PHY 121
Tables and Formulas
You may refer to this handout on quizzes and exams. Do not add additional information.
e
Sec. 1:
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Sec. 2:
Projectiles: No new formulas.
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Sec. 3:
Weight: W = mg
-2-
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Sec. 4:
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Sec. 5:
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Sec. 6:
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Sec. 7:
Newton's 3rd law: If A exerts a force on B, then B exerts an equal and opposite force on A.

Momentum: p

mv
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Sec. 8:
Moments of inertia: Particle of mass m, following orbit of radius r: I = mr2
Rigid bodies, total mass = M, outside radius = R:
Hoop or tube, rotating about center: I = MR2
Solid cylinder or disk, rotating about center: I = (½)MR2
Solid sphere, rotating about center: I = (2/5)MR2
Thin spherical shell, rotating about center: I = (2/3)MR2
Thin rod, length L, rotating about center: I = (1/12)ML2
Thin rod, length L, rotating about one end: I = (1/3)ML2
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Sec. 9:
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Sec. 10:
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Sec. 11:
Pascal's Principle: P increase at one point in an enclosed fluid = P increase at any other point.
Archimedes' Principle: Buoyant force = weight of displaced fluid = (ρV)g
-4-
Ideal gas law: PV = nRT
P & T: Absolute pressure and temperature,
V = volume,
n = number of moles, R = 8.314 J/mole.K
Sec. 12:
Heat gained from a change of temperature: Q = m c ΔT
c = specific heat
Heat gained from a change of state: Q = mLf or Q = mLv
L = heat of fusion or vaporization
_
In an insulated container, ∑Q = 0
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Sec. 13:
First law of thermodynamics: Q = ΔEint + W
Q = heat added, ΔEint = internal energy gained,
Isobaric process = no pressure change, Isothermal = No temperature change,
2nd law: Entropy won't spontaneously decrease. (Or, Heat won't spontaneously go cold to hot.)
Work done in a cycle = Area enclosed on P-V diagram.
e
W
QIN = W + QOUT
emax
1
TOUT
QIN
TIN
Efficiency:
Efficiency of Carnot Cycle:
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-5-
2
Quadratic Formula: If ax + bx + c = 0
then
x
b
b2
2a
4ac
Some fundamental constants:
Speed of light:
c = 2.998 x 108 m/s
Electron rest mass:
me= 9.110 x 10-31 kg = (.5110 MeV)/c2
Proton rest mass:
mp = 1.673 x 10-27 kg = (938.3 MeV)/c2
Neutron rest mass:
mn = 1.675 x 10-27 kg = (939.6 MeV)/c2
Universal gas constant: R = 8.314 J/mole K
Avogadro's Number:
N0 = 6.022 x 1023 molecules/mole
Some Physical Properties:
Density of air at 20 C and 1 atmosphere
1.29 kg/m3
Density of water at 20 C
1000 kg/m3 (=1.0 gram/cm3)
Mass of earth
5.99 x 1024 kg
Radius of earth
6.37 x 106 m
Standard atmospheric pressure
1.013 x 105 Pa
Approximate Coefficients of Friction:
S
k
wood on wood 0.5 0.3
steel on steel
0.74 0.57
teflon on teflon 0.04 0.04
S
k
rubber on dry concrete 1.0 0.8
rubber on wet concrete 0.7 0.5
metal on ice
0.03 0.01
-6-
Expansion Coefficients (near room temperature):
°C-1)
24 x 10-6
20 x 10-6
17 x 10-6
9 x 10-6
3.2 x 10-6
29 x 10-6
12 x 10-6
12 x 10-6
150 x 10-6
Aluminum
Brass & bronze
Copper
Glass (ordinary)
Glass (pyrex)
Lead
Steel & iron
Concrete
Vinyl siding
°C-1)
Ethyl alcohol 7.5 x 10-4
Benzene
1.24 x 10-4
Acetone
1.5 x 10-4
Glycerin
4.85 x 10-4
Mercury
1.82 x 10-4
Gasoline
9.6 x 10-4
Specific heat, c (at 25 C):
Substance cal/g C
Aluminum 0.217
Concrete
0.2
Copper
0.093
Gold
0.0308
Ice(-25-0 C) 0.48
Iron & Steel 0.112
Lead
0.0305
J/kg C
908
840
390
129
2010
469
128
CP
CV
(J/mol K) (J/mol K)
He
Ar
Ne
Kr
20.8
20.8
20.8
20.8
12.5
12.5
12.7
12.3
Substance cal/g C
Silver
0.056
Tin
0.054
Zinc
0.092
J/kg C
234
226
385
Ethyl alcohol 0.58
Mercury
0.033
Water
1.00
Steam (1atm) 0.47
2430
140
4186
1970
CP
CV
(J/mol K) (J/mol K)
1.67
1.67
1.64
1.69
H2
N2
O2
CO
28.7
29.1
29.2
29.2
20.4
20.8
20.9
20.9
CP
CV
(J/mol K) (J/mol K)
1.41
1.40
1.40
1.40
CO2
SO2
H2O
CH4
36.9
40.4
35.4
35.5
Heat of Fusion of water = 79.6 cal/g = 3.34 x 105 J/kg
Heat of Vaporization of water = 539 cal/g = 2.26 x 106 J/kg
28.5
31.4
27.0
27.1
1.30
1.29
1.30
1.31
-7Units:
Fundamental Units:
Standard SI Unit:
Conversion Factors:
LENGTH
meter = m
1 m = 3.28 ft, 1 mile = 1609 m = 5280 ft, 1 inch = 2.54 cm
TIME
second = s
1 hour = 3600 s, 1 day = 86,400 s, 1 year = 3.16 x 107 s
MASS
kilogram = kg
TEMPERATURE
kelvin = k
1kg = .0685 slug, weighs 2.21 lb in standard gravity
1 atomic mass unit = 1 u = 1.66 x 10-27 kg
T (in kelvins) = T (in Celsius) + 273.15
VOLUME
m3
1 Liter = 10-3 m3 = 10+3 cm3
SPEED
m/s
1 mi/hr = 0.447 m/s = 1.47 ft/sec
FORCE
newton = N
1 N = 0.225 pound
ENERGY
& WORK
joule = J
1 calorie = 4.186 J 1 J = 0.738 ft lb
1 electronvolt = 1.602 x 10-19 J, 1 BTU = 252 cal
POWER
watt = W
1 horsepower = 746 W = 550 ft lb/sec
ANGLE
radian = rad
1 revolution = 360 = 2π rad
Derived Units:
FREQUENCY
hertz = Hz
1 Hz = 60 rev/min = 1 cycle/sec
IMPULSE &
MOMENTUM
kg m/s = N S
PRESSURE
pascal = N/m2 1 atmosphere = 1.013 x 105 Pa = 14.7 lb/in2
SI prefixes:
Power:
10-24
10-21
10-18
10-15
10-12
10-9
10-6
10-3
10-2
10-1
Prefix:
yocto
zepto
atto
femto
pico
nano
micro
milli
centi
deci
Abbreviation:
y
z
a
f
p
n
Power:
101
102
103
106
109
1012
m
c
d
1018
1021
1024
Prefix:
deka
hecto
kilo
mega
giga
tera
peta
exa
zetta
yotta
Abbreviation:
da
h
k
M
G
T
P
E
Z
Y