Study Tips

Learning Physics

Last revised 1999/08/20
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The Nature of Physics

In the evolution of western, scientific human thought the step out of the "ocean" onto the "shore" was the very revolutionary idea that we should seek some sort of understanding of phenomena by looking at the numbers generated by (freely designed) measuring devices. I think this began with Boyle, et al, in the 1600's. Prior to this, such a mode of understanding was not even a part of human thinking. Since then it has become the essential feature of every human invention which goes by the name of quantitative science .
Bob Sciamanda
Physics, Edinboro Univ of PA (retired)
PHYS-L mailing list, 1998/05/13

Physics is a logical structure composed of quantitative statements, and the language it is written in is mathematics. Historically mathematical expressions have often proven to be applicable far beyond the phenomena that first gave rise to the expression. As a result I believe that the mathematical nature of physics is a reflection of reality itself being mathematical. However, pure mathematics is not physics; physics must correspond to observable and measurable events. In physics there are always pictures behind the mathematics. If there are no pictures there is no physics, and if you don't understand the pictures you don't understand the physics. In essence, mathematics is most useful as a compact description of the pictures.

Physics has levels of understanding, and in fact physics is more deep than broad. If the mathematics at the first level is properly understood, that mathematics acts as one of the pictures for the next level. Thus full understanding at deeper levels cannot be achieved without first having obtained reasonable understanding of the mathematics of simpler levels. At each stage you must translate the pictures into a mathematical understanding that you can use to construct your qualitative understanding of the next stage. The interplay between qualitative understanding and quantitative calculation is vital. Neither alone is physics.

The Nature of Physics Knowledge

Psychologists have studied the question of how physics knowledge is stored and used in the human brain. I am most familiar with the work of Jill Larkin, although certainly many others have contributed. Larkin's work involved having beginners and experts work standard physics problems aloud.The records of this work were analyzed for patterns of thought, and especially for differences in the patterns of thought of beginners and experts. I will come back to this work in talking about how to solve physics problems, but for now what I am interested in is the way people store physics information mentally. The most compact form of physics information is of course equations, and equations are stored mentally.But they are not stored alone.Two features of the storage stand out:

  1. Equations are stored in related groups: ask an expert for a particular equation and he/she also recalls several other equations automatically.
  2. Pictures of various types and English explanations always accompany the equations.

An example of a group of equations that are always stored together are the equations for motion under constant acceleration. Incidentally, experts always store a label of this type with the equations. The label ensures that the equations are not misused in situations to which they don't apply. The equations for constant acceleration are

x = x0 + v0t + (1/2) a t2

v = v0 + a t

The definitions of the quantities are recalled whenever an expert recalls the equations themselves:

x is the position of a moving object
v is the velocity of the object
a is the acceleration of the object (a constant, remember)
t is the time at which the position and velocity are measured

A subscript of 0 means the value of that quantity when t=0.

There are some additional things I have observed in myself and other trained physicists. I carry a picture of the graph of the equations in my head which I recall whenever I see an equation of reasonably simple form. For complicated equations I generate a mental graph of individual terms or even of factors within the terms. Given v = (1/2) a t2, my mind reacts with "parabolic in t, it will rise quickly." However, the reaction is conceptual, not in terms of a statement in English.

Another form of visualization is providing interpretations for the symbols. I read "x", I say "x", I write "x", but my mind always reacts "position." I may even translate an equation mentally, just as I would with a difficult phrase in a article in French. Hence

v - v0 = a t

is read mentally as "the change in velocity is given by the acceleration times the elapsed time."

Experts always keep the physical meaning of equations in mind. The equation itself is just a sequence of nonsense syllables. What is important is what the symbols mean. I have a mental image of my moving around a fixed starting point, changing velocity or not according to the situation. Sometimes I am the starting point and it is a car moving. Often I visualize a checkerboard pattern on the ground as a kind of graph paper. I do similar things with other equations, whenever possible.

How to Learn Physics

Keep up with the homework. In a recent class I was led to calculate the correlation between number of homework problems attempted and the overall semester grade for each student. I found that 87% of the variation of the semester scores of students in the class could be predicted using only the percentage of homework problems they attempted. A couple of extraneous things raise this correlation: All of these students were honors students quite capable of learning physics, so there was little competing talent effect on the correlation, and some of this correlation comes about because the same personal qualities that lead to getting homework done on time are good for other aspects of learning physics. Nonetheless, the correlation is too large to be ignored. Do the homework.

Physics must be "understood." You will hear this from me and other physics teachers again and again, only typically we don't explain what we mean. "Understanding" refers to making the connections between phenomena we know about and the logical/mathematical descriptions of the phenomena that make up physics theory. For each principle and equation, find something you are familiar with or at least have seen demonstrated that is an application of the principle. Figure out how changes in the principle that seem otherwise plausible to you would conflict with the familiar events. Use these conflicts to "understand" why the principle is expressed the way it is rather than in some alternate form. Practice making these connections. Ideally, after you are done, you find it difficult to understand how a piece of physics could be any different than it is. If you have to memorize physics by rote, you don't understand it yet.

I do not mean to say that memorization is unnecessary. Definitions are essentially arbitrary, and at least some will have to be memorized. Moreover, memorization provides fast recall of equations for tests, is a familiar process you already know how to do, and by now you have a pretty good feel for when you have something reliably memorized. It is also a boring, time-consuming task, and memorized information is prone to disappearance in the middle of a test when you need it most. So you want to memorize judiciously and have backup ways of recalling information if necessary. If you know you can derive or reconstruct an equation, you are far less likely to forget it anyway.

So here are some tips on what to memorize and how to organize your memory work:

  1. The structure of physics can be used to help you learn equations. Prepare study sheets (sample) with equations in logical groups and in logical order within the groups. Arrange the groups themselves in a logical order. It is easier to remember structured information than isolated facts.
  2. You have to know the meaning of equations to use them, so memorize the meaning in English and practice translating the English into equations. Or if you prefer, make sure you practice translating the equations into English in order to retrieve the meaning.
  3. On study sheets, always include diagrams with your equations to show the meaning of the variables in the equations. When possible include a graph that shows the behavior of the equation.
  4. Use units to help construct equations.
  5. Make use of the fact that most quantities come into simple equations to the first power only. Use qualitative arguments to figure out whether the quantity is in the numerator or denominator. Take special note of quantities that are not present to the first power, and if possible figure out why they occur the way that they do. This technique is especially effective in checking that an equation you are not sure of is in fact correct.