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Constants: 2
s
m g =
11 2 2
G = 6. 673 10 Nm /kg
− e C
19
- 60 10
− =
9 2 2 kc = 9. 00 10 Nm /C
2
2 12 0 8.^8510 N m
C
−
A
T m =
− 7
0 4 10 h = Js
−
- 63 10
34 = J s
−
- 055 10
34
melectron kg
31
- 11 10
− = mproton kg
27
- 67 10
− = c 3. 00 10 m/s
8 =
Metric Multipliers:
-12 -6 -2 6
Pico p = 10 Micro = 10 Centi c= 10 Mega M= 10
9 -3 3 9
n = 10 m= 10 k= 10 G= 10
−
Nano Milli Kilo Giga
Conversion Equivalents:
1 .00 inch = 2.54 cm 1.00 ft. = 30.5 cm 1.00 m = 3.28 ft. = 39.4 inches
1.00 cm = 0.394 inches 1.00 km = 0.621 miles 1.00 mile = 5280 ft = 1.61 km
1 Rev = 2 rad = 360 eV J
19
−
kc=
Trigonometric Relations:
2 2 2
C
A
C
B
For RightTriangles: A B C A
B
Adj
Opp Tan Hyp
Adj Cos Hyp
Opp
Sin = = = = = = + =
For AllTriangles :
2 2 2
C A B AB Cos C
Sin
B
Sin
A
Sin = = = + −
Vector Relations (assuming defined with respect to the positive x-axis)
−
x
y x y x y V
V
V V Cos V V Sin V V V Tan
2 2 1
Vector Dot and Cross Products (assuming is the angle between the vectors)
AB AB i AB AB j AB AB k
B B B
A A A
i j k
A B y z z y z x x z x y y x
x y z
x y z ( )ˆ ( )ˆ ( )ˆ
ˆ ˆ^ ˆ
= det = − + − + −
ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ 0
ˆ ˆ ˆ ˆ ˆ 0 ˆ ˆ ˆ
ˆ ˆ 0 ˆ ˆ ˆ ˆ ˆ ˆ
=− = =
= = =−
= =− =
i k j j k i k k
i j k j j k j i
i i j i k k i j
| A B| |A||B| Sin
= A B Ax Bx AyBy AzBz | A||B| Cos
Kinematic Equations in 1 Dimension:
0
0
0
0 0 t t
v v
t
v a t t
x x
t
x x x vt v −
dt
dx
t
x
vinst = lim t→ 0 2
2
a (^) inst limt 0 dt
d x
dt
dv
t
v = =
= (^) →
a dt=v
v dt=x
Kinematic Equations in 1 Dimension with Constant Acceleration:
x (^00)
2 0
2 2 v =v 0 +at =x 0 + v+v 0 t x=x 0 +v 0 t+ at v =v + ax−x v= v+v
Kinematic Equations in 2 Dimensions:
0
0
0
0 0 t t
v v
t
v a t t
r r
t
r r r v t v avg avg −
dt
dr
t
r
vinst = lim t→ 0 2
2
a (^) inst limt 0 dt
d r
dt
dv
t
v
= =
= (^) →
a dt=v
v dt=r
Kinematics in 2 Dimensions with Constant Acceleration:
0 0
2 0
2 2 v (^) x =v 0 x+axt x=x 0 + vx+v 0 xt x=x 0 +v 0 xt+ axt vx =vx+ ax x−x vx= vx+vx
0 0
2 0
2 2 v (^) y =v 0 y+ayt y=y 0 + vy+v 0 y t y=y 0 +v 0 yt+ ayt vy =vy+ ay y−y vy= vy+vy
Forces: F ma max may W mg gApparent g aFrame
=^ Fx^ = Fy= = = −
Work: W = Fs=Fs Cos( )
Translational Kinetic Energy:
2
2
KE = mv
Gravitational PE: U GRAV =mgh Conservation on Energy: WNC =KE+U Power:
t
W
P =
Coulomb’s Law : 2
r
Q Q
F =kc
Electric Field : q
F
E
= F qE
E (Point Charge) : 2
