PHY 131
Tables and Formulas
You may refer to this handout on quizzes and exams. Do not add additional information.
i
Sec. 1:
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Sec. 2:
Memorize: Definitions of trig functions, and Pythagorean theorem.

A

B
( Ax
B x )iˆ ( Ay
B y ) ˆj
( Az
B z )kˆ
(n = some scalar)

A
Ax2 Ay2 Az2
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-2Sec. 3:
Memorize: Newton’s three laws, and relationship between weight and mass.
Sec. 4:
Projectiles: Treat each component like one dimensional motion.
Horizontal range:
vi2 sin( 2 i )
R
g
Sec. 5:
Memorize: Formulas for kinetic energy, gravitational potential energy and total energy. Understand
conservation of energy.
Work-energy theorem:
W = ΔKE (W = work done by any kinds of forces)
or
Ei + Wnc = Ef (Wnc = work done by non-conservative forces.)
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Sec. 6:
Memorize: Formula for momentum. Understand conservation of momentum.

Impulse-momentum theorem: I


p , where I


F t and p = momentum, not power.
Elastic collision: one where mechanical energy is conserved. ______________________________
Sec. 7: REMEMBER: Some equations require use of radians.
-3-
Moments of inertia:
2
Particle of mass m, following orbit of radius r: I = mr2. System of such particles: I = Σmiri
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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Understand conservation of angular momentum.
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-4Sec. 10:
Memorize: Relationship between frequency and period.

Hooke's law: F

k x (F = force, k = spring constant, x = displacement from equilibrium.)
Harmonic oscillator:
Displacement: x = A cos(ωt + )
Velocity:
v = -vmax sin(ωt + )
Acceleration: a = -amax cos(ωt + )
Elastic potential energy: Us = ½ k x
Pendulum:
Sec. 11:
where ω = 2πf = k / m
where vmax = ωA
2
where amax = ω A
(f = frequency.)
2
g
(ω = 2πf)

Memorize: Relationship between wavelength, speed and frequency.
A wave traveling to the right: y = f(x – vt)
A wave traveling to the left: y = f(x + vt)
f = some function
Harmonic wave traveling to the right: y = A sin(kx – ωt + )
Angular wave number: k = 2π/λ
Angular frequency: ω = 2πf
F = string tension (force),
Speed of sound in air: v
402T
= mass per unit length
T = kelvin temperature (Celsius + 273)
Doppler effect:
v = speed of waves, vo = observer’s speed, vs = source’s speed
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Sec. 12: Memorize: Ideal gas law.
Law of universal gravitation:
G = 6.67 x 10
-11
2
2
N·m /kg
Kepler’s laws:
1. Orbits are elliptical, with sun at one focus.
2. Line from sun to planet sweeps through equal areas in equal times.
4 2
2
a 3 T = period, a = semi-major axis
3. T
G (m1 m2 )
-5-
Stefan’s Law: P = AeT4
= 5.67 x 10-8 W/m2 K4, A = Area,
e = Emissivity (0 to 1)
T = Temp.
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Sec. 14:
Memorize: Definitions of P = pressure and ρ = density.
P = Power Radiated,
Variation of pressure with depth: ΔP = -ρgΔh
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
MATHEMATICAL BACKGROUND:
Quadratic Formula: If ax2 + bx + c = 0
then
x
b
b2
2a
Logarithms: if x = by then logb(x) = y (b = base)
log (xy) = log x + log y
log (x/y) = log x - log y
log (xa) = a log x
logb (bx) = x
4ac
-6Derivatives:
If y = ax
n
then
dy
dx
If y = a constant, then
a ( nx n 1 ) where a & n are constants ≠ 0
dy
dx
0
3
2
Example: If y = 7x + 4x + 8, then dy/dx = 21x + 4 + 0
Product rule: If y = f(x)g(x), then
dy
dx
f
dg
dx
g
df
(First times the derivative of the second +
dx
second times the derivative of the first.)
dy df dg
(Derivative of what’s outside the parentheses times
dx dg dx
3
2
derivative of what’s inside the parentheses. Example: If y = (7x) then dy/dx = [3(7x) ][7].)
Chain rule: If y = f(g(x)), then
Some Fundamental Constants:
-11
2
Gravitational constant:
G = 6.672 x 10
Speed of light:
c = 2.998 x 108 m/s
Electron rest mass:
me= 9.110 x 10-31 kg
Proton rest mass:
mp = 1.673 x 10-27 kg
Neutron rest mass:
mn = 1.675 x 10-27 kg
2
N·m /kg
Universal gas constant: R = 8.314 J/mole K
Avogadro's Number:
N0 = 6.022 x 1023 molecules/mole
Boltzmann’s constant:
k = 1.381 x 10-23 J/K
Some Physical Properties:
Density of air at 20 C and 1 atmosphere
1.29 kg/m3
Speed of sound in air at 20 C and 1 atm.
343 m/s
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
-7Approximate Coefficients of Friction:
S
k
S
wood on wood 0.5 0.3
steel on steel
0.74 0.57
teflon on teflon 0.04 0.04
k
rubber on dry concrete 1.0 0.8
rubber on wet concrete 0.7 0.5
metal on ice
0.03 0.01
Expansion Coefficients (near room temperature):
Aluminum
Brass & bronze
Copper
Glass (ordinary)
Glass (pyrex)
Lead
Steel
Concrete
Vinyl siding
24 x 10-6
19 x 10-6
17 x 10-6
9 x 10-6
3.2 x 10-6
29 x 10-6
11 x 10-6
12 x 10-6
150 x 10-6
Ethyl alcohol
Benzene
Acetone
Glycerin
Mercury
Gasoline
1.12 x 10-4
1.24 x 10-4
1.5 x 10-4
4.85 x 10-4
1.82 x 10-4
9.6 x 10-4
Specific heats (at 25 C):
Substance cal/g C
Aluminum 0.215
Concrete
0.2
Copper
0.0924
Gold
0.0308
Ice(at -5 C) 0.50
Iron & Steel 0.107
Lead
0.0305
J/kg C
900
840
387
129
2090
448
128
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) 0.48
&100°
2400
140
4186
2010
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
Thermal Conductivities, in W/m· C (solids at 25 C, gases at 20 C):
Aluminum
Copper
Gold
Iron
Lead
Silver
Wood
238
397
314
79.5
34.7
427
0.08
Asbestos
Concrete
Diamond
Glass
Ice
Rubber
Water
0.08
0.8
2300
0.8
2
0.2
0.6
Air
Helium
Hydrogen
Nitrogen
Oxygen
0.0234
0.138
0.172
0.0234
0.0238
-8Units:
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
1kg = .0685 slug, weighs 2.21 lb in standard gravity
TEMPERATURE
kelvin = k
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
Derived Units:
ENERGY& WORK joule = J
1 calorie = 4.186 J, 1 J = 0.738 ft lb, 1 BTU = 252 cal
POWER
watt = W
1 horsepower = 746 W = 550 ft lb/sec
ANGLE
radian = rad
1 revolution = 360 = 2π rad
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