AP Physics 1 - Introductory Material
This material should mostly be review. However, there is a chance you may not have studied it before
this course. Regardless, this information is important and lays a foundation for our studies this year.
1 WHAT IS PHYSICS?
While it is difficult to concisely define Physics, Physics is described by some as the most fundamental of the
physical sciences. One of the main goals in physics is to explain with mathematical precision why the physical
world works the way it does. For example, if you drop your pencil it falls in a predictable manner. In Physics we
want to know why the pencil falls, the rate at which it falls, what parameters effect its fall, whether or not other
objects will fall in a similar manner, and the ultimate question…why? In many ways, you can think of Physics as
the science of answering the question “Why?” in terms of our observations of physical phenomena. In
answering the question, “Why?” we also seek mathematical precision in our answers. Thus, we will use a lot of
equations to model the world around us. As we will see, all models have uses (pros) and limitations (cons).
Learning Physics is exciting as it will change the way you view the world around you. As you learn to view the
world through the “eyes of Physics,” you will view the world with new appreciation and understanding. Learning
Physics is also challenging. There are times where “common sense” and society in general have created
misconceptions that you will have to “unlearn.” The mathematics of the course doesn’t exceed Algebra 2 in
terms of concepts, but you will likely work with more symbols and literal equations in this course than you are
used to. The mathematics will always be used in some real physical context – which may be new to you as well.
With a lot of practice, you will see how mathematics and physics harmonize to give you (and mankind in
general!) powerful tools that can be used in many fields of study and careers.
This course corresponds to a first semester university-level algebra-based course. Typically such a course is for
those declaring a non-physics or non-engineering major. However, this course gives a valuable foundation for
anyone who needs or wants a knowledge of physics. This course focuses mostly on classical mechanics – the
study of the motion of macroscopic objects without regard for relativistic of quantum effects.
1.1 WHAT WILL WE STUDY THIS YEAR?
The course can be broken down into 9 major units of study, as listed below. For a more detailed list, please
consult the course syllabus.
1. Linear Kinematics (also known as rectilinear motion)
1.1. We will study 1D and 2D motion without regard for the cause of the motion or the effects of an object’s
mass.
2. Linear Dynamics
2.1. Here we will mostly focus on Newton’s three main laws of motion.
3. Uniform Circular Motion, Gravitation, and Kepler’s Laws
4. Work and Mechanical Energy
5. Linear Momentum
6. Simple Harmonic Motion
7. Rotational Motion
7.1. Rotational kinematics, rotational dynamics, angular momentum, rotational energy
8. Mechanical Waves
9. Basic Electrostatics and Circuits
2 STANDARDS OF MEASUREMENT AND PREFIXES
Since Physics’ ultimate goal is to describe the physical world, we measure everything we possibly can.
As you know, a measurement without units is meaningless. If I tell you I’m a little over 6.5 tall, what
does that mean? Five and a half feet, centimeters, meters, miles? You also have to consider that the
Physics community is international. Thus, someone finally said, “Hey, we need one standard way of
doing things the world around1.” Enter the Système International – better known to us as SI. The SI is
the international standard of units in science2 and what we will be using in AP Physics.
There are seven basic units that all others are composed of. For now we will focus on length, time and
mass (we’ll deal with the others later on). The SI units and the abbreviations for these three are:
 Length and Distance – meter (m)
 Time – second (s)
 Mass – kilogram (kg)
Later on, we will learn about the unit of force called the Newton. However a Newton is actually
composed of the three units above:
.
To get an intuitive feel for these units, I recommend visiting http://htwins.net/scale2/ and
http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/.
3 SCIENTIFIC NOTATION AND PREFIXES
Using Scientific Notation helps make very large numbers (1,000,000,000,000,000 kg [the mass of a
small satellite in space]) and very small numbers (0.000000001 m [the size of an Atom]) more
manageable whenever a number must be written down or used in a calculation. We will use scientific
notation heavily in this course. It saves a lot of writing and often makes the math easier. If you’re not
familiar with scientific notation I recommend the following sources in conjunction with the example
problems that are to be worked in class:
 http://www.purplemath.com/modules/exponent3.htm
 https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8thscientific-notation/v/scientific-notation
 Your text book likely has an appendix covering scientific notation. If not, there are dozens of
good resources readily found with an Internet search engine.
*Note: Another phrase for powers of ten is “order of magnitude.”
The SI is composed of prefixes attached to base units that can be expressed as abbreviations. The
base units represent the measurement that you are making (meter for length, second for time, etc…)
while the prefix tells you how much of the base unit that is being considered. You should also be
familiar with what the powers of ten mean in terms of “regular” numbers based on the common prefixes
used in AP Physics and other sciences. The table below is worth memorizing.
Table 1 - Unit Prefixes
1
2
(nano)
One one-billionth of base unit
One hundred bases of base unit
(micro)
One one-millionth of base unit
(kilo)
One thousand bases of base unit
(milli)
One one-thousandth of base unit
(mega)
One million of base unit
(centi)
One one-hudredth of base unit
(giga)
One billion of base unit
The actual history and development of the SI is slightly more complex.
