Physics Equations

x6-Physics Insert SINGLE PGS 3/21/01 3:24 AM Page 2 TABLE OF INFORMATION FOR 2002 CONSTANTS AND CONVERSION FACTORS 1 un

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x6-Physics Insert SINGLE PGS 3/21/01 3:24 AM Page 2

TABLE OF INFORMATION FOR 2002 CONSTANTS AND CONVERSION FACTORS 1 unified atomic mass unit,

1u

UNITS

= 1.66 ™ 10 -27 kg

Name

Symbol

= 931 MeV/c 2

meter

Proton mass,

m p = 1.67 × 10 −27 kg

kilogram

Neutron mass,

mn = 1.67 × 10 −27 kg

second

Electron mass, Magnitude of the electron charge,

PREFIXES

me = 9.11 × 10

−31

kg

Prefix

m

10 9

giga

G

kg

10 6

mega

M

s

10 3

kilo

k

centi

c

milli

m

ampere

e = 1.60 × 10 −19 C

Symbol

Factor

A

kelvin

K

10 10

−2 −3

Avogadro’s number,

N0 = 6.02 × 10 23 mol −1

R = 8.31 J / ( mol ¼ K )

mole

mol

10 −6

micro

µ

Universal gas constant, Boltzmann’s constant,

k B = 1.38 × 10 −23 J / K

hertz

Hz

10 −9

nano

n

Speed of light,

c = 3.00 × 10 8 m / s

newton

N

pico

p

Planck’s constant,

h = 6.63 × 10 −34 J ⋅ s

pascal

Pa

= 4.14 × 10

−15

eV ⋅ s

hc = 1.99 × 10 −25 J ⋅ m = 1.24 × 10 3 eV ⋅ nm

Vacuum permittivity, Coulomb’s law constant, Vacuum permeability, Magnetic constant, Universal gravitational constant, Acceleration due to gravity at the Earth’s surface, 1 atmosphere pressure,

⑀ 0 = 8.85 × 10

−12

C / N⋅m

k = 1 / 4π ⑀ 0 = 9.0 × 10 N ⋅ m / C 9

2

2

2

µ 0 = 4π × 10 −7 (T ⋅ m ) / A

k = µ 0 / 4π = 10 (T ⋅ m ) / A −7

G

= 6.67 ™ 10 -11 m 3 / kg ¼ s 2

g = 9.8 m / s

2

1 atm = 1.0 × 10 5 N / m 2 = 1.0 × 10 5 Pa

1 electron volt,

2

1 eV = 1.60 × 10 −19 J

10

−12

VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES

joule

J

watt

W

θ

coulomb

C

0

volt

V

ohm



henry

H

farad

F

tesla

T

45o

o

sin θ

cos θ

tan θ

0

1

0

3 /2

3 /3

30o

1/2

37o

3/5

degree Celsius

o

C

53o

electronvolt

eV

60o 90o

2 /2

4/5

4/5 2 /2

3/4 1

3/5

4/3

3 /2

1/2

3

1

0



The following conventions are used in this examination. I. Unless otherwise stated, the frame of reference of any problem is assumed to be inertial. II. The direction of any electric current is the direction of flow of positive charge (conventional current). III. For any isolated electric charge, the electric potential is defined as zero at an infinite distance from the charge. *IV. For mechanics and thermodynamics equations, W represents the work done on a system. *Not on the Table of Information for Physics C, since Thermodynamics is not a Physics C topic.

x6-Physics Insert SINGLE PGS 3/21/01 3:24 AM Page 3

ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2002 NEWTONIAN MECHANICS

u = u 0 + at 1 2 at 2

x = x0 + u0 t +

0

u 2 = u 0 2 + 2a x - x 0

5

Ê F = Fnet = ma F fric ˆ mN ac =

u2 r

t = rF sin q p = mv J = FDt = K =

Dp

1 mu 2 2

DUg = mgh W = F ⴢ Dr = FDr cos q Pavg =

W Dt

P = F ⴢ v = Fu cos q Fs = - k x 1 2 kx 2

Us =

Ts = 2 p

m k

Tp = 2 p

l g

T =

1 f

a = F = f = h = J = K = k = l = m= N = P = p = r = r = T = t = U= u = W= x = m= q = t =

acceleration force frequency height impulse kinetic energy spring constant length mass normal force power momentum radius or distance position vector period time potential energy velocity or speed work done on a system position coefficient of friction angle torque

ELECTRICITY AND MAGNETISM F=

1 q1 q 2 4 p⑀ 0 r 2

E=

F q

UE = qV = E avg = − V=

Gm1m2

UG = -

Gm1m2 r

r2

1 q1 q 2 4 p⑀ 0 r

V d

∑r

qi

1 4 p⑀ 0

i

i

Q V ⑀0 A C= d 1 1 Uc = QV = CV 2 2 2 C=

I avg =

DQ Dt

ρl A V = IR P = IV R=

C p = ∑ Ci i

1 1 =∑ Cs i Ci Rs = ∑ Ri i

1 1 =∑ Rp i Ri FB = qu B sin θ FB = BIl sin θ B=

FG = -

A B C d E

m0 I 2p r

fm = B • A = BA cos θ

eavg = − e = Blu

Dfm Dt

= = = = = = = = = = = = = = = = =

area magnetic field capacitance distance electric field e emf F force I current l length P power Q charge q point charge R resistance r distance t time U potential (stored) energy V electric potential or potential difference u = velocity or speed r = resistivity fm = magnetic flux

x6-Physics Insert SINGLE PGS 3/21/01 3:24 AM Page 4

ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2002 FLUID MECHANICS AND WAVES AND OPTICS THERMAL PHYSICS p = p0 + rgh Fbuoy = rVg A1u1 = A2 u 2 1 p + rgy + ru 2 = const. 2 D l = a l 0 DT Q = mL Q = mcDT p =

