ADVANCED PLACEMENT PHYSICS 2 EQUATIONS, EFFECTIVE 2015 CONSTANTS AND CONVERSION FACTORS Proton mass, m p = 1.67 ¥ 10 -27 kg Neutron mass, mn = 1.67 ¥ 10 -27 kg

1 electron volt, 1 eV = 1.60 ¥ 10 -19 J

Electron mass, me = 9.11 ¥ 10 -31 kg

c = 3.00 ¥ 108 m s

Speed of light, Universal gravitational constant, Acceleration due to gravity at Earth’s surface,

Avogadro’s number, N 0 = 6.02 ¥ 10 23 mol-1

R = 8.31 J (moliK)

Universal gas constant,

e = 1.60 ¥ 10 -19 C

Electron charge magnitude,

G = 6.67 ¥ 10 -11 m 3 kg is 2 g = 9.8 m s 2

Boltzmann’s constant, k B = 1.38 ¥ 10 -23 J K 1 u = 1.66 ¥ 10 -27 kg = 931 MeV c 2

1 unified atomic mass unit,

h = 6.63 ¥ 10 -34 Jis = 4.14 ¥ 10 -15 eVis

Planck’s constant,

hc = 1.99 ¥ 10 -25 Ji m = 1.24 ¥ 103 eVinm e0 = 8.85 ¥ 10 -12 C2 N i m 2

Vacuum permittivity,

Coulomb’s law constant, k = 1 4 pe0 = 9.0 ¥ 10 9 N i m 2 C2

m0 = 4 p ¥ 10 -7 (Ti m) A

Vacuum permeability,

Magnetic constant, k ¢ = m0 4 p = 1 ¥ 10 -7 (T i m) A 1 atm = 1.0 ¥ 10 5 N m 2 = 1.0 ¥ 10 5 Pa

1 atmosphere pressure,

UNIT SYMBOLS

Factor 1012

meter, kilogram, second, ampere, kelvin,

PREFIXES Prefix Symbol tera T

m kg s A K

mole, hertz, newton, pascal, joule,

mol Hz N Pa J

watt, coulomb, volt, ohm, henry,

farad, tesla, degree Celsius, electron volt,

W C V W H

F T ∞C eV

VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES q

0

30

37

45

53

60

sin q

0

12

35

2 2

45

3 2

1

90

10 9

giga

G

106

mega

M

cosq

1

3 2

45

2 2

35

12

0

10 3

kilo

k

tan q

0

33

34

1

43

3

•

10 -2

centi

c

10 -3

milli

m

10 -6

micro

m

-9

nano

n

10 -12

pico

p

10

The following conventions are used in this exam. I. The frame of reference of any problem is assumed to be inertial unless otherwise stated. II. In all situations, positive work is defined as work done on a system. III. The direction of current is conventional current: the direction in which positive charge would drift. IV. Assume all batteries and meters are ideal unless otherwise stated. V. Assume edge effects for the electric field of a parallel plate capacitor unless otherwise stated. VI. For any isolated electrically charged object, the electric potential is defined as zero at infinite distance from the charged object.

ADVANCED PLACEMENT PHYSICS 2 EQUATIONS, EFFECTIVE 2015 MECHANICS Ãx = Ãx 0 + a x t

x = x 0 + Ãx 0 t +

1 2 a t 2 x

Ãx2 = Ãx20 + 2ax ( x - x0 )   Fnet  ÂF a = = m m

  Ff £ m Fn Ã2 r   p = mv

ac =

  Dp = F Dt K =

1 2 mv 2

DE = W = Fd = Fd cos q P =

DE Dt

q = q0 + w0 t +

1 2 at 2

w = w0 + at x = A cos ( wt ) = A cos (2 p ft ) xcm =

 mi xi  mi

  t net  Ât a= = I I t = r^ F = rF sin q L = Iw

DL = t Dt 1 K = I w2 2

  Fs = k x

a = A = d = E = F = f = I = K = k = L =  = m = P = p = r = T = t = U = v = W= x = y = a = m= q = t = w=

ELECTRICITY AND MAGNETISM

acceleration amplitude distance energy force frequency rotational inertia kinetic energy spring constant angular momentum length mass power momentum radius or separation period time potential energy speed work done on a system position height angular acceleration coefficient of friction angle torque angular speed

Us =

1 2 kx 2

DUg = mg Dy T =

2p 1 = w f

 FE =

1 q1q2 4 pe0 r 2

  FE E = q  E =

1 q 4 pe0 r 2

DU E = qDV 1 q 4 pe0 r

V =

 DV E = Dr DV =

Q C

C = ke0

A d

Q e0 A

E =

UC =

1 1 QDV = C ( DV )2 2 2

I =

DQ Dt

R=

r A

P = I DV I =

DV R

= = = = = e= F = I =  = P = Q = q = R = r = t = U =

V = v = k = r= q = F=

area magnetic field capacitance distance electric field emf force current length power charge point charge resistance separation time potential (stored) energy electric potential speed dielectric constant resistivity angle flux

   FM = qv ¥ B

   FM = qv sin q B    FM = I  ¥ B

i

   FM = I  sin q B   F B = B A

 Ri

Rs =

A B C d E

m k

1 = Rp

 R1i

 Tp = 2 p g

Cp =

 Ci

  FB = B cos q A

 mm Fg = G 1 2 2 r   Fg g= m

1 = Cs

 C1i

B e = - DF Dt

Ts = 2 p

UG = -

Gm1m2 r

B=

i

i

i

m0 I 2p r

e=

B v

ADVANCED PLACEMENT PHYSICS 2 EQUATIONS, EFFECTIVE 2015 FLUID MECHANICS AND THERMAL PHYSICS

r=

m V

P=

F A

A F h k K L m n N P Q

P = P0 + rgh Fb = rVg A1v1 = A2 v2

P1 + rgy1 +

1 rv 2 2 1

= P2 + rgy2 + kA DT Q = Dt L

PV = nRT = NkBT K =

1 rv 2 2 2

= area = force = depth = thermal conductivity = kinetic energy = thickness = mass = number of moles = number of molecules = pressure = energy transferred to a system by heating T = temperature t = time U = internal energy V = volume v = speed W = work done on a system y = height r = density

3 k T 2 B

MODERN PHYSICS

h l= p E = mc

2

v f

n=

c Ã

n 1 sin q1 = n 2 sin q2 1 1 1 + = si so f

M =

hi s = i ho so

DL = m l d sin q = m l

E= f = K= m= p = l= f=

energy frequency kinetic energy mass momentum wavelength work function

d = separation f = frequency or focal length h = height L = distance M = magnification m = an integer n = index of refraction s = distance v = speed l = wavelength q = angle

GEOMETRY AND TRIGONOMETRY

Rectangle A = bh

Circle

DU = Q + W

K max = hf - f

l=

Triangle 1 A = bh 2

W = - P DV

E = hf

WAVES AND OPTICS

A = pr 2 C = 2 pr Rectangular solid V = wh Cylinder

V = pr 2 S = 2 pr + 2 pr 2 Sphere

V =

A= C= V= S = b = h = = w= r =

area circumference volume surface area base height length width radius

Right triangle

c 2 = a 2 + b2 a sin q = c b cos q = c a tan q = b

4 3 pr 3

S = 4 pr 2

c

a 90°

q b