Physics 151 – Exam Equation Sheet
Exam 1 Equations
Unit Conversions
1 m = 1.094 yd = 3.281 ft = 39.4 in
1 mile = 1609 m
1 in = 2.54 cm
Constants
g = 9.81 m/s2 = 32.0 ft/s2
c = 2.99 x 108 m/s
Geometric Formulae
Circle
C  2 r
A   r2
Rectangle
P  2  l  w
opp
hyp
adj
cos  
hyp
opp
tan 
adj
1-D Kinematics
sin  
distance
elapsed time
displacement
average velocity 
elapsed time
average speed 
If
a=0
then
If
a≠0
A  lw
v  v0  at
Cube
A  6l 2
V  l3
Sphere
A  4 r 2
4
V   r3
3
Cylinder
A  2 r 2  2 rl
V   r 2l
Triangle Trigonometry
x  vt
1
 v0  v  t
2
1
x  v0t  at 2
2
2
2
v  v0  2ax
x
then
Horizontal Range
 v2 
R   0  sin 2
g
Exam 2 Equations
Friction
Static Friction
f s  s N
Kinetic Friction
f k  k N
Springs
Hook’s Law
Fx   kx
Centripetal Acceleration
v2
ac 
r
Newton’s 2nd Law


F  ma
Torque
   rF sin 
Torque Equilibrium
  0
Exam 3 Equations
Work
W  Fd cos 
Work-Energy Theorem
Wtotal  KE 
1 2 1 2
mv f  mvi
2
2
Energy
1 2
mv
2
Gravitational Potential Energy PE  mgh
1
Elastic Potential Energy PE  kx 2
2
Kinetic Energy KE 
Conservation of Energy
KEi  PEi  KE f  PE f
Work Done by NonConservative Forces
WNC  KE  PE
Momentum


p  mv
Impulse
 

I  Fave t  p
Exam 4 Equations
Simple Harmonic Motion
Position vs. Time
 2 
x  A cos 
t
 T 
1
f 
T
Mass on a Spring
F  kx
1 2
kx
2
m
T  2
k
PEElastic 
T  2
Pendulum
Waves
Fluids
Density  
M
V
F
A
5
Pa = 1.01 x 10 Pa
Pressure P 
L
g
vf
Waves on a String
T
where μ is the linear density
v

(mass/length)
Wave Formula
2 
 2
y  x, t   A cos 
x
t
T 

Sound vSound = 343 m/s (at room
temperature)
I
Standing Waves
String
v
n T
fn  n
n  1, 2,3...

2L 2L 
Open-Closed Pipe
v
fn  n
n  1,3,5...
4L
v
Open-Open Pipe f n  n
n  1, 2,3...
2L
P
P

A 4 r 2
 I 

 I0 
  10 log10 
I 
 2  1  10 log10  2 
 I1 
where I0 = 10-12 W/m2
Pressure at Depth P  Pa   gh
Pascal’s Principle – An external
pressure applied to an enclosed fluid is
transmitted unchanged to every point
within the fluid
P1  P2
F1 F2

A1 A2
Archimedes’ Principle – An object
completely immersed in a fluid
experiences an upward buoyant force
equal in magnitude to the weight of fluid
displaced by the object.
FB   flV fl g
Equation of Continuity
v1 A1  A2 v2
Bernoulli’s Equation
1
1
P1   v12   gy1  P2   v22   gy2
2
2
Exam 5 Equations
Temperature Scales
Q  mcT
9
TF  TC  32
5
TK  TC  273.2
Substance
Thermal Expansion
L   L0 T
V  BV0 T
For many substances β=3α
Substance
Lead
Aluminum
Brass
Copper
Steel
Concrete
Coefficient of
Linear Expansion, α (Cº-1)
29 x 10-6
24 x 10-6
19 x 10-6
17 x 10-6
12.2 x 10-6
12 x 10-6
Thermal Conductivity
Q
AT A


t
L
L
Substance
Silver
Copper
Gold
Aluminum
Steel
Lead
Ice
Concrete
Glass
Wood
Air
Calorimetry
Thermal Conductivity
κ (W/(m·Cº)
417
395
291
217
66.9
34.3
1.6
1.3
0.84
0.10
0.0234
Water
Ice
Steam
Air
Aluminum
Glass
Steel
Copper
Silver
Gold
Lead
Specific Heat c
(J/(kg·Cº)
4186
2090
2010
1004
900
837
448
387
234
129
128
One can convert c values to cal/g-Cº by
dividing by 4186
Latent Heats
Q  mL f
Q  mLv
For water these values are:
Lf = 33.5 x 104 J/kg = 79.7 cal/g
Lv = 32.6 x 105 J/kg = 540 cal/g
One can convert L values to cal/g by
dividing by 4186
Ideal Gas Law
PV = nRT,
PV = NkT
where n = amount of substance and N the
number of particles,
R=8.314 J/mol·K
NA=6.02 1023 particles
k =1.38 10-23 J/K
n = N / NA and n = m/M
where m is the total mass and M the molar
mass
Young’s Modulus
Stress 
Y
F
A
Strain 
L
L0
Stress FL0

Strain AL
Thermal Stress
Y
FL0
AL
L
 T
L0
F
 Y T
A
Substance
Tungsten
Steel
Copper
Brass
Aluminum
Pyrex
Lead
Substance
H2
O2
CO2
N2
Methane,
CH4
CO
Air
Water
vapor
Young’s Modulus Y
(N/m2)
36 x 1010
20.1 x 1010
11 x 1010
9.0 x 1010
6.9 x 1010
6.2x 1010
1.6 x 1010
Molar mass (g/mol)
2.016
32
44.01
28.01
16.04
28.01
28.966
18.02
Exam 6 Equations
Electric Charge
Photons
cf
Coulomb’s Law
E  hf 
hc

F k
h = 6.626 10-34 J·s
c=2.99 10 m/s
8
q1q2
R2
where k = 8.99  109 N·m2 /C2
Doppler Shift
Fundamental charge
 u
f '  f 1  
 c
e = 1.602 x 10-19 C
Reflection
Electric Circuits
i   r
V  IR
Spherical Mirrors
1
f convex   R
2
1
f concave  R
2
1 1 1
 
d o di f
m
hi
d
 i
ho
do
Refraction
n1 sin 1  n2 sin  2
sin  c 
n2
n1
Thin Lenses
1 1 1
 
d o di f
m
hi
d
 i
ho
do
P  IV  I 2 R 
V2
R
Resistivity
R
L
A
Resistors
Series Reff  R1  R2  ...
Parallel
1
1
1
 
 ...
Reff R1 R2