Interestingly, certain types of engineers still work in Imperial/US Engineering units.
There are times when we deal with very large or very small units. Instead of repeatedly saying “five
times ten to the sixth pascals,” we could say, “Five megapascals.” These prefixes are simply “verbal
shortcuts” and knowing them is important.
*Note: We will most often use the prefixes from micro to mega.
4 DIMENSIONAL ANALYSIS AND UNIT CONVERSIONS
We often use the word “dimension” when discussing units. The phrases “dimensional analysis” and
“unit analysis” are synonymous in this course. Unit conversion is a fairly simple but crucial skill in
physics. On the theoretical side, problems will often provide values in one unit and require the answer
in another unit. Practically speaking, in the lab you may have equipment that only allows you to
measure in a certain unit, but you may desire a different unit in your final result. Mathematically, we
treat units just like algebraic variables. We convert units by applying some basic algebraic properties.
Dimensional analysis will not be used in each problem on the AP Physics exam, but we do need to
learn the method of converting units in the rare situations in which it is necessary. In case you are still
unfamiliar, Dimensional Analysis looks a bit like this:
It’s expected that you already know how to perform unit conversions. However, if you need some help,
the following links below offer great resources on how to complete these problems:
 http://www.alysion.org/dimensional/fun.htm
 https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/metric-system-tutorial/v/unitconversion
The following sources may prove useful to double check your work when unit conversions are involved:
 Google will perform unit conversions for you. For example type “5 feet in meters” in the search
bar and you will receive “5 meters = 16.4041995 feet” as a result.
 Wolfram Alpha (www.wolframalpha.com) will perform unit conversions very similarly to Google.
*Note: I mentioned Google and Wolfram Alpha as convenient tools to double check your calculations on
your homework and labs, but DO NOT COMPLETELY RELY ON THEM. Your quizzes, exams, and the
AP Exam will require you to know how to convert units without any assistance from a computer.
5 LITERAL EQUATIONS
The method of using literal equations is related to dimensional analysis in that we will often be
concerned with the “unit” of the measurement or quantity that we are looking for. When using this
method, you will algebraically rearrange an equation to solve for an unknown variable WITHOUT
substituting numbers into the equation.
While you are allowed to use a calculator on the Multiple Choice section of the exam AND the Free
Response section of the exam, MANY problems can only be worked without the aid of a calculator.
Showing your work will be a requirement in order to receive credit – no exceptions.
There are a few key principles to keep in mind:
 Both sides of an equation must be dimensionally balanced (“equals” means equal in value and
in units).
o Being dimensionally balanced does not automatically make an equation valid.
 We treat units exactly like algebraic variables.
o You can only add or subtract like units.
 You “cancel” units or calculate their exponents as if they are algebraic variables.
 Some equations contain constants. There are two main types of constants:
o Fundamental Physical Constants
 They have units!
 For example, the speed of light in a vacuum is roughly
.
o

Constants of Proportionality
 They may or may not have units.
 They are numbers we multiply an equation by to make the equation match the
experimental observations.
When performing dimensional analysis and/or utilizing the method of literal equations, we write
the physical variable in brackets [ ] to separate it from the units themselves.
The following source may prove useful in understanding the algebraic handling of units:
 https://www.khanacademy.org/math/algebra/introduction-to-algebra/unitsalgebra/v/dimensional-analysis-units-algebraically
PROCEDURE
In general, we solve a literal equation for a particular variable by following the basic procedure
below.
1. Recall the conventional order of operations, that is, the order in which we perform the
operations of multiplication, division, addition, subtraction, etc.:
a. Parentheses
b. Exponents
c. Multiplication and Division
d. Addition and Subtraction
This means that you should do what is possible within parentheses first, then exponents, then
multiplication and division from left to right, then addition and subtraction from left to right.
If some parentheses are enclosed within other parentheses, work from the inside out.
2. If the unknown is a part of a grouped expression (such as a sum inside parentheses), use the
distributive property to expand the expression.
3. By adding, subtracting, multiplying, or dividing appropriately,
(a) move all terms containing the unknown variable to one side of the equation, and
(b) move all other variables and constants to the other side of the equation. Combine like
terms when possible.
4. Factor the unknown variable out of its term by appropriately multiplying or dividing both
sides of the equation by the other literals in the term.
5. If the unknown variable is raised to an exponent (such as 2, 3, or ½), perform the appropriate
operation to raise the unknown variable to the first power, that is, so that it has an exponent
of one.
Examples:
P1V1 = P2V2 . Solve for V2.
Divide both sides by P2:
P1V1 = V2
P2
6 REASONING AND PROPORTIONALITY
Throughout this class, you will need to develop a sophisticated ability to understand how one number in
an equation affects another number in the same equation. Such questions can be qualified as
“proportionality problems.” Developing a sense of how one quantity can numerically effect another
quantity will be heavily tested on the AP Physics exam. As we work example problems throughout the
year, you will repetitively be asked how changing one variable in an equation changes the final answer
and/or changes the physical system that is being studied. For example, consider the following equation:
Ex. 1. What happens to C if A is doubled?