F A

pV = nRT 3 k T 2 B

K avg =

3 RT = M

u rms =

W = - pDV Q = ncDT

DU = Q + W DU = ncV DT e = ec =

W QH

3k B T

m

A = area c = specific heat or molar specific heat e = efficiency F = force h = depth Kavg = average molecular kinetic energy L = heat of transformation l = length M= molecular mass m = mass of sample n = number of moles p = pressure Q = heat transferred to a system T = temperature U = internal energy V = volume u = velocity or speed urms = root-mean-square velocity W = work done on a system y = height a = coefficient of linear expansion µ = mass of molecule r = density

TH - TC TH

ATOMIC AND NUCLEAR PHYSICS E = hf = pc Kmax = hf − f l =

h p

DE = ( Dm) c 2

E f K m p l f

= = = = = = =

energy frequency kinetic energy mass momentum wavelength work function

u = fl c n = u n 1 sin q1 = n 2 sin q 2 sin q c =

n2 n1

1 1 1 + = si s0 f M =

hi s = - i s0 h0

R 2 d sin q = ml f =

xm ⬇

d = separation f = frequency or focal length h = height L = distance M= magnification m = an integer n = index of refraction R = radius of curvature s = distance u = speed x = position l = wavelength q = angle

ml L d

GEOMETRY AND TRIGONOMETRY Rectangle A = bh Triangle 1 A = bh 2 Circle A = pr 2 C = 2 pr Parallelepiped V = lwh Cylinder V = pr 2 l S = 2 pr l + 2 pr 2 Sphere 4 V = pr 3 3 S = 4 pr 2 Right Triangle a 2 + b2 = c2 a sin q = c b cos q = c a tan q = b

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

area circumference volume surface area base height length width radius

c q

a 90

b

x6-Physics Insert SINGLE PGS 3/21/01 3:24 AM Page 5

ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2002 MECHANICS

u = u 0 + at 1 2 at 2 u 2 = u 0 2 + 2a x - x 0 Ê F = Fnet = ma dp F = dt J = F dt = Dp p = mv F fric ˆ mN x = x0 + u 0 t +

0

I

IF

W =

œ

dr

1 mu 2 2 dW dt Fⴢv = mgh

K = P = P = DU g ac =

u 2 = w2r

r t=r™F Ê t = t net = Ia

I

I = r 2 dm = Ê mr 2 rcm = Ê mr Ê m u = rw L = r ™ p = Iw 1 K = Iw 2 2 w = w0 + at q = q 0 + w0 t + 1 at 2 2 Fs = - kx 1 Us = kx 2 2 2p 1 T = = f w m Ts = 2 p k l Tp = 2 p g Gm1m2 FG = r$ r2 Gm1m2 UG = r

5

a = F = f = h = I = J = K = k = l = L = m= N = P = p = r = r = T = t = U= u = W= x = m= q = t = w= a =

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

ELECTRICITY AND MAGNETISM F=

1 q1 q 2 4 p⑀ 0 r 2

E=

F q

e

Q ⑀0

养 E • dA = dV dr 1 V= 4 p⑀ 0

A B C d E

E=−

∑r

UE = qV =

qi

i

i

1 q1 q 2 4 p⑀ 0 r

Q V k⑀ A C= 0 d C p = ∑ Ci C=

i

1 1 =∑ Cs i Ci dQ dt 1 1 Uc = QV = CV 2 2 2 rl R= A V = IR I=

Rs = ∑ Ri i

1 1 =∑ Rp i Ri P = IV FM = qv × B 养 B • d ø = m0 I

I

F = I dø × B Bs = m0 nI

I

fm = B • dA

dfm dt dI e = −L dt 1 2 U L = LI 2

e=−

F I L l n

= = = = = = = = = = =

P = Q= q = R = r = t = U= V = u = r = fm = k =

area magnetic field capacitance distance electric field emf force current inductance length number of loops of wire per unit length power charge point charge resistance distance time potential or stored energy electric potential velocity or speed

resistivity magnetic flux dielectric constant

x6-Physics Insert SINGLE PGS 3/21/01 3:24 AM Page 6

ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2002 GEOMETRY AND TRIGONOMETRY Rectangle A = bh Triangle 1 A = bh 2 Circle A = pr 2 C = 2 pr Parallelepiped V = lwh Cylinder V = pr 2 l S = 2 prl + 2 pr 2 Sphere 4 V = pr 3 3 S = 4 pr 2 Right Triangle a 2 + b2 = c2 a sin q = c b cos q = c tan q =

a b

CALCULUS df d f du = dx du dx

2 7 2 7

d n n -1 x = nx dx d x e = ex dx d 1 (1n x) = dx x d (sin x) = cos x dx d (cos x) = - sin x dx 1 n +1 xn dx = x , n ž -1 n +1 e x dx = e x

I I

I

dx = 1n x x cos x dx = sin x

I I sin x dx = - cos x

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

area circumference volume surface area base height length width radius

c q

a 90

b