten minutes spent in this review can save hours by preventing similar mistakes in the future.
More suggestions are available in the page Solving Problems in Physics.
Tips regarding lab work
Skim the lab instructions before coming to lab. You won't be able to understand things fully without the equipment in front of you, but you'll get a general overview that will serve you well and ultimately save you time.
Don't be afraid to fiddle with lab equipment unless you have been specifically warned away from it. Many students are reluctant to play with electrical equipment because they're afraid of being shocked. Unless you are told otherwise, the stuff used in lab won't hurt you.
Tips regarding exams
Keep up with the course. Don't cram at the last minute.
Get a good night's sleep. Even if you ignored the advice above and have to cram, limit cramming in favor of sleep.
Prepare a one-page summary of the material being examined.
Don't memorize. Your teacher expects you to work with ideas and solve problems, not plug numbers into equations.
Bring to the exam a calculator (fully charged) and several pens or pencils (sharpened).
As you read an exam problem, place a check mark beside the given data and underline the unknown quantity to be found. This will help you prepare a strategy and help you avoid answering a question that is similar to but different from the one that is asked.
Make a sketch or graph to familiarize yourself with the situation. Make sure you understand the problem before plunging in.
Weaknesses
If you need help with mathematical background, consult either Arthur Beiser, Essential Math for the Sciences (McGraw-Hill, New York, 1969) or Daniel Kleppner and Norman Ramsey, Quick Calculus (Wiley, New York, 1985).
Guard against the two most common failings: reliance on memorization and on "plug and chug" problem technique.
3. General information about study techniques can be found at http://www.how-to-study.com/