5 Steps to a 5 - AP Physics B and C ( PDFDrive.com )

Appendixes

Constants
Physics B Equations
Physics C Equations
Four-Minute Drill Prompts
Web Sites
Glossary
Bibliography

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1 amu CONSTANTS
mass of proton
mass of neutron u 1.7 × 10−27 kg
mass of electron mp 1.7 × 10−27 kg
charge of proton mn 1.7 × 10−27 kg
Avogadro’s number me 9.1 × 10−31 kg
Universal gas constant e 1.6 × 10−19 C
Boltzmann’s constant N 6.0 × 10−23 mol−1
Speed of light R 8.3 J / (mol˙K)
Planck’s constant kB 1.4 × 10−23 J / K
c 3.0 × 108 m/s
Planck’s constant . speed of light h 6.6 × 10−34 J˙s
h 4.1 × 10−15 eV˙s
Permittivity of free space hc 1.99 × 10−25 J˙m
Coulomb’s law constant hc 1.24 × 103 eV˙nm
Permeability of free space εo 8.9 × 10−12 C2 / N˙m2
Universal gravitation constant k 9.0 × 109 N˙m2 / C2
Earth’s free fall acceleration µo 4π × 10−7 T˙m / A
1 atmosphere of pressure G 6.7 × 10−11 N˙m2 / C2
1 electron-volt g 9.8 m/s
atm 1.0 × 105 Pa
eV 1.6 × 10−19 J

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PHYSICS B EQUATIONS

Read Chapter 6 about memorizing equations for more help with learning not only what
the equations say, but also what they mean.

Remember, your textbook might use slightly different symbols.

NEWTONIAN MECHANICS

vf = vo + at I = ∆p = F ⋅∆t T = 2π m
KE = 12 mv 2 k
x − x0 = v0t + 12 at 2 PE g = mgh
T = 2π L
( )v2 g
f = v02 + 2a x − x0
T=1
Fnet = ma W = F ⋅ ∆x f
P =W
Ff = µFn
∆t
ac = v2 P = F ⋅v FG =G M1M2
r F = −kx r2

τ = F ⋅d

p = mv PE s = 1 kx 2 PEG =G M1M2
2 r

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Physics B Equations ❮ 389

ELECTRICITY AND MAGNETISM

F = 1 q1q2 PEC = 12 CV 2 ∑1 = 1
4πε0 r2 Ri
Rp

F = qE I = ∆Q F = qvB sin θ
∆t

PE E = qV = 1 q1q2 R=ρL F = ILB sin θ
4πε0 r A B = µ0I

E =V V = IR 2πr
d φm = BA cos θ
ε = −N ∆φ
∑V = 1 qi P = IV
ri ∆t
4πε0 ε = Blv

Q = CV ∑C p = Ci

C = ε0 A ∑1 = 1
d Ci
Cs

∑Rs = Ri

FLUID MECHANICS AND THERMAL PHYSICS

P = Po + ρgh KE avg = 3 kBT
2

Fb = ρVg vrms = 3kBT
m

A1v1 = A2v2 W = − p∆V

P1 + ρgy1 + 1 ρv12 = P2 + ρgy2 + 1 ρv 2 ∆U = Q +W
2 2 2

∆L = αL0∆T e= W
QH

H = kA∆T eideal = TH −TC
L TH

P=F
A

PV = nRT

390 ❯ Physics B Equations

v =λf WAVES AND OPTICS d sinθ = mλ
1= 1+1 x = mλL
n= c f do di
v d
m = hi = di
n1 ⋅ sin θ1 = n2 ⋅ sin θ2 ho d0 λ= h
p
sin θc = n2 f =r
n1 2 E = (∆m)c 2

ATOMIC AND NUCLEAR PHYSICS

E = hf = pc
KE = hf −W

PHYSICS C EQUATIONS

Read Chapter 6 about memorizing equations for more help with learning not only what
the equations say, but also what they mean.

You’ll notice that the C equation sheet often expresses relationships in calculus terms.
Don’t let that confuse you; for example, though impulse is expressed as an integral of force
with respect to time, you should also interpret that as force times time if the force is
constant, or as the area under a force vs. time graph.

