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Physics is a tough subject. Here are some general concepts that I have observed which may help your understanding:

1. No free lunches, but...

Intuitively, this makes sense. The universe does not give out energy, and you can't get something for nothing. This fact and its corollary (rule #2) appear all over the place. The philosophical/theological question remains: where did our lunches (i.e., the energy of the universe) come from in the first place?

2. ...You can't lose your lunch, either
Thankfully, the universe is fair. If energy exists, it can't be lost. Someone can take your "lunch" (like friction), or you can use it yourself to make heat. But either way, your lunch is transformed into another kind of energy. This idea of conservation is crucial. By using the notion of flux conservation (the pulling strength of a field does not change) we can derive Gauss's law and the general form of fields in nature (inverse square laws). All from the simple idea that once something exists, it cannot disappear.

[Interesting note: whenever something moves up, something else must move down (the center of gravity of the universe stays constant). When we jump up, the earth is pushed down. When we walk left, the earth is pushed right. This is in interesting -- we can only move by displacing other mass -- we cannot turn energy into motion without moving other mass. Even gravity, in which we fall towards the earth, results in the earth falling upwards towards us. Conservation is everywhere.]

3. Understand the formula
If you simply want to pass a class, memorize the equations. But to learn an equation, you must understand where each and every part comes from. Know the meaning and role of every variable. Why do we integrate and not differentiate? Multiply and not divide? Why do we need the constants -- are they a mathematical/physical necessity or simply inserted to make the units simpler? If you can't answer these questions about something you've learned, ask someone who seems to know. If they can't answer them, then you both have something to learn :).

Why is this so important? Physics builds on many fundamental principles. Gaps in understanding will come back to haunt you (as they have with me) because many ideas are based on or related to other concepts. Try learning algebra without mastering multiplication. Try learning calculus without knowing algebra. Try learning physics without knowing calculus. Get the picture?

[Note: this isn't meant to discourage people who don't know calculus yet or don't like math. Most articles will focus on intuition, with optional math sections to show students how to solve problems. These sections will justify students' time here, aside from academic curiosity alone :) ].

4. Piece by piece

This relates to the above discussion. Try to break down a complex idea into its constituent parts. Superposition is an incredible tool - components can be considered separately (like acceleration in the x and y directions). Superposition applies in other areas as well, as we shall see. Learn to recognize when a problem can be broken down (I'll write more about this).

5. Learn by analogy

I originally doubted the power of analogy (essentially an abstraction). Then I personally saw the difference in viewing flux as a mathematical definition and a physical process (reflected by the difference in my grades on the midterm and final). Analogies are not as rigorous as formulas, but they are key to developing an understanding. Do you tell a 3rd grader that a circle is "round" or "the set of all points in a plane equidistant from a given point"? The math/physics definition is easier to follow when you know what is going on. Besides, physics is full simplifications -- electrons are point charges (they have finite, not infinitesimal size), gases are made ideal, systems are approximated as linear, etc. The nitpicky details come after, not before, intuition.

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Last modified: 4/4/02