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Advanced Placement Physics C: Table of Information, Thesis of Differential Equations

Colorado School of MinesDifferential Equations

The advanced placement physics c: table of information document provides a comprehensive reference for students taking the ap physics c exam. It includes a list of important constants and conversion factors, as well as equations and formulas for both the mechanics and electricity & magnetism topics covered in the course. The table also includes information on units, prefixes, trigonometric functions, and calculus concepts relevant to the exam. This document serves as a valuable resource for students to review and reference throughout their preparation for the ap physics c exam.

Typology: Thesis

2010/2011

Uploaded on 04/12/2024

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bg1
C
ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION
CONSTANTS AND CONVERSION FACTORS
Proton mass, 27
1.67 10 kg
p
m
Neutron mass, 27
1.67 10 kg
n
m
Electron mass, 31
9.11 10 kg
e
m
Avogadro’s number, 23 1
06.02 10 molN
Universal gas constant, 8.31 J (mol K)R <
Boltzmann’s constant, 23
1.38 10 J K
B
k
Electron charge magnitude, 19
1.60 10 Ce
1 electron volt, 19
1 eV 1.60 10 J
Speed of light, 8
3.00 10 m sc
Universal gravitational
constant,
11 2 2
6.67 10 N m kgG
<
Acceleration due to gravity
at Earth’s surface,
2
9.8 m sg
1 unified atomic mass unit, 27 2
1 u 1.66 10 kg 931 MeV c
Planck’s constant, 34 15
6.63 10 J s 4.14 10 eV sh
<<
25 3
1.99 10 J m 1.24 10 eV nm
hc <<
Vacuum permittivity,
12 2 2
08.85 10 C N me
<
Coulomb’s law constant,

922
0
1 4 9.0 10 N m Ckpe <
Vacuum permeability, 7
0410 (Tm)Amp
<
Magnetic constant,
7
04110 (Tm)Akmp
<
1 atmosphere pressure, 52 5
1 atm 1.0 10 N m 1.0 10 Pa
UNIT
SYMBOLS
meter, m
kilogram, kg
second, s
ampere, A
kelvin, K
mole, mol
hertz, Hz
newton, N
pascal, Pa
joule, J
watt, W
coulomb, C
volt, V
ohm,
henry, H
farad, F
tesla, T
degree Celsius,
Welectron volt, eV
PREFIXES
Factor Prefix Symbol
9
10 giga G
6
10 mega M
3
10 kilo k
2
10centi c
3
10 milli m
6
10micro m
9
10nano n
12
10pico p
VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES
q0D30D37D45D53D60D90D
sinq0 12 35 22 45
32 1
cosq1 32 45 22 35 12 0
tanq033 34 143 3
The following assumptions are used in this exam.
I. The frame of reference of any problem is inertial unless otherwise
stated.
II. The direction of current is the direction in which positive charges
would drift.
III. The electric potential is zero at an infinite distance from an isolated
point charge.
IV. All batteries and meters are ideal unless otherwise stated.
V. Edge effects for the electric field of a parallel plate capacitor are
negligible unless otherwise stated.
ADVANCED PLACEMENT PHYSICS C EQUATIONS
MECHANICS
ELECTRICITY AND MAGNETISM
0
ÃÃ
xx
at
x
2
00
1
2
Ã
x x
xxtat
2
2
0
2
ÃÃ
xx x
ax x
0
net
F
F
amm
Ç
dp
Fdt
D
Ô

JFdt p
pmv

m

f N
F F
D
Ô
EWFdr
2
1
2
à Km
dE
Pdt
PFv
DD
g
Umgh
22
Ãw
c
a
rr
t
rF
t
t
aÇ
net
II
2
Irdmmr
Ç
Ô
2
ii
cm
i
mx
xm
Ç
Ç
Ãw
r
w

LrpI
2
1
2
KIw
0
tww a
2
00
1
2
ttqq w a
a = acceleration
E = energy
F = force
f = frequency
h = height
I = rotational inertia
J = impulse
K = kinetic energy
k = spring constant
= length
L = angular momentum
m = mass
P = power
p = momentum
r = radius or distance
T = period
t = time
U = potential energy
v
= velocity or speed
W = work done on a system
x = position
m
= coefficient of friction
q
= angle
t = torque
w = angular speed
a = angular acceleration
f
= phase angle
D
s
Fkx
2
1
2
D
s
Ukx
max
cos(xx twf
21
Tf
p
w
2
s
m
Tk
p
2
p
Tg
p
12
2
G
Gm m
Fr
12
G
Gm m
Ur
2
12
0
1
4pe
E
qq
Fr
E
F
Eq
0
e
Ô
Q
EdA
x
dV
Edx
D
Ô
VEdr
0
1
4pe
Ç
i
i
i
q
Vr
12
0
1
4pe
E
qq
UqV r
D
Q
VC
0
ke
A
Cd
pi
i
CC
Ç
11
si
i
CC
Ç
dQ
Idt