Remember, your textbook might use slightly different symbols.

MECHANICS

vf = vo + at p = dW ω f = ω0 + αt
dt
x − xo = vot + 12 at 2 ∆θ = ω0t + 1 αt 2
P = F ⋅v 2

2( )v
f = v02 + 2a x − xo PE g = mgh F = −kx

Fnet = ma ac = v2 = ω 2r PEs = 12 kx 2
F = dp r

dt τ = F ⋅d T = 2π = 1
ωf

I = ∆p = ∫F ⋅dt τnet = I α T = 2π m
k
p = mv ∫ ∑I = r 2dm = miri2
T = 2π L
g

Ff = µFn ∑Mxcm = mi xi FG =G M1M2
r2

W = ∫F ⋅ dx v = rω PEG =G M1M2
r

KE = 1 mv 2 L = I ω = mvr
2

KE = 1 I ω 2
2

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392 ❯ Physics C Equations

ELECTRICITY AND MAGNETISM

F = 1 q1q2 ∑1 = 1 F = ILB sinθ
4πεo r2 Ci
Cs

F = qE I = dQ Bs = µonL
dt

∫ E ⋅ dA = Qenclosed PEC = 1 CV 2 φm = ∫B ⋅dA
2
ε0 ε = d φm
dt
E = − dv R =ρL
dr A ε = Blv

PE E = qV = 1 q1q2 V = IR
4πεo r

∑V = 1 qi ∑Rs = Ri ε = −L dI
ri dt
4πεo

Q = CV ∑1 = 1 PE L = 1 LI 2
Ri 2
Rp

C = κε0 A P = IV
d

∑C p = Ci F = qvB sinθ

∫B ⋅dl = µ0Ic

FOUR-MINUTE DRILL PROMPTS

The lists that follow are designed to help you Force of a spring (The negative sign reminds you
study equations. Each prompt refers to a specific that the spring force is a restoring force,
equation on the AP Equations Sheet (we’ve listed always acting toward the equilibrium point.)
the prompts in the same order in which the
equations appear on the Equations Sheet). So, Potential energy of a spring
for example, the prompt “Net force” refers to the Period of a mass on a spring
equation, “Fnet = ma.” Period of a pendulum
Period in terms of frequency
There are several ways to use these prompts. Gravitational force between two massive objects
First, you can use them as a self-test: for each Gravitational potential energy between two
prompt, write down the corresponding
equation on a separate sheet of paper. Then massive objects. (Don’t use unless an object
check the equations you wrote down against the is far from a planet’s surface.)
AP Equations Sheet to see if you got any wrong.
You can also use these prompts when you study Electricity and Magnetism
with a friend: have your friend read the
prompts to you, and you respond by reciting the Electric force between two point
appropriate equation. Try to go through the
list as fast as possible without making a charges—remember, 1 is just
mistake. Last, your physics teacher can use these 4πεo
prompts to lead your class through a Four-
Minute Drill, which is an activity we describe in the Coulomb’s law constant, k = 9.0 × 109
Chapter A. N.m2/C2!!!
Electric force in terms of electric field
PHYSICS B Potential energy in terms of potential, and then
potential energy between two point charges
Newtonian Mechanics (this line on the equation sheet really has
two different equations. PE = qV is always
1st kinematics equation valid, but PE = kqq/r is only valid between
2nd kinematics equation two point charges.)
3rd kinematics equation Uniform electric field between two parallel plates
Net force The potential at some point due to surrounding
Force of friction point charges
Centripetal acceleration Definition of capacitance
Torque Capacitance of a parallel plate capacitor
Momentum Energy stored on a capacitor
Impulse Definition of current
Kinetic energy Resistance of a wire
Potential energy due to gravity (near Earth) Ohm’s law
Work Power in an electrical circuit
Power How to add parallel capacitors
Power—alternate expression How to add series capacitors
How to add series resistors
How to add parallel resistors
Magnetic force on a charge
Magnetic force on a wire
Magnetic field (not force) due to a long, straight
wire

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394 ❯ Four-Minute Drill Prompts Physics C

