AP Physics 1
AP Physics 1 Summer Packet
Name _________________________
Date _________________Per. _____
Welcome to AP Physics 1! The first Semester of College Physics
The science of physics was developed to explain the physical environment around us. Physics
will help you understand how our world works. Physics is about understanding the
mathematical relationships that describe the universe. In this course, we will cover:
 Forces & Newton’s Laws
 Simple Harmonic Motion
 Work & Energy
 Impulse & Momentum
 Gravity
 Wave Behaviors
 Linear Motion
 Waves & Sound
 Circular Motion
 Electric Forces & Fields
 Rotational Motion
 Electric Circuits
 Projectile Motion
All of these topics correlate to the first 6 Big Ideas of the AP Physics Curriculum Framework. Because there
is a lot of material to cover, this class will be fast-paced and rigorous. Be prepared for daily work of 30-40
minutes in addition to class time. You must be committed to this class in order to do well. The purpose of
this packet is for all students to have a head start on the mathematical concepts used in AP Physics. You
need to be comfortable with the following materials since they will be used all throughout the year. All
assignments are due on the first day of school, bring your questions and be prepared for a quiz on the
material during the first week of school. If you have any questions about the assignment, feel free to email
me: [email protected]. Do not hesitate to ask for help. I love helping! Also, form a study group with other
AP Physics 1 students. Join remind.com. Collaborating (not copying) with others is a valuable skill that will
serve you well in this class and in the future. Discussing the problem, sharing ideas and thoughts, and
working out mistakes, all act to create understanding of the underlining concepts in physics.
ASSIGNMENT:
1. Purchase a scientific calculator (graphing or not) and a metric ruler (know what a
centimeter is); that you will bring to class every day and use on exam day.
2. Join Remind.com at
https://www.remind.com/join/skayler
3. Asking questions is the most important thing to do in this class. Note (write down) all of your
questions that come up as you are reading or doing problem sets. Write all the vocabulary
you don’t know and look it up, or ask about it. Being able to identify what you know and
what do you not understand is a critical skill that will determine your level of success. Always
read with note paper ready.
4. Read this packet while highlighting, noting questions, and annotating.
5. Read Chapter 1 of the AP Physics textbook, College Physics by Serway and Vuille. Take notes
and compare them to the reading provided.
6. Math Review. Complete the math questions. Please show ALL work for your computations (not
calculator work) and have units for all your final answers (if applicable).
AP Physics 1
Scientific Notation
In science, very large and very small decimal numbers are conveniently expressed in terms of powers
of ten. Numbers expressed with the aid of powers of ten are said to be in scientific notation.
Examples: Earth’s radius = 6,380,000 m = 6.38 x 106 m
Bohr radius of H atom = 0.0000000000529 m = 5.29 x 10-11m
All scientific notations are composed of an integer (0 < m ≤ 1) and powers of ten.
On the calculator: you must use the correct button for optimal order of operations, depending
on your calculator:
EE
Example: to enter 6.38 x 106 push: 6.38
NOTE: Do not punch 6.38
by an extra 10.
×
10
Exp
p
or
EE
EE
or
x10n
6 It may look like 6.38E6 on the calculator
6, or your notation will be incorrect, multiplied
Significant Figures or Significant Digits (Sig Figs)
The number of significant figures in a number is the number of digits whose values are known
with certainty. All non-zero numbers are significant; the trick is to determine whether or not
zeros are significant.
Rules used in determining significant figures:
1. All non-zero numbers are significant.
2. All zeros between 2 non-zero numbers are significant.
3. All final zeros after the decimal point are significant.
(Ex: 4.00 both of those zeros count)
4. Zeros that act as placeholders are not significant.
(Ex: 0.0004 or 400, these don’t count)
Math and sig figs
1. When adding/subtracting: round answer to the least number of decimal places
Example: 24.25 m + 3.5 m = 27.75 m = 27.8 m
Has 2 decimal places
Has 1 decimal place
Best Answer has 1 decimal place
2. When multiplying/dividing: round answer to the least number of total sig figs
Example: 36.5 ÷ 3.414 = 10.69127… = 10.7
Has 3 sig figs
Has 4 sig figs
Best Answer has 3 sig figs
**Never write the entire number from the calculator as your answer. Always round answers to
the correct sig figs.
AP Physics 1
Units of Measurement
In science, almost all numbers involve units, because most numbers are measurements of a
quantity. Numbers without units lack meaning.
In this class, we use the system of units
known as SI (Système International) units.
By agreement of the scientific world, the SI
system is used as the standard.
SI
Length
Meter (m)
Mass Kilogram (kg)
Time
Second (s)
The units for length, mass, and time, along with a few other units that will arise later, are
regarded as base SI units. The word “base” refers to the fact that these units are used along with
various laws to define additional units for other quantities. The units for these other quantities
are referred to derived units, since they are a combination of the base units.
