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Physics I
Helpful Physics I Information
Constants
 0  8.85  10 12 C
2
Nm
2
k
2
1
 8.99  10 9 Nm 2
C
4  0
e   1eV  q proton  16
.  10 19 C
h  6.63  10 34 Js
c  3  108 m s
m proton  1.67 1027 kg
melectron  9.11031kg
G  6.67  10 11 N  m 2 / kg 2
g  9.81 m/s 2  32.2 ft / s 2
1D, 2D and Rotational Kinematic Equations (constant acceleration projectile motion)
x
v=
t
v
a=
t
vf = vo + at

 dx
v=
dt

 dv
a=
dt
x f = x o + v o t + 12 at 2
vf2 = vo2 + 2a(xf - xo)
A  B  A B cos( )
2r 2
T

v

A x B  A  B sin( )
a = r
v = r
s = r
v
d
ac  t 
  2r
r
dt
2
Electrostatics and Magnetic Fields
1 q1q 2
F12 
4  0 r 2

 FE
E
q

E
 
FB  q(v x B)
1 q
r
4  0 r 2
Forces, Friction and Motion Rules and Equations
Newton’s Laws
1. Law of inertia | The total force on an object moving at constant velocity is zero.
2. F = ma | The net force F equals the vector sum of all forces acting on the object of mass m.
3. FAB = -FBA | If A exerts a force on B, then B exerts an equal and opposite force on A.
f  N
Fs  kx
1
D  CAv 2
2
vt 
2mg
CA
mv 2
Fc 
r
FG
ma mb
r2
Energy, Work and Power
xf
1
K  mv 2
2
W= -U =K=  F ( x )dx
xO
Wapp  Eint   f k d
Us 
Ws  U   12 kx 2
P
1 2
kx
2
W
t
U 
E=K+U
P
dE
dt
GMm
r
Ug=mgy
F ( x)  
dU ( x )
dx
Etot  K  U  Eint  0
Kf + Uf = Ko + Uo
Center of Mass and Conservation of Momentum
xcm
m x  mb xb
 a a
ma  mb
1

rcm 
M
n
 m r
i 1
F
i i


p = mv
ext
 Macm
p initial = p final
Impulse and Collisions


J  p
t
 f 
J   F (t )dt
tO


J  np

 J
n 
F
  p
t
t
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Physics II
Helpful Physics II Information
Constants
 0  8.85  10 12 C
2
Nm
k
2
e   q proton  16
.  10 19 C
mc  2.43  10
h  6.63  10 34 Js
12
c  3  108 m s
.  10 27 kg
melectron  9.1  10 31 kg mproton  167
1eV  16
.  1019 J
h
2
1
 8.99  10 9 Nm 2
C
4  0
  h 2
m
A  B  ABcos()
A x B  ABsin()
Chapter 9, Rotation of Rigid Bodies and Chapter 10, Dynamics of Rotational Motion
d v t


dt
r
s

r
I   mi ri 2
I   r 2 dm  I cm
vt2
d d 2  a t

 2 
ac 
  2r
dt
r
r
dt
  
2
  r  F  I
 Mh
f
W
 d  KE
i
dW
d

 
dt
dt
1
1
KE  I cm  2  mvcm 2
2
2
1
  0   0 t   t 2
2
P
 2   0 2  2 (   0 )
L  I
Chapter 21, Sound and Hearing
T  1 f  2 k m  2
U
l
g
x(t )  A cos(t  )  
kx 2
2
Chapter 20, Wave Interference and Normal Modes
2
 km
T
y( x, t )  ym sin( kx  t  )
k
2


2
T

 
  f 
k T

fL

2

n
Chapter 22, Electric Charge and Electric Field and Chapter 23, Gauss’s Law

 F
1 q
1 p
E 
2 
q 4 0 r
2 0 z 3

F

0
E conductor surface 
  q
   E  dA  enclosed
1 q q'
4  0 r 2
E line ch arg e 
0

2  0 r
E sheet ch arg e 

2 0
Chapter 24, Electric Potential (Voltage)

W
1 q
1 p cos 
V      E  ds 

q
4 0 r 4 0 r 2
i
1 qq '
U W 
4  0 r
f
Es  
V
s
Chapter 25, Capacitance and Dielectrics
q  CV
C
q 0 A

V
d
n
1
C parallel   C j
Cseries
j 1
n
1
j 1 C j

   0
Chapter 26, Electric Current and Chapter 27, Circuits
dq  EMF   t RC
i

e
dt  R 
dW
EMF 
 iR
dq
V  iR
n
1
j 1
R parallel
Rseries   R j

charging capacitor: q  C  EMF  1  e
 t RC
V2
P  iV  i R 
R
n
1

j 1 R j
2
 discharging capacitor:
q  q0 e
 t RC
Chapter 40, Photons, Electrons, and Atoms, Chapter 41, The Wave Nature of Particles,
and Chapter 43, Atomic Structure
E  hf  Kmax  
 h2  2
me 4 1
En  
n