Magnetic flux Mechanics
Induced EMF
Induced EMF in the special case of a rectangular 1st kinematics equation
2nd kinematics equation
wire with constant speed 3rd kinematics equation
Net force
Fluid Mechanics and Thermal Physics Force in terms of momentum
Impulse
Pressure in a static fluid column Definition of momentum
Buoyant force—Archimedes’ principle Force of friction
Continuity equation Work
Bernoulli’s equation Kinetic energy
Thermal expansion Power
Definition of pressure Power—alternate expression
Ideal gas law Gravitational potential energy near a planet
Average kinetic energy per molecule in an Centripetal acceleration
Torque
ideal gas Newton’s second law for rotation
rms speed of the molecules of an ideal gas Definition of moment of inertia
Work done on a gas in an isobaric process (This Position of the center of mass
Conversion between linear and angular velocity
reminds you that work done on a gas in any Angular momentum
process can be found by the area under the Rotational kinetic energy
PV graph.) 1st rotational kinematics equation
First law of thermodynamics 2nd rotational kinematics equation
Definition of efficiency Force of a spring (The negative sign reminds you
Efficiency of an ideal heat engine
that the spring force is a restoring force,
Waves and Optics always acting toward the equilibrium point.)
Potential energy of a spring
Velocity of a wave Period in terms of angular frequency and
Definition of the index of refraction standard frequency
Snell’s law Period of a mass on a spring
How to find the critical angle for total internal Period of a pendulum
Gravitational force between two massive objects
reflection Gravitational potential energy between two mas-
Lensmaker’s equation / Mirror equation (They’re sive objects (Don’t use unless an object is far
away from a planet’s surface.)
the same thing.)
Magnification Electricity and Magnetism
Focal length of a spherical mirror
Position of constructive interference points for Electric force between two point charges
Definition of electric field
light passing through slits Gauss’s law (Though you should never actually
Position of constructive interference points for
take an integral when using this.)
light passing through slits if the angle to the How to find electric field in terms of potential
screen is small Potential energy in terms of potential, and then

Atomic and Nuclear Physics potential energy between two point charges
(This line on the equation sheet really has
Energy of a photon—the second expression gives
energy in terms of a photon’s momentum

Kinetic energy of an electron ejected from a metal
surface, where W is the work function

De Broglie wavelength
Conversion between mass and energy

two different equations. PE = qV is always Four-Minute Drill Prompts ❮ 395
valid, but PE = kqq/r is only valid between
two point charges.) Ohm’s law
The electric potential at some point due to How to add series resistors
surrounding point charges How to add parallel resistors
Definition of capacitance Power in an electrical circuit
Capacitance of a parallel plate capacitor with a Magnetic force on a charge
dielectric substance of constant κ added Ampére’s law
How to add parallel capacitors Magnetic force on a wire
How to add series capacitors Magnetic field of a solenoid
Definition of current Magnetic flux
Energy stored on a capacitor Induced EMF
Resistance of a wire Voltage across an inductor
Energy stored in an inductor

WEB SITES

The internet offers some great resources for preparing for the AP Physics exam.
• Your textbook may have an associated Web site . . . if so, check it out! For example, Paul A. Tipler’s Physics
C-level text provides this Web site: http://www.whfreeman.com/tipler4e/
• All kinds of stuff associated with the AP Physics B program is contained in Dolores Gende’s Web site,
http://apphysicsb.homestead.com/. This is the best of the unofficial AP physics sites out there.
• Of course, the official site of the College Board, www.collegeboard.com, has administrative information and
test-taking hints, as well as contact information for the organization that actually is in charge of the exam.
• Did you enjoy your first taste of physics? If so, you can try your hand at physics debating. The United States
Association for Young Physicist Tournaments hosts a national tournament which consists of “physics
fights,” or debates, over experimental research projects check out www.usaypt.org for details.

Copyright © 2008, 2004 by The McGraw-Hill Companies, Inc. Click here for terms of use.