Unit Prefixes: you do NOT need to memorize these, but it is helpful to know the common ones:
Prefix
teragigamegakilodecicentimillimicronanopicofemto-
Symbol
T
G
M
k
d
c
m
μ
n
p
f
Factor
1012
109
106
103
10-1
10-2
10-3
10-6
10-9
10-12
10-15
Other useful conversion factors:
1 h = 3600 s
1 yr = 365.24 days
1 in = 2.54 cm
1 kg = 2.205 lb
1 m = 3.281 ft
1 m3 = 1000 L
1 mile = 5280 ft = 1.609 km
These prefixes can be used with any base unit. cg, cm, or cs are all allowed.
Example: 0.01 m = 1 cm -or- 1 m = 100 cm
Unit Conversion
Quantities can be measured in several different units. Therefore, it is important to know how to
convert from one unit to another.
**Note: Only quantities with identical units can be added or subtracted. If not the same unit,
convert them to the same units before doing the math.
When multiplying and dividing, units can be treated as algebraic quantities.
Example: Express 979.0 m in kilometers and in feet.
979.0 m x (1 km/103 m) = 0.9790 km
979.0 m x (3.281 ft/1 m) = 3212 ft
AP Physics 1
Math Review
Solving equations
It is often necessary to solve the equation so that a variable whose value is unknown is
expressed in terms of known quantities. In doing so, you will need to manipulate equations to
solve for the unknown.
Example: Solve for t in the following equation: v = vo +at
v = vo + at
v – vo = at
(v – vo)/a = t
Make sure you are comfortable with manipulating equations.
Trigonometry
Know the basic trig functions: sine, cosine, tangent, **Be sure your calculator is in “DEGREE”
mode when using these functions
SOHCAHTOA
sin θ = opposite/hypotenuse
H
cos θ = adjacent/hypotenuse
O
tan θ = opposite/adjacent
θ
Know the Pythagorean Theorem (in this case): O2 + A2 = H2
A
Dimensional Analysis
Using the units to test the validity of an equation. Replace each variable in an equation with its
units. Ignore any numerical values. Replace any derived units with base units. Simplify to ensure
the units on one side of an equals sign are equal to the units on the other side of an equal sign.
v = vo + at
F = ma
2
m/s = m/s + (m/s )(s)
N = (kg)(m/s2)
m/s = m/s
kgm/s2 = kgm/s2
Uncertainty in Measurements
There is no such thing as an exact measurement. All measurements are estimates. In labs, we strive
to make the most accurate measurements possible, and hence keep measurement error low.
Suppose you measured a cart to be 16.0 cm long with a ruler. The zero at the end and after the
decimal place is significant. That is your estimated digit. The actual length of the cart might be
15.9 or 16.1. You would report your length as 16.0 cm +/- 1mm.
Suppose instead, you wrote down 16 cm in your notes. Then the “6” is the estimated digit.
The length might be 15 or 17 cm. You would report the length as 16 +/- 1 cm.
Which is the better measurement? Why or why not?
Would 16.0000 be even better? Why or why not?
AP Physics 1
Vectors
Some quantities can be described with a single number (with units) giving its size or magnitude.
Such quantities are called scalar quantities. Examples of scalar quantities are time, temperature,
and mass. But many quantities not only have a magnitude but also a direction. Such quantities
are called vectors. An example of a vector quantity is displacement. Displacement describes how
far you’ve traveled and in which direction you have traveled. For example, a car has traveled 2
km due east. Other vector quantities are velocity, acceleration, and force. An arrow is used to
represent a vector. The length of the arrow represents the magnitude and the way
the arrow points is the direction of the quantity.
N
Vector Sign Conventions
Positive and negative signs are used to indicate the direction of a vector
mathematically. Usually a positive sign means to the east or north (right
or up) and a negative sign means to the west or south (left or down).
However, sign is arbitrary and may be chosen for convenience.
E
W
S
Know the
conventional
directions,
north, south,
east and west
Adding Vectors
The answer when adding vectors is called the resultant vector (R, usually), which is
the sum of all the vectors added together. Learning how to add vectors is important,
because many of the quantities in Physics are vectors. And you will be using this method a lot in
the first semester. Make sure you are familiar with it.
Head-Tail Method = graphically adding vectors
-without any rotation, place the tail of the 2nd vector at the head of the 1st vector,
connect the first tail to the second tip, that is the resultant.
Adding Mathematically
-Vectors that are in the same direction ADD
-Vector that are in the opposite direction SUBTRACT
-Vectors that are perpendicular to each other ADD BY THE Pythagorean Theorem
Resolving vectors into components. This is what we use the trig functions for! Replacing an
angled vector with 2 vectors that are on the axes.
x-component: parallel to x-axis:
cos θ = Ax/A so Ax = Acosθ
y-component: parallel to y-axis:
Ay
A
θ
sin θ = Ay/A so Ay = Asinθ
Do not memorize a trig function and a component, it
depends on which angle you have.
