How to Study Physics
In this section we make some suggestions on how to approach this
course. Individuals are all different, and not every suggestion
will apply equally to everyone. But in our experience, most
suggestions will apply to most people.
- Plan on spending a lot of time -- a minimum of three to
five hours of study for each hour in class, not
including the time you spend on labs.
- Physics texts cannot be read quickly. You may find an
initial skimming of a section or chapter useful,
but by and large you should read with paper and
pencil in hand. Don't just read derivations, but
work them through yourself, and try to understand
every step. Try both to develop an intuitive, qualitative grasp
of the material, and to understand how the
intuitive picture is expressed and developed
- Treat the worked examples in the text and study guide in
the same way -- work them through. When you're done,
try closing the book and seeing if you can work out
the example without help. Also, try explaining the example to
yourself or someone else -- not just the mathematical
steps and equations, but why you are using those
equations, and what physical principles are involved.
- Work large numbers of problems; the assigned homework
problems should be regarded as a warm-up. You
should do a substantial fraction of the problems in
the text and study guide for each chapter. There are at least two
reasons for this extraordinary demand. First,
working problems helps you understand the physics
more thoroughly; it is a common experience (among physicists as
well as physics students!) to read through new
material carefully, think you understand it, and
then be stumped when you try to do a calculation. Second, there
are specific techniques that are involved in
solving problems. We will lay out some general
guidelines below, but the more practice you get, the more you will
- Work with others. It often helps to study and work problems
with one or two others in the class. And by working in
groups, you can often work more problems, and cover more
material, than you can working alone.
- Don't get behind in your work. Physics is a cumulative
subject; the material you will study later in the
semester (and the year) builds on what you have
- GET HELP WHEN YOU NEED IT. We expect you to have a lot
of questions about this material, and to experience
a certain amount of confusion and frustration at
times. It is a necessary, if unfortunate, part of learning. One
of the most important functions of the faculty at
St. John's is to be available for individual help;
in addition. The only stupid questions are the ones
that don't get asked.
In addition, some tutoring help is available on both campuses.
See your instructor or the appropriate counseling
office for details.
Understanding an Equation
In this section we make some suggestions that we hope will help
you to think about equations, and use them effectively.
- State the equation in words, and try to understand what
the equation is saying about nature. Learning an
equation is NOT the memorization of symbols, but
the understanding of a physical process.
- Describe each quantity in the equation. What does the
quantity describe physically? Is it a vector or a
scalar? What are its units? What sign conventions
- Describe each operation in the equation (e.g.,
differentiation, scalar or vector multiplication,
summing, etc.) How would you actually perform these
operations given all the quantities?
- Describe the relationships implied by the equation. How
does each quantity depend on the others? Do these
dependencies relate to your own experience?
- What is the origin of the equation? Is it a definition
(for example, momentum as the product of mass and
velocity) or a relationship between independently
measurable quantities? If the latter, what experiment could check
the validity? Does it represent an empirical law,
or is it derived from more fundamental laws? Do
you understand the derivation?
- Try to think of a simple physical system described by
How to Solve Physics Problems
The suggestions given here are suggested not only by our own
experience, but are the results of considerable research conducted
in recent years on how successful scientists and engineers solve
problems. See for example the article by Robert Fuller, "Solving
Physics Problems," in the journal Physics Today, September 1982,
p. 43. (The SJU library and the physics library both have this
- First, get an intuitive idea of what the problem
involves. Describe the problem to yourself. Make
a careful sketch. Ask yourself what the qualitative features of
the solution are likely to be. Learning physics
involves combining an intuitive understanding and a
mathematical description of nature. If you jump too
quickly to the mathematical description, it is easy
either to head off in a wrong direction, or to get
a result that you don't understand fully -- even if it's correct.
- Once you understand the problem intuitively, plan a
solution. What information are you given, and what
do you need to calculate? What physical laws pertain
to this problem?
- Now, proceed to a mathematical description of the
problem. What equations will you need? How will
you use them? Try not to think of the equations as
"formulas", but rather ask yourself what they tell you about
nature. (See the discussion above on understanding
- Carry out your calculations algebraically at first; that is,
don't put in numerical values until the end. If you
substitute in numbers too soon, it is easy to lose sight
of how various quantities affect each other. Suppose, for
example, that you are considering a ball tossed into the
air. How does the maximum height depend on the initial
velocity? If you put in numbers too soon, you can easily lose
sight of relations of this sort, which are often the main
point of the problem!
