Mrs. Hamilton’s SPH4U Physics Formula Sheet
Kinematics
 d v1  v2
vav 

t
2
1
 d  v1 t  a t 2
2
2
2
v2  v1  2a d
Dynamics
Gm1m2
d2
v2
ac 
r
Fg  mg
GM
R2
vesc 
GmE
v 
r
2
Fc  mac 
 d  v2  t 
1
a t 2
2
Fnet  ma
mv 2
r
r 3 GM

T 2 4 2
2GM
r
F1 m1  d 2 
 

F2 m2  d 1 
v2  v1  a t
Ff   FN
Fg 
F  kx
g
v2  v1
t
(v  v )  t
d  1 2
2
aav 
tan  
ac 
4 2 r
 4 2 rf
T2
2
Momentum, Energy & Power
W  F d cos
Eelastic 
1 2
kx
2
W F d

 Fvav
t
t
Eth  Ff  d
P
E g  mgh  
GMm
r
Woutput
efficiency 
 100%
Winput
1 2
mv
2
m
T  2
k
J  F t  m v   p
p  mv
F  IlB sin
F  qvB sin 
V 
B
W  Ee

q
q
kq
r
q
I
t
kq q
 1 2
r
V 
0 NI
L
q  Ne
F2  o I 1 I 2
V

(parallel plates only)
r
l
2 d
Waves
1
N

f 
v   f
T
t
T
f
sin  1 v1 1 n2
c
n



v
sin  2 v 2  2 n1
xn
x 

 (n  21 )( d )
L
d
L
 
Ek 
p  p'
Electricity and Magnetism
kq q
F kq
Fe  1 22
  2
d
q0 r
 I
 Ee
B 0
V 
  d
2 r
q0
v2
gr
Eelectric
q V  21 mv22  21 mv12
i  r
sin  n  (n  21 )( d )
PS1  PS 2  (n  21 )
2
Physical Constants
Quantity
speed of light in a vacuum
gravitational constant
Coulomb’s constant
charge on electron
charge on proton
electron mass
proton mass
neutron mass
atomic mass unit
Planck’s constant
Symbol
c
G
k
-e
e
me
mp
mn
u
h
Approximate value
3.00 × 108 m/s
6.67 × 10-11 N.m2/kg2
9.00 × 109 N.m2/C2
-1.60 × 10-19 C
1.60 × 10-19 C
9.11 × 10-31 kg
1.673 × 10-27 kg
1.675 × 10-27 kg
1.660 × 10-27 kg
6.63 × 10-34 J.s
Coefficients of Kinetic Friction and Static Friction
Materials in contact
oak on oak, dry
waxed hickory on wet snow
waxed hickory on dry snow
Copper on copper
steel on steel, dry
steel on steel, greasy
steel on ice
rubber on asphalt, dry
rubber on asphalt, wet
rubber on concrete, dry
rubber on concrete, wet
rubber on ice
leather on oak, dry
K
0.30
0.18
0.04
1.0
0.41
0.12
0.010
1.07
0.95
1.02
0.97
0.005
0.50
S
0.40
0.22
0.06
1.6
0.60
0.18
1.2
1.0
1.0
0.99
0.006
0.70
Important Mathematical Relationships for Physics
Indexes of Refraction
Medium
Index of
refraction (n)
1.000000
vacuum
gases (at 0°C, 101.3 kPa)
air
1.000293
carbon dioxide
1.000450
hydrogen
1.000139
liquid (at 20°C)
water
1.33
ethyl alcohol
1.36
glycerin
1.47
benzene
1.50
solid (at 20°C)
ice (0°C)
1.31
glass (crown)
1.52
glass (flint)
1.65
sodium chloride
1.53
zircon
1.92
diamond
2.42
Note: Indexes are for yellow light (589 nm).
Solar, Terrestrial and Lunar Data
Quantity
Symbol
mass of Sun
radius of Sun
mass of Earth
radius of Earth at equator (mean)
radius of Earth’s orbit (mean)
acceleration due to gravity
on Earth at equator
(sea level)
on Earth at poles (sea
level)
on the Moon
Earth-Moon distance (mean)
mass of Moon
radius of the Moon (mean)
Period of orbit
radius of the Moon’s orbit (mean)
Earth-Sun distance (mean)
standard atmospheric pressure
length of Earth year
mS
rS
mE
rE
rEO
9.7804 m/s2
g
9.8322 m/s2
g
1.62 m/s2
3.84 × 108 m
7.35 × 1022 kg
1.74 × 106 m
2.36 × 106 s
3.84 × 108 m
1.50 × 1011 m
1 atm or 1.013 × 105 Pa
3.16 × 107 s
patm
Ty
sin θ  ac
cos θ  bc
tan θ  ba
b
B
g
mM
rM
TMO
rMO
A
c
Approximate value
1.99 × 1030 kg
6.96 × 108 m
5.98 × 1024 kg
6.38 × 106 m
1.50 × 1011 m
C
a
SINE LAW
a
b
sin A
sin B

c
 sinc C
a
COSINE LAW

b A
c 2  a 2  b 2  2ab cos C
QUADRATIC FORMULA
x
b
b  4 ac
2a
2
QUADRATIC EQUATION
ax 2  bx  c  0