Ax
Adding Vectors That Are Neither Parallel nor Perpendicular to Each Other, follow these steps:
1-all vectors must be resolved into an x-component and a y-component.
2-all x-components are combined.
3-all y-components are combined.
4-the resulting x and y components are then combined by the Pythagorean Theorem
AP Physics 1
Math Review
1. How many significant figures are there in each of the following?
a. 273.16 ______
e. 2,000,000 ______
i. 5280. ______
b. 186,000 ______
f. 13.8 ______
j. 708.003 ______
c. 505 ______
g. 0.00928 ______
k. 0.0652 ______
d. 1000 ______
h. 60.080 ______
l. 3.040 x 105 _____
2. In the following, convert numbers in common notation to scientific notation, or vice versa.
a. 93,000,000 _____________________
d. 2.997 x 108 _______________________
b. 0.000019 ______________________
e. 6.02 x 10-5 ________________________
c. 606.39 ________________________
f. 2.5359 x 102 _______________________
3. In the following, how many decimal places will the solution have? Solving is optional.
a. 6.0 m + 10.73 m + 111.250 m ________
d. 93.4 cm + 10.975 cm _________
b. 4050 L – 2.06 L _________
e. 0.005070 cm + 6.90 cm + 2000.860 cm _____
c. 96.75 km + 108.43 km + 77 km _______
f. 10.970 mL – 5.0 mL ________
4. Solve the following problems, expressing the answer in the proper number of sig figs and units.
a. (797.6 m)(54 m) _________
d. 93.4 m ÷ 10.975 m _________
b. (851 cm)(24.3 cm) ________
e. (6.02 x 1023 m)(12.00 m)(1.660 x 10–24 m) _________
c. 1075 kg ÷ 15 L _________
f. (453.6 m)(9.050 x 104 m)(239.1 m) _________
5. Express the sum of 20.6 mm, 49.5 cm and
5.03 m in meters.
8. If the tank in Problem 7 has a volume of
2.25 x 104 cm3, what is its height?
6. If 22.5 L of gasoline is drawn from a tank
originally containing 65 L of gasoline, what
volume of gasoline remains in the tank?
9. How many centimeters are there in 35.0
inches?
7. What is the area of the bottom of a tank
30.0 cm long and 15.0 cm wide?
10. What is the distance, in kilometers, of a
2.5 mile cross-country course?
AP Physics 1
11. Convert each of the following measurements into meters.
a. 42.3 cm
d. 0.023 mm
b. 6.2 pm
e. 214 μm
c. 21 km
f. 570 nm
12. Rank the following mass measurements from smallest to largest:
11.6 mg, 1021 μg, 0.0000006 kg, 0.31 mg
13. State the number of sig figs in the following measurements.
a. 248 m _____ b. 0.00003 m _____ c. 64.01 m _____ d. 80.001 m _____
14. State the number of sig figs in the following measurements.
a. 2.400 x 106 kg _____
b. 6 x 106 kg _____
c. 4.07 x 1016 m ______
15. You are driving into St. Louis, Missouri, and in the distance, you see the famous Gateway-tothe-West arch. This monument rises to a height of 192 m. You estimate your line of sight with
the top of the arch to be 2.0° above the horizontal. Approximately how far (in kilometers) are
you from the base of the arch? Draw a diagram.
16. The gondola ski lift at Keystone, Colorado, is 2830 m long, and takes skiers straight up a
mountain. On average, the ski lift rises 14.6° above the horizontal. How high is the top of the ski
lift relative to the base? Draw a diagram.
AP Physics 1
17. A highway is to be built between two towns, one of which lies 35.0 km south and 72.0 km
west of the other. What is the shortest length of highway that can be built between the two
towns, and at what angle would this highway be directed with respect to due west? Draw a
diagram.
18. Two bicyclists, starting at the same place, are riding toward the same campground by two
different routes. One cyclist rides 1080 m due east and then turns due north and travels another
1430 m before reaching the campground. The second cyclist starts out by heading due north for
1950 m and then turns and heads directly toward the campground. (a) At the turning point, how
far is the second cyclist from the campground? (b) What direction (measured relative to due
east) must the second cyclist head during the last part of the trip? Draw a diagram.
19. Vector A points along the (+) y-axis and has a magnitude of 100.0 units. Vector B points at an
angle of 60.0° above the (+) x-axis and has a magnitude of 200.0 units. Vector C points along the
(+) x-axis and has a magnitude of 150.0 units. Which vector has (a) the largest x component and
(b) the largest y component. Draw each vector and its components (calculate the values).
20. Density is the ratio of an object’s mass to its volume. Would you expect density to be a
vector or a scalar quantity? Explain.