2
11
22
C
UQVCD VD
RA
r
r

E J
d
INevA
D
V
IR
ii
s
R R
Ç
11
ii
p
R R
Ç
D
PIV
A = area
B = magnetic field
C = capacit ance
d = distance
E = electric field
ε
=
emf
F = force
I = current
J = current density
L = inductance
= length
n = number of loops of wire
per unit length
N = number of charge carriers
per unit volume
P = power
Q = charge
q = point charge
R = resistance
r = radius or distance
t = time
U = potential or stored energy
V
= electric potential
v = velocity or speed
r
= resistivity
F
= flux
k = dielectric constant
M
Fqv B

0
m
Ô

BdI
0
2
4
m
p
Id r
dB r
Ô

FId B
0
s
BnI
m
F
Ô
B
BdA
e
F
Ô

B
d
Ed dt
dI
Ldt
e
2
1
2
L
ULI
ADVANCED PLACEMENT PHYSICS C EQUATIONS
GEOMETRY AND TRIGONOMETRY CALCULUS
Rectangle
Abh
Triangle
1
2
Abh
Circle
2
A
p
r
2Crp
srq
Rectangular Solid
Vw h
Cylinder
2
Vr
p
2
22Sr rp p
Sphere
3
4
3
Vr
p
2
4
Sr
p
Right Triangle
222
abc
sin a
c
q
cos b
c
q
tan a
b
q
A = area
C = circumference
V = volume
S = surface area
b = base
h = height
= length
w = width
r = radius
s = arc length
q
= angle
ca
b
90°
q
d f d f du
dx du dx

1n
dxnx
dx
n

ax ax
deae
dx

dax
dx x
1
ln

>@

sin cos
dax a ax
dx

>@

cos sin
dax a ax
dx
1
1,1
1
nn
xdx x n
n
Ô
1
Ô
ax ax
edx e
a
ln
Ô
dx x a
xa
 
1
cos sin
Ô
ax dx ax
a
 
1
sin cos
Ô
ax dx ax
a
VECTOR PRODUCTS
cosAB AB q
sin
AB AB
q
s
r
q

Partial preview of the text

Download Advanced Placement Physics C: Table of Information and more Thesis Differential Equations in PDF only on Docsity!

’C

ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION

CONSTANTS AND CONVERSION FACTORS

Proton mass,

27 1.67 10 kg p

m

 –

Neutron mass,

27 mn 1.67 10 kg

 –

Electron mass,

31 me 9.11 10 kg

 –

Avogadro’s number,

23 1 N 0 (^) 6.02 10 mol

 –

Universal gas constant, R 8.31 J (mol K)<

Boltzmann’s constant,

23

1.38 10 J K

B

k



Electron charge magnitude,

19 e 1.60 10 C

 –

1 electron volt,

19 1 eV 1.60 10 J

 –

Speed of light,

8

c 3.00 – 10 m s

Universal gravitational

constant,

11 2 2

G 6.67 10 N m kg



Acceleration due to gravity

at Earth’s surface,

2

g 9.8 m s

1 unified atomic mass unit,

27 2

1 u 1.66 10 kg 931 MeV c



Planck’s constant,

34  15

h 6.63 10 J s 4.14 10 eV s



25 3



hc 1.99 – 10 J m< 1.24 – 10 eV nm<

Vacuum permittivity,

12 2 2

e 0 8.85 10 C N m



Coulomb’s law constant,

9 2 2

k 1 4 pe 0 9.0 – 10 N m< C

Vacuum permeability,

7

m 0 4 p 10 (T m) A



Magnetic constant,

7

k m 0 4 p 1 10 (T m) A



1 atmosphere pressure,

5 2 5

1 atm 1.0 – 10 N m 1.0 – 10 Pa

UNIT

SYMBOLS

meter, m

kilogram, kg

second, s

ampere, A

kelvin, K

mole, mol

hertz, Hz

newton, N

pascal, Pa

joule, J

watt, W

coulomb, C

volt, V

ohm,

henry, H

farad, F

tesla, T

degree Celsius,

W electron volt, eV

PREFIXES

Factor Prefix Symbol

9

10 giga^ G

6

10 mega^ M

3

10 kilo^ k

2 10



centi c

 3

10 milli^ m

6 10

 micro

m

9 10



nano n

12 10



pico p

VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES

q 0

D 30

D 37

D 45

D 53

D 60

D 90

D

sin q 0 1 2 3 5^ 2 2 4 5 3 2 1

cos q 1 3 2 4 5^ 2 2 3 5 1 2 0

tan q 0 3 3 3 4^1 4 3^3 ‡

The following assumptions are used in this exam.