GLOSSARY

absolute pressure—the total pressure of a fluid at centrifugal force—a made-up force; when dis-
the bottom of a column; equal to the pressure cussing circular motion, only talk about “cen-
acting on the top of the column plus the pressure tripetal” forces
caused by the fluid in the column
centripetal force—the force keeping an object in
acceleration—the change in an object’s velocity uniform circular motion
divided by the time it took to make that change;
equal to the derivative (slope) of an object’s coefficient of friction—the ratio of the friction
velocity–time function force to the normal force. The coefficient of static
friction is used when an object has no velocity; the
adiabatic process—a process during which no heat coefficient of kinetic friction is used for a moving
flows into or out of the system object

alpha particle—two protons and two neutrons concave lens—a translucent object that makes the
stuck together light rays passing through it diverge

amplitude—the maximum displacement from the conservative force—a force that acts on an object
equilibrium position during a cycle of periodic without causing the dissipation of that object’s
motion; also, the height of a wave energy in the form of heat

angular momentum—the amount of effort it constructive interference—the overlap of two
would take to make a rotating object stop waves such that their peaks line up
spinning
convex lens—a translucent object that makes the
antineutrino—a subatomic particle; see “neutrino” light rays passing through it converge
antinode—point on a standing wave where the wave
critical angle—the angle past which rays cannot be
oscillates with maximum amplitude transmitted from one material to another
Archimedes’ principle—the buoyant force on an
current—the flow of positive charge in a circuit; the
object is equal to the weight of the fluid displaced amount of charge passing a given point per unit
by that object time
atom—the fundamental unit of matter; includes
protons and neutrons in a small nucleus, cutoff frequency—the minimum frequency of light
surrounded by electrons that, when absorbed, is capable of making an
atomic mass unit (amu)—the mass of a proton; atom eject an electron
also the mass of a neutron
atomic number—the number of protons in an cycle—one repetition of periodic motion
atom’s nucleus daughter nucleus—the nucleus left over after an
average speed—the distance an object travels
divided by the time it took to travel that distance atom undergoes nuclear decay
(see “speed”) de Broglie wavelength—the wavelength of a
beats—rhythmic interference that occurs when two
notes of unequal but close frequencies are played moving massive particle
beta particle—an electron or a positron density—the mass of an object divided by that
buoyant force—the upward force exerted by a fluid
on an object that is wholly or partially submerged object’s volume
in that fluid destructive interference—the overlap of two waves
capacitor—a charge-storage device, often used in
circuits so that the peaks of one wave line up with the
troughs of the other
dipole—something, usually a set of charges, with
two nonidentical ends
direction—the orientation of a vector
displacement—a vector quantity describing how far
an object moved

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398 ❯ Glossary ground state energy—the lowest energy level of an
atom
Doppler effect—the apparent change in a wave’s
frequency that you observe whenever the source heat—a type of energy (related to molecular vibra-
of the wave is moving toward or away from you tions) that can be transferred from one object to
another
elastic collision—a collision in which kinetic energy
is conserved heat engine—a system in which heat is added to
a gas contained in a cylinder with a moveable
electric field—a property of a region of space that piston; when the gas heats up, it expands, doing
affects charged objects in that particular region work by moving the piston up

electric flux—the amount of electric field that impulse—the change in an object’s momentum
penetrates a certain area index of refraction—a number that describes by

