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1
VISUAL PHYSICS ONLINE
EQUATION MINDMAPS
Equations are essential part of physics, without them, we can’t
start to explain our physical world and make predictions. An
equation tells a story – a collection of a few symbols contains a
wealth of information. Many examination questions can be
answered by having an in-depth understanding of equations. To
help you maximize your examination marks, you should use the
equation mindmaps to gain this in-depth understanding. You
need to commit to memory much of the information contained
in the equation mindmaps so that you can appreciate the story
told by each equation.
2
MECHANICS (Kinematics and Dynamics)
av
rv
t
x
dxv
dt
avg
v v ua
t t
dva
dt
Average velocity
Instantaneous velocity in X direction
Average acceleration
Instantaneous acceleration in X direction
F m a
Fa
m
F m g
2
C
vF m
r
2
c
C
F va
m r
Newton’s Second Law
acceleration
Weight of an object
Centripetal force: uniform circular motion
Centripetal acceleration
AB BA
F F Newton’s Third Law
3
rocket gasesF F
eg rocket propulsion
p mv
impulse J F t
J F t mv mu
0 0F p
Momentum of a moving object
Impulse of a force F acting for a time interval t
Impulse = change in momentum
Law of Conservation of momentum
4
W F s
212K
E K mv
2 21 12 2
W F s mv mu
W qV
212K
E K mv e V
Work done by a force during a displacement (force and displacement in same direction [1D]
Kinetic energy of a moving object
Work done = change in KE [1D] only
Work done on a charge in an electric field
Gain in KE electron due to a constant accelerating voltage
5
0
212
2 22
2
2
av
av
v u a t u v
s u t a t
v u a s
u vv
u vs v t t
Equation for uniform accelerated motion in one-dimension a = constant
2 2
212
0
cos
sin
2
2
x
x
x x x
y
y
y y y
y y y
y y
y y
a
u u
v u x u t
a g
u u
v u a t
v u a y
y u t a t
u vy t
2 2 2
2 2 2
tan
tan
y
x y s
x
y
x y v
x
ss s s
s
vv v v
v
Equations for
Projectile Motion
g = 9.8 m.s-2
ay = - g = - 9.8 m.s-1
6
1 2
2
G m mF
r
planet
planet
planet
G Mg
R
1 2
p
m mE U G
r
pE U m g h
22
E E
E
G M G Mg
r R h
2L
Tg
Gravitational force
Acceleration due to gravity at surface of a planet
Gravitational potential energy
Gravitational potential energy near Earth’s surface
Acceleration due to gravity (Earth)
Period of pendulum g
7
3
2 24
r G M
T
3 3
1 2
2 2
1 2
r r
T T
32
3 3
1 2
2 2
1 2
22 1
1
r r
T T
rT T
r
orb
G Mv
r
2
orb
rT
v
2esc
G Mv
r
Kepler’s Third Law for satellite motion
orbital velocity
orbital period
geostationary satellite T = 24 hours
escape velocity
8
SPECIAL RELATIVITY
2
2
1
1
v
cv
c
0
02
21
tt t
v
c
2
0
0 21
LvL L
c
2E mc
2
21
mvp mv
v
c
2 2 2 2 4 2 2 2
0E p c m c p c E
22
02
21
mcK E E mc
v
c
212
K mv
00
EE E p c p
c
mass m is a constant time dilation length contract total energy momentum total energy kinetic energy kinetic energy v << c
photon
9
ELECTRICITY
VR
I
P V I
Energy V I t
Resistance
Electrical power
Electrical energy
10
MAGNETISM
1 2I IF
kL d
sinF B I L
0
2
IB
r
cos
F d
n B I A
Magnetic force between two parallel conductors
Magnetic force on a
conductor
Magnetic field surrounding a long straight conductor
Torque Torque on a coil in a magnetic field
cosB
B A
B
t
Bd
dt
cos
sin
BB A t t
B A t
battery backI R
Magnetic flux
average induced emf
induced emf
electric motor: back
emf back
11
p p
s s
V n
V n
ps
s p s p
p s
nnV V I I
n n
s p s s p pP P V I V I
2
lossP I R
Transformer equation: step up or step down voltages
ideal transformer
Power loss (eddy currents – transformer, induction heating; transmission lines)
sinF qv B
FE
q
VE
d
Force on a charged particle moving in a magnetic field
Electric field
Electric field (constant) between two parallel charged plates
12
NATURE OF LIGHT
E h f
c f
Energy of a photon
Speed of light Speed of electromagnetic radiation
212mv eV
212
21max min2
21max min2
h f m v W
h f m v W
m v h f W
21max2
min
s
s
eV mv
Wh fV
e e
21max2
min
min
0s
c c
eV mv
Wh f W f
h
Gain in KE of electron due to accelerating voltage
Photoelectric Effect
Stopping voltage
Cut-off (critical)
frequency
13
14
THE ATOM
sinn d
2 2
1 1 1
f i
Rn n
2 1E E h f
2
hL mv r
1
1213.6 eV
n
EE E
n
2 11
1 15.29 10 m
nr r n r
Bragg’s Law – crystal structure (constructive interference)
Hydrogen atom -
spectrum
Energy levels
Bohr Model of atom
Angular momentum quantized
n = 1, 2, 3, … Energy levels hydrogen atom
Allowed orbits for
electrons in hydrogen
atom
15
h
mv
hE h f c f p
h hp
p
4
hx p
de Broglie wavelength de Broglie relationship
Photon
Matter wave
Heisenberg Uncertainty Principle
16
The NUCLUES
products reactantsm M M
2E mc
9 4 12
4 2 6
1
0Be He C n
Beta minus decay
en p e
232 228 4
90 88 2
4
2
Th Ra He
He
Mass defect
Einstein – mass/energy
Chadwick discovers neutron
Beta decay Pauli & Fermi neutrino
Alpha decay
Beta plus decayp+ n + e+ + e
19Ne10 19F9 + e+ + e
e+ +
p[d(-1/3) u(+2/3) u(+2/3)] n[d(-1/3) u(+2/3) d(-1/3)]
17
Standard model
Proton
Neutron
Nuclear fission
protond (-1/2)u (+2/3)u (+2/3)
neutrond (-1/3)u (+2/3)d (-2/3)
235U92 + 1n0
236U92* 136Xe56 + 88Sr36 + 121n0