I. The frame of reference of any problem is inertial unless otherwise

stated.

II. The direction of current is the direction in which positive charges

would drift.

III. The electric potential is zero at an infinite distance from an isolated

point charge.

IV. All batteries and meters are ideal unless otherwise stated.

V. Edge effects for the electric field of a parallel plate capacitor are

negligible unless otherwise stated.

ADVANCED PLACEMENT PHYSICS C EQUATIONS

MECHANICS ELECTRICITY AND MAGNETISM

0

à à 

x x

a t x

2 0 0

x x  Ãx t  a tx

2 2 à (^) x à (^) x 0  2 a (^) xx  x 0

F F net a m m

Ç

 dp

F

dt

D

Ô

J F dt p

p mv

m

f N

F F

D

Ô

E W Fd r

K mÃ

dE P dt

P Fv

D D

g

U mg h

2 Ã 2 ac w r

r

t –

r F

t t a

Ç

 (^) net

I I

2 I r dm Ç mr

Ô

2

i i cm i

m x x m

Ç

Ç

à rw

– w

L r p I

K I w

0

w w  at

2 0 0

q q  w t  at

a = acceleration

E = energy

F = force

f = frequency

h = height

I = rotational inertia

J = impulse

K = kinetic energy

k = spring constant

 = length

L = angular momentum

m = mass

P = power

p = momentum

r = radius or distance

T = period

t = time

U = potential energy

v = velocity or speed

W = work done on a system

x = position

m = coefficient of friction

q = angle

t = torque

w = angular speed

a = angular acceleration

f = phase angle

 D

F s k x

D

s

U k x

x x max (^) cos( wt  f

T

f

p

w

s

m

T

k

p

p

T

g

p

1 2

2

G

Gm m F

r

1 2 G

Gm m

U

r

2

1 2

0

4 pe

E

q q

F

r

E

F

E

q

e 0

Ô

Q

E dA

x^ 

dV E dx

D 

Ô

V E dr

0

4 pe

Ç

i

i i

q V r

1 2

0

4 pe

E

q q

U qV

r

D

Q

V

C

0

k e A

C

d

p i i

C Ç C

s i i

C C

Ç

dQ

I

dt

C

U Q D V C D V

R

A

r 

r

E J

I Nev A d

D V

I

R

i

s i

R Ç R

p^ i^ i

R R

Ç

P I D V

A = area

B = magnetic field

C = capacitance

d = distance

E = electric field

ε = emf

F = force

I = current

J = current density

L = inductance

 (^) = length

n = number of loops of wire

per unit length

N = number of charge carriers

per unit volume

P = power

Q = charge

q = point charge

R = resistance

r = radius or distance

t = time

U = potential or stored energy

V = electric potential

v = velocity or speed

r = resistivity

F = flux

k = dielectric constant

F M qv B

Ô m^0

B d I

0 2 4

m

p

I dr dB

r

Ô

F I dB

Bs m 0 nI

F

Ô

B

B dA

e

F

Ô

dB

E d

dt

dI L dt

e 

U L LI

ADVANCED PLACEMENT PHYSICS C EQUATIONS

GEOMETRY AND TRIGONOMETRY CALCULUS

Rectangle

A bh

Triangle

A bh

Circle

2 A p r

C 2 pr

s rq

Rectangular Solid

V  w h

Cylinder

2 V pr

2

S 2 pr  2 pr

Sphere

V pr

2 S 4 pr

Right Triangle

2 2 2 a  b c

sin

a

c

q

cos

b

c

q

tan

a

b

q

A = area

C = circumference

V = volume

S = surface area

b = base

h = height

 (^) = length

w = width

r = radius

s = arc length

q = angle

c a

b

q^90 °

d f d f du

dx du dx

d n 1

x nx

dx

n 

d ax ax

e ae

dx

d

ax

dx x

ln

> sin^ @ cos

d

ax a ax

dx

> cos @ sin

d

ax a ax

dx

n n

x dx x n

n



Ô

Ô

ax ax

e dx e

a

ln 

Ô

dx

x a

x a

cos sin

Ô

ax dx ax

a

sin  cos

Ô

ax dx ax

a

VECTOR PRODUCTS

A B  AB cos q

A – B AB sin q

s

r

q