electric potential—potential energy provided by an how much light slows down when it passes
electric field per unit charge through a certain material
induced EMF—the potential difference created by
electromagnetic induction—the production of a a changing magnetic flux that causes a current to
current by a changing magnetic field flow in a wire; EMF stands for “electro-motive
force,” but the units of EMF are volts.
electron—a subatomic particle that carries a nega- inductance—the property of an inductor that
tive charge describes how good it is at resisting changes in
current in a circuit
electron-volt—a unit of energy equal to the amount inductor—a coil in a circuit that makes use of
of energy needed to change the potential of an induced EMF to resist changes in current in the
electron by one volt circuit
inelastic collision—a collision in which kinetic
energy—the ability to do work energy is not conserved, as opposed to an elastic
entropy—a measure of disorder collision, in which the total kinetic energy of all
equilibrium—when the net force on an object objects is the same before and after the collision
inertia—the tendency for a massive object to resist
equals zero a change in its velocity
equipotential lines—lines that illustrate every point internal energy—the sum of the kinetic energies of
each molecule of a substance
at which a charged particle would experience ion—an electrically charged atom or molecule
a given potential ionization energy—the minimum amount of
field—a property of a region of space that can affect energy needed for an electron to escape an atom
objects found in that particular region isobaric process—a process during which the
first law of thermodynamics—the change in the pressure of the system remains the same
internal energy of a system equals the heat added isochoric process—a process during which the
to the system plus the work done on the system volume of the system remains the same
flowing fluid—a fluid that’s moving isotherm—a curve on a PV diagram for which the
free-body diagram—a picture that represents one or temperature is constant
more objects, along with the forces acting on isothermal process—a process during which the
those objects temperature of the system remains the same
frequency—the number of cycles per second of peri- isotope—an atom with the same atomic number as
odic motion; also, the number of wavelengths of a another atom but a different atomic mass
wave passing a certain point per second kinetic energy—energy of motion
friction—a force acting parallel to two surfaces in Kirchoff ’s laws—in a circuit, 1) at any junction,
contact; if an object moves, the friction force the current entering equals the current leaving;
always acts opposite the direction of motion 2) the sum of the voltages around a closed loop
fulcrum—the point about which an object rotates is zero
fundamental frequency—the frequency of the
simplest standing wave
g—the acceleration due to gravity near the Earth’s
surface, about 10 m/s2
gamma particle—a photon
gauge pressure—the pressure of a fluid at the
bottom of a column due only to the fluid in the
column

Lenz’s law—the direction of the current induced by Glossary ❮ 399
a changing magnetic flux creates a magnetic field
that opposes the change in flux period—the time it takes for an object to pass
through one cycle of periodic motion; also, the
longitudinal wave—when particles move parallel to time for a wave to propagate by a distance of one
the direction of a wave’s motion wavelength

magnetic field—a property of a region of space that photoelectric effect—energy in the form of light
causes magnets and moving charges to experience can cause an atom to eject one of its electrons, but
a force only if the frequency of the light is above a certain
value
magnetic flux—the amount of magnetic field that
penetrates an area photon—a particle of light; a photon has no mass
plane mirror—a flat, reflective surface
magnitude—how much of a quantity is present; see positron—like an electron, but with a positive
“scalar” and “vector”
charge
mass defect—the amount of mass that is destroyed potential energy—energy of position
and converted into kinetic energy in a nuclear power—the amount of work done divided by the
decay process
time it took to do that work; also, in a circuit,
mass number—the number of protons plus neu- equal to the product of the current flowing
trons in an atom’s nucleus through a resistor and the voltage drop across that
resistor
mass spectrometer—a device used to determine the pressure—the amount of force applied to a surface
mass of a particle divided by the area of that surface
principal axis—the imaginary line running through
moment of inertia—the rotational equivalent of the middle of a spherical mirror or a lens
mass principle of continuity—the volume flow rate is
equal at all points within an isolated stream of
momentum—the amount of “oomph” an object has fluid
in a collision, equal to an object’s mass multiplied proton—a subatomic particle found in an atom’s
by that object’s velocity nucleus that carries a positive charge
PV diagram—a graph of a gas’s pressure versus its
net force—the vector sum of all the forces acting on volume
an object real image—an image created by a mirror or a lens
that is upside-down and can be projected onto
neutrino—A subatomic particle emitted during a screen
beta decay that affects only the kinetic energy of refrigerator—like a heat engine, only work is done
the products of the decay process to remove heat
resistance—a property of a circuit that resists the
neutron—a subatomic particle found in an atom’s flow of current
nucleus that has no electric charge resistor—something put in a circuit to increase its
resistance
node—point on a standing wave where the medium restoring force—a force that restores an oscillating
through which the wave is propagating does not object to its equilibrium position
move scalar—a quantity that has a magnitude but no
direction
normal force—a force that acts perpendicular to the second law of thermodynamics—heat flows natu-
surface on which an object rests rally from a hot object to a cold object but not
from cold to hot; equivalently, the entropy of a
nucleus—the small, dense core of an atom, made of system cannot decrease unless work is done on
protons and neutrons that system
series—the arrangement of elements in a circuit so
oscillation—motion of an object that regularly that they are connected in a line, one after the
repeats itself over the same path other

parallel—the arrangement of elements in a circuit so
that the charge that flows through one element
does not flow through the others