- Finally, check your answer. Is it "reasonable," both
numerically or algebraically? Or have you, for example,
calculated a velocity that is faster than light, or
inadvertently predicted that a ball thrown into the air will
accelerate upwards? Checks of this sort can either give
you confidence in your solution, or point up possible
All of this, of course, is more easily said than done. As you
begin studying physics, both your intuition and your mathematical
skills are relatively undeveloped; it can be hard to know what to
trust, or where to begin. Nor can the above suggestions be
followed mechanically, or by rote. Try things. You may think you
know the right equation, but aren't sure. Try it. You may get
the "right" answer; so far, so good. But don't stop there! Go
back and understand the equation, where it comes from, how it's
derived, what it says about nature, why it applies to this
problem. And get help if you need it. Then you'll have learned
As an example of this problem-solving strategy, consider the
following problem, which is typical of the ones we will be doing
early in the semester.
Problem: A ball is thrown vertically upward with an initial
velocity of 5 m/s.
- What is its velocity after 0.5 seconds?
- What is its velocity after 1.0 seconds?
- How long does it take to reach its maximum height?
Step 1: Examine the qualitative features of the motion.
The only force acting on the ball is the force
of gravity, which near the surface of the Earth produces
a constant acceleration. That force will act
to slow the ball, bring it to a stop at some
maximum height, and then speed it downwards; the
speed will continue to increase until the
ball hits the ground. (This sort of analysis
is fairly simple here, but it will become more sophisticated as we
encounter more and more challenging problems.)
Step 2: We know the initial velocity (call it v0) and the
constant acceleration of gravity g. Since the
ball can move both up and down, we need to choose
a sign convention; arbitrarily we will choose
the positive direction to be up (any choice is
OK, as long as you're consistent). We don't know how long
the ball will take to reach the top of its
arc, or what the velocity will be at any
instant; so we must look for a mathematical description that
relates v0 and g, which we know, to the
(unknown) velocity at any instant.
Step 3: An appropriate equation would seem to be
v = v0 - gt.
Notice that at t = 0, v is positive, so our sign convention
is obeyed. Since the force of gravity is downward,
we have "-g" for downward acceleration.
(How would we write this equation if we
had chosen down to be positive?) At this point,
you should ask yourself if you really understand
this equation. Where does it come from? How is
it derived? Does its form depend on the fact
that the acceleration is constant? How would the
equation look if the maximum height were near the
Moon's orbit, where the acceleration of gravity
is much smaller?
Note also (step 5) that the equation agrees with our
qualitative analysis of the problem. As the time
increases from zero, the velocity, which is
initially v0, decreases to zero and then
increases in a negative sense (i.e., is directed
Note also that the equation is seriously misleading in one
way. As time gets larger and larger, the
equation predicts an increasing downward
velocity. But this prediction is wrong!
Eventually the ball will hit the ground, and
either come to rest or bounce up again. Even in a simple
problem, apparently, we can come to grief if we
use the mathematics blindly.
Step 4: Now let's get some numbers out. For part a,
v = 5.0 m/s - 9.8 m/s2 (0.5 s) = 0.1 m/s (+ hence up).
The ball is apparently close to the top of its arc here,
since the velocity is small compared to v0, but
still positive. Note too that the units are
correct. Get used to the habit of checking
units; as problems become more complicated,
analysis of units can be a helpful check. Part b, of
course, is very similar:
v = 5.0 m/s - 9.8 m/s2 (1 s) = -4.8 m/s (- hence down).
Here we must be careful. Do we know the ball hasn't hit the
ground yet? How? What would the situation be at
2 seconds? 60 seconds?
Now consider part c: We know the velocity must be zero at
the instant that the ball reaches its maximum
0 = v0 - gt;
we can solve this equation for its only unknown, the time of
maximum height, to obtain
t = v0/g = 5.0 m/s / 9.8 m/s2 = 0.51 s.
This result is certainly consistent with part a. Does it
tell us any more about part b? Again, note that
the units work out.
Step 5: In this instance, we have done our checking as we
went along. We checked units, and also looked
for internal consistency. If for example we had found
t to be 0.45 s in part c, we would have the
ball still going up after it had reached its
maximum height. What other checks of this sort occur to you?