r
Q
E =kc
Electric Potential : q
W
q
U
V
ab ab ab = =− U^ =qV
Electric Potential (Point Charge) :
r
Q
V =kc Electric Potential (in uniform E field) : V =−Ed
Electric Fields and Potentials :
V = − Edl
x
V
E (^) x
y
V
E (^) y
z
V
E (^) z
Electric Potential Energy (Point Charges):
r
QQ
U kc
1 2 = Gauss’s Law :
Enclosed E
Q
= E dA=
Capacitance : Q =CV Capacitor Energy Storage :
C
Q
PE QV CV
2 2 = = =
Parallel Plate Capacitor :
d
A
d
k A C
d^ = =
0
E Field Energy Density :
2 0 2
E
volume
PE
Electric Current :
dt
dq
I = Ohm’s Law : V =IR Resistance :
A
L
R= R^ =R 0 [^1 +(T−T 0 )]
Electric Power :
R
V P IV I R
2 2
= = = Battery Terminal Voltage : VT = E −Ir
Capacitors In Parallel : CEQ =C 1 +C 2 Capacitors In Series :
1 2
CEQ C C
= + or
1 2
1 2
C C
C C
CEQ
Series RLC AC Circuit: z =R+( XL −XC)i
2 2 z = R +( XL −XC)
−
−
R
X X Tan
1 L C
Index of Refraction: c f
= =
0 0
1
n
c
n
f vEM = = f = =
1
n
Law of Reflection:
i= R
Snell’s Law: n 1 Sin 1 =n 2 Sin 2 Total Int. Refl.:
1
2 1 n
n Sin =
Energy Density:^2
0 2
1 E Volume
EEnergy =
0
2
2
B
Volume
B Energy
Electromagnetic Waves: E 0 =cB 0 E RMS =cBRMS
0
2 2 0
2
0
2 0 2
1
2
1
RMS RMS RMS RMS
B E B E Volume
Total Energy = + = =
Doppler Effect for EM Waves:
= c
V f f
REL 0 s 1
Polarization: E =E 0 Cos
Mirrors/Lenses:
2
R f = 0
1 1 1
f di d
= + Magnification:
O
i
O
i
d
d
h
h M = =−
Lens Sign Conventions: Focal Length (f): “+” for converging, “-“ for diverging
Object Distance (dO): “+” on left (real), “-“ on right (virtual)
Image Distance (di): “+” on right (real), “-“ on left (virtual)
Magnification (M): “+” upright, “-“ inverted
Double Slit Interference:
(^ )
m Destructive
m Constructive d 1 / 2
sin
L
Y Sin =
Small AngleApproximat ion
Single Slit Interference:
m Destructive
m Constructive d
sin
Thin Film Interference:
(^ )
m Destructive
m Constructive t
F
F F 2 1 /^2
PhaseShift
Reflected
Differencein
with
n
F
Bragg (X-Ray) Diffraction:
(^ )
m Destructive
m Constructive d 1 / 2
2 sin
Special Relativity:
2 2 1 /
1
−v c
= t^ =t 0 0
L L
= m=^ m 0 p^ =mv=^ m 0 v
2 c
V V
V V
V
AB BC
AB BC AC
2 4 0
2 2 2 E =p c +m c
2 E 0 =m 0 c
2 E= m 0 c
2
KE =( − 1 )m 0 c
Quantum Energy/Momentum:
h pc p
hc E =hf = = =
Photoelectric Effect: KEMax =hf−W 0 Compton Effect: ' ( 1 Cos )
mc
h
e
Bohr Radius/Energy: 0
2 2
2 0 0 r n r me
h r (^) n
e
2
(^220) 2 2 0
4
0 (^13.^6 )
8 n
E
Z eV Z E h
em E (^) n
e =− =− =
Heisenberg Uncertainty:
h E t
h x p