C is also doubled.
Ex. 2 What happens to C if B is tripled?
C will be 1/3 of its original value.
What happens to C if B is reduced by one-fourth?
This is equivalent to dividing C’s value by ¼, which is mathematically the same as
multiplying C by a value of 4. Thus C is quadrupled.
7 UNCERTAINTY AND SIGNIFICANT FIGURES
Significant Figures ARE NOT tested on the AP Physics exam(s). When solving a problem, (within
reason) do not round any values except for your final answer. Rounding intermediate calculations
may result in an erroneous answer. A good general rule is to “be reasonable.” If most values provided
in a problem contain 2 or 3 significant digits, then report your answer to 2 or 3 significant digits. As long
as the amount of digits recorded is reasonable and accurate then you should not worry about losing
any points on the AP Exam.
8 LET THE GAMES BEGIN…
Please be aware that once we are done with introductory/background material that we will work several
more examples than we will here. I’m operating on the assumption most of this is old material that
you’re already familiar with. If this is all brand new, don’t despair! It will become second nature
throughout the year, as we will be inherently practicing these skills in most problems throughout the
year.
9 PROBLEMS – THESE ARE DUE THE FIRST DAY YOU WALK IN THE DOOR.
Unit Conversion Problems
1. The Milky Way Galaxy has a diameter of 9.5 x 1017 km. Express the diameter of the Milky Way
Galaxy in meters by writing your answer in standard form.
2. The radius of an atom is so small, that scientists prefer to use the unit of Angstroms to describe its
dimensions. Express the radius of an atom (approximately one angstrom) in the units of millimeters by
writing the answer in scientific notation.
3. The age of the Universe believed to around 13.78 billion years. Express the age of the Universe in
the unit of seconds by writing the answer in scientific notation.
4. Through the use of simple Physics that will be studied in this AP Physics course, we will determine
that the mass of the Earth is approximately 5.972 x 1024 kg. Express the mass of the Earth in Mg
(Megagrams) by writing the answer in standard form.
5. Lake Cumberland holds an average of volume 7.5 km3 of water according the latest statistical
calculations. Express the volume of water that Lake Cumberland can hold in the units of cm3 by writing
your answer in scientific notation.
6. In order for an old tube-television to work properly, electrons were needed to be shot through a
potential difference of 21,000 Volts, which ends up giving an electron a kinetic energy of 21,000 eV
(Electron-Volts). Express the value of the kinetic energy of the electron in the unit of joules by writing
your answer in standard form.
7. An experimental constant commonly used in Physics is the Fundamental Gravitational Constant,
which has a value of 6.67 x 10-11
. Express the Fundamental Gravitational Constant in the unit of
by writing your answer standard form.
Use the metric prefixes to answer the following questions:
8. The radius of the earth is 6378 km. What is the diameter of the earth in meters?
9. In an experiment, you find the mass of a cart to be 250 grams. What is the mass of the cart in kilograms?
10. How many megabytes of data can a 4.7 gigabyte DVD store?
11. A mile is farther than a kilometer. Consider a fixed distance, like the diameter of the moon. Would the
number expressing this distance be larger in miles or in kilometers? Explain.
12. One US dollar = 0.73 Euros (as of 8-07.) Which is worth more, one dollar or one Euro? How many dollars is
one Euro?
13. In 2012, Germans paid 1.65 Euros per liter of gasoline. At the same time, American prices were $3.90 per
gallon.
a. How much would one gallon of European gas have cost in dollars?
b. How much would one liter of American gasoline have cost in Euros?
(One US dollar = 0.76 Euros, 1 gallon = 3.78 liters)
14. A mile is equivalent to 1.6 km. When you are driving at 60 miles per hour, what is your speed in meters per
second? Clearly show how you used proportions to arrive at a solution.
15. For each of the following mathematical relations, state what happens to the value of y when the following
changes are made. (k is a constant)
a. y = kx, x is tripled.
b. y = k/x, x is halved.
c. y = k/x2, x is doubled
d. y = kx2, x is tripled.
16. When one variable is directly proportional to another, doubling one variable also doubles the other. If y
and x are the variables and a and b are constants, circle the following relationships that are direct
proportions. For those that are not direct proportions, explain what kind of proportion does exist between x
and y.
a. y = 3x
b. y = ax + b
c. y = x
d. y = ax2
e. y = a/x
f. y = ax
g. y = 1/x
h. y = a/x2
y
a
17. The diagram shows a number of relationships between x and y.
b
c
a. Which relationships are linear? Explain.
d
b. Which relationships are direct proportions? Explain.
e
c. Which relationships are inverse proportions? Explain.
f
x
18. Manipulating Variables and constants. For each
of the following equations, solve for the variable in
bold (and slightly enlarged font). Be sure to show each step you take
to solve the equation.
1. v=at
2. P = F/A
3. F∆t = m∆v
4. U = - Gm1m2
r
5. x = x0 + v0t + 1/2at2
6. n1sinƟ1 = n2sinƟ2