Pascal’s principle—if a force is applied somewhere
on a container holding a fluid, the pressure
increases everywhere in the fluid, not just where
the force is applied

peak—a high point on a wave
perfectly inelastic collision—a collision in which

the colliding objects stick together after impact

400 ❯ Glossary velocity—how fast an object’s displacement changes,
equal to the derivative (slope) of an object’s
specific gravity—the ratio of a substance’s density position–time function
to the density of water
virtual image—an image created by a mirror or lens
speed—the magnitude of an object’s velocity that is upright and cannot be projected onto
spherical mirror—a curved, reflective surface a screen
standing wave—a wave that, when observed,
volume flow rate—the volume of fluid flowing past
appears to have peaks and troughs that don’t move a point per second
static fluid—a fluid that isn’t flowing
temperature—a quantity related to the average wave—a rhythmic up-and-down or side-to-side
motion that moves through a material at constant
kinetic energy per molecule of a substance speed
tension—a force applied by a rope or string
thermal expansion—enlargement of an object that wavelength—a wave’s peak-to-peak or trough-
to-trough distance
is heated
time constant—a value related to how long it takes wave pulse—when a single peak travels through
a medium
to charge or discharge a capacitor
torque—the application of a force at some distance weight—the force due to gravity; equal to the mass
of an object times g, the gravitational field
from a fulcrum; if the net torque on an object isn’t
zero, the object’s rotational velocity will change work—the product of the distance an object travels
total internal reflection—the reflection of light off and the components of the force acting on that
a surface that occurs when the light cannot pass object directed parallel to the object’s direction of
from a medium with a high index of refraction to motion
one with a low index of refraction
transverse wave—occurs when the particles in a work-energy theorem—the net work done on an
wave move perpendicular to the direction of the object equals that object’s change in kinetic energy
wave’s motion
trough—a low point on a wave work function—the minimum amount of energy
vector—a quantity that has both magnitude and needed for an electron to be ejected from the
direction surface of a metal

BIBLIOGRAPHY

Your AP physics textbook may have seemed dif- If you are having trouble seeing the meaning
ficult to read early in the year. But now that you behind the mathematics, check out this book.)
have heard lectures, solved problems, and read
our guide, try reading your text again—you’ll be Just for fun, we also recommend these
amazed at how much more clear the text has books . . . they might not help you too much for
become. the AP exam, but they’re great reads.

If you’d like to look at another textbook, • Feynman, R. (1997). Surely you’re joking,
these are a few that we recommend: Mr. Feynman! New York: W. W. Norton.
(Collected stories of the 20th century’s most
Physics B charismatic physicist. If you ever thought that
physicists were a bunch of stuffy nerds without
• Giancoli, Douglas C., (1998). Physics (5th ed.). personality, you should definitely read this
New York: Prentice Hall. book. One of our all-time favorites!)

• Cutnell, J. D., Johnson, K. W. (2000). Physics • Hawking, S. (1998). A Brief History of Time.
(6th ed.). New York: Wiley. New York: Bantam. (The canonical introduction
to cosmology at a layperson’s level.)
• Jones, Edwin R., Childers, R. L. (2000).
Contemporary College Physics (3rd ed.). • Lederman, L. (1993). The God Particle. New York:
New York: McGraw-Hill. Dell. (Written by a Nobel Prize-winning experi-
mental physicist, this book not only discusses
Physics C what kinds of strange subatomic particles exist,
• Tipler, P. A. (1999). Physics (4th ed.). New York: but goes through the amazing and interesting
details of how these particles are discovered.)
W. H. Freeman.
• Walker, J. (2007). The Flying Circus of Physics,
You might also find this book helpful: 2nd edition, New Jersey: Wiley. (This book pro-
vides numerous conceptual explanations of
• Hewitt, P. G. (2002). Conceptual Physics. San physics phenomena that you have observed. The
Francisco: Addison Wesley. classic “Physics of the world around you” book.)

(Hewitt’s is the classic text for readable, non-
mathematical expositions of physics principles.

Copyright © 2008, 2004 by The McGraw-Hill Companies, Inc. Click here for terms of use.

NOTES