3 20 h 2 n 2
 8mL2 
p
hf
h

c

 
h
1  cos
mc
L  l (l  1) 
x, ps  
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Physics III
Helpful Physics III Information
Constants
 0  8.85  10 12 F m
h  6.63  10 34 Js
 0  4  10 7 Tm A
e   q proton  16
.  10 19 C
Magnetic Fields (chapter 28)



  


FB  qm B
F  q ( E  v  B)
FE  qE
R
T
m proton  17
.  10 27 kg 
melectron  9.1  10 31 kg
n glass  150
.
nwater  1333
.
nair  1000293
.
c  3  108 m s
near point  25.0 cm
vs  E B
Ek  qV  12 mq v 2
mv

qB
2m

qB
V
vd  H
hB


U B    B
n
IB
qwVH
Source of Magnetic Fields (chapter 29)


 f  0 I (dl  r)
 I
Bp  0
 dB   4 r 2
2 r
0

 B  dl   0 I enclosed
circular loop: Bx

 0 IR 2
3
2( x 2  R 2 ) 2
0 I
infinitely long wires: Boutside 
2 r

 B   B  dA  0
center of loop:
  

FB  I (l  B)   NIAn
F21 
 I
Bp  0
2R
Binside 
 0 Ir
2 a 2
 
 B    B
 0 I1 I 2
l
2d
far from loop:
solenoid:
Faraday’s Law and Induction (chapter 30)
d E
( BLv ) 2
I  BLv R P 
Einduced = IR
I


displacement
0
R
dt
 0 IR 2
Bp 
2x3
  IN
B 0
l
I enclosed  I net  I displacement
 Maxwell’s Equations 
Gauss’s Law for

m

E:

 B  dA  0
  q
 E   E  dA  enclosed
0
Gauss’s Law for

B:
4

d
 d B 
Einduced = 
   E  dl = -  B  dA
 dt 
dt
d E 


 B  dl   0  I net   0 dt 
Faraday’s Law:
Inductance (chapter 31)

dI
L B
E= - L
I
dt
2
LI
B2
uB 
U
2
2 0
I (t ) 
Electromagnetic Waves (chapter 33)
E
E0
1
E rms  0
c   

B0
2
 0 0
 
 EB
S
0
P
P
I 
A 4 r 2
2I
reflection): Pr 
c
momentum:
U
p
c
Ampere’s Law (modified):
t
E
(1  e  L )
R
I (t )  I 0 e
t
L

B2
uT   0 E 
0
I
2

F
pressure: P 
A
E t  L
(e
)
R
(complete absorption):

E 0 B0
 S
2 0
Pr 
I
c
(perfect
The Nature and Propagation of Light (chapter 34)


1  n1
Snell’s Law: n sin  i  ns sin  t  c  sin 
n  cv  0 
i   r
 n2 
ncore  ncladding

ncore
2
2
NA  sin   ncore
 ncladding
Law:
Brewster’s Law:
n 
 p  tan 1  2 n 
1
I  I 0 cos2 
Geometrical (Paraxial) Optics (chapter 35)
paraxial approximation:
  sin   tan 
1 1 1
 
o i
f
ni
mag  1  1
n2 o
spherical mirrors:
plane mirrors:
M lateral 
hi
i

ho
o
oi
M lateral 
plane lenses:
hi
ho
n1 n2

0
o
i
Malus’
curved lenses:
n0 n1 n1  n0
 
o
i
R
M lateral 
hi
ni
 0
ho n1o
refracting element:
 1
1 1
(n  1)   
 R1 R2  f
25cm
h' h
M  
optical microscope: tan  

f
L f0
 L  25cm
M   mobjective meyepiece 
f objective f eyepiece
h'
h'
optical telescope:
mobjective 
meyepiece 
f objective
f eyepiece
mag 
mobjective
meyepiece

f objective
f eyepiece
Interference of Light (chapter 37)
E net  E1  E2
Young’s double slit:
ym  L tan m

2 r

path difference 
r  d sin  m  m
rm2
rm2
2
Newton’s rings: R 

(2nt ) (add  from low n to high n)
0
2d m
Diffraction of Light (chapter 38)
y
a2
 a sin  
2  
I total  I max sinc     2 
(screen in focal plane of
tan   ; L 

 2
  
L

y
lens): tan  
f

2 a
 
 
I  I max sinc 2   cos2  
irradiance minima: a sin  m   122
.

sin 
 2
 2
a

2d

sin 

thin film interference:
