INVESTIGATING PHYSICS
DERIVATIONS OF FORMULAE
AND LINKS
ANDREW
KENNY
GILL & MACMILLAN
Contents
Derivations of Formulae
Links
1
11
Derivations of Formulae
Derivation of Formula T Fd
With reference to the illustration, consider the moments of each force acting on the
lever about an axis O:
F1 = F
x
O
d
F2 = F
M1 F1x
moment of F1 about the axis O
M1 Fx
F1 F ; moment as illustrated is clockwise
M2 F2(d x)
moment of F2 about the axis O
M2 F(d x)
F2 F ; moment as illustrated is clockwise
M1 M2 Fx F(d x)
adding the moments due to both forces
M1 M2 Fd
simplifying the right-hand side of the equation
T Fd
as the forces are equal in magnitude, opposite in
direction and whose lines of action do not coincide,
they constitute a couple; therefore the sum of their
moments equals the torque of the couple
D E R I VAT I O N S O F F O R M U L A E
1
Derivation of Formula P rgh
Based on the definition of pressure, pressure is force per unit area, we have:
A
2
F
A
mg
p
A
rVg
p
A
r(Ah)g
p
A
p rgh
p
h
I N V E S T I G AT I N G P H YS I C S
since the force is due to the weight of the fluid
subbing ‘rV ’ for ‘m’
subbing ‘Ah’ for ‘V ’
dividing above and below by ‘A ’
Derivation of Formula a v 2r
Based on the definition of sine and cosine we get the displacement vector of a point
on a circle:
j - axis
(r cos , r sin )
r
i - axis
B
B
r r cos u i r sin u j
B
with reference to the diagram
B
B
r r cos vt i r sin vt j
B
subbing ‘vt’ for ‘u’, where v angular
velocity, t time
drB
B
B
vr sin vt i vr cos vt j
dt
B
B
differentiating displacement to get velocity
drB
’
dt
v vr sin vt i vr cos vt j
subbing ‘Bv ’ for ‘
dvB
B
B
v2 r cos vt i v2r sin vt j
dt
differentiating velocity to get acceleration
aB v2(r cos vt i r sin vt j )
subbing ‘aB ’ for ‘
B
B
aB v2Br
B
dvB
’
dt
B
B
B
subbing ‘ r ’ for ‘r cos vt i r sin vt j ’
D E R I VAT I O N S O F F O R M U L A E
3
l
Ag
Derivation of Formula T 2p
Simple Pendulum
With reference to the illustration, taking the direction of displacement of the pendulum
bob from its rest position as positive, based on Newton’s second law we have:
F mg sin u
l
ma mg sin u
subbing ‘ma’ for ‘F ’
ma mg u
making the assumption that sin u u,
we can only make this assumption as U<5°
a gu
dividing both sides by ‘m’
x
l
a g
mg sin mg
g
a x
l
g
v2x x
l
g
v2 l
v
g
Al
g
2p
T
Al
T
2p
g
2l
l
Ag
T 2p
4
I N V E S T I G AT I N G P H YS I C S
x
where x is the arc length
l
Since g and l are constant we can say that the pendulum is undergoing simple harmonic motion if we assume the arc x is linear.
we can only make this assumption as U<5°
since u rearranging the equation so that it is in the standard form for
simple harmonic motion
subbing ‘v2x ’ for ‘a’
dividing both sides by ‘x’
square rooting both sides
subbing ‘
2p
’ for ‘v’
T
Derivation of Formula I.L. 10 log10
I
I0
The relative increase in sound intensity is the ratio of one intensity to another. It is
measured in bels, B. If the intensity of one sound is 10 times the intensity of another,
then the difference between their intensities is one bel.
The relative increase in intensity from I1 to I2 is 1 B if I2 10I1
It follows that the relative increase in intensity from I1 to I2 is 2 B if I2 10 (10I1)
102I1
Continuing this on, the relative increase in intensity from I1 to I2 is 3 B if I2 103I1
This can be generalised, the relative increase in intensity from I1 to I2 is n B if
I2 10nI1
Based on this equation we get:
10 n I2
I1
n log10
I2
I1
rewrite the equation, changing it from index notation to logarithm
notation
I2
I1
A decibel, dB, is one-tenth of a bel, as the prefix ‘deci’ means 101.
Number of bels log10
Therefore 1B 10 dB.
Number of decibels 10 log10
I2
I1
Sound intensity level
Sound intensity level (I.L.) is defined as the ratio of sound intensity (I) at a point to
the sound intensity at the threshold of hearing (I0).
I2
Subbing ‘I’ for ‘I2’ and ‘I0’ for ‘I1’ in the equation, Number of decibels 10 log10 we
I1
get:
I
I.L. 10 log10 , where I.L. is measured in decibels.
I0
Doubling sound intensity causes an increase of 3 dB in sound intensity level.
Consider the situation where I2 2 I1.
I2
Number of decibels 10 log10
I1
2I1
I1
10 log10 2
10 log10
subbing ‘2I1’ for ‘I2’
10(0.30103)
3.0
D E R I VAT I O N S O F F O R M U L A E
5
Derivation of the Wheatstone Bridge
Formula
R3
R1
ⴝ
where R1, R2, R3 and R 4 are the resistances of the four resistors, as illustrated
R2
R4
B
I1
R1
R2
I1
A
D
I2
R4
R3
I2
C
When the Wheatstone bridge is balanced, no current flows through the galvanometer.
This means that the current flowing through R 1 equals the current flowing through R 2;
call this current I1.
Similarly, the current flowing through R 3 equals the current flowing through R 4; call this
current I2.
As no current is flowing through the galvanometer, the points B and C must be at the
same potential.
This means that the potential difference across R1 equals the potential difference
across R3; call this voltage V.
V I1R1
Ohm’s law applied to R1
V I2R3
Ohm’s law applied to R3
I1R1 I2R3
call this equation (i)
Similarly, since the potential difference across R2 equals the potential difference across
R4 we get
6
I N V E S T I G AT I N G P H YS I C S
I1R2 I2R 4
call this equation (ii)
I1R1 I2R3
I1R2 I2R4
dividing equation (i) by equation (ii)
R1 R3
R2 R4
simplifying both fractions
Derivation of Formulae
I0
V0
& Vrms Irms 22
22
Joule’s law states that W I2Rt; this means that the heating effect of an electric
current is proportional to its current squared.The law holds true for both alternating
and direct currents.
When an a.c. supply is said to have a voltage V or cause a current I, what is being
described is the equivalent voltage or current from a d.c. supply that would have the
same heating effect.
The voltage is called the root mean squared voltage (Vrms ); it is equal to the peak
voltage (V0) divided by the square root of two.
Vrms V0
22
Similarly, the current is the root mean squared current (Irms ); it is equal to the peak
voltage (I0) divided by the square root of two.
Irms I0
22
The derivations of these formulae are not on the Leaving Cert. course and are merely
described here for illustrative purposes.
The derivation of each one is similar to the other, so I will just outline the derivation
I0
of Ir ms .
22
The current–time graph for an a.c. supply is sinusoidal, as illustrated in the diagram below.
sin 0
The current, I, at any instant is given by I I0 sin u.
I0
I
0
I = I0 sin The current changes as a function of time, so it should therefore be clear that u
should be defined in terms of time.
u 2pft
where f is the frequency of the a.c. supply.
D E R I VAT I O N S O F F O R M U L A E
7
The derivation of this equation is given below.
v
u
t
where v angular frequency, u angle (measured in radians),
t time
T
2p
v
where T periodic time
T
1
f
where f frequency
1 2p
f
v
combining the equations T 2p
1
and T v
f
v 2pf
rearranging the above equation
u
2pf
t
u
subbing ‘ ’ for ‘v’
t
u 2pft
rearranging the above equation
Therefore the current, I, can be expressed as a function of time, where I0 the peak
current and f the frequency of the supply.
I I0 sin 2pft
I0
I
I = I0 sin 2 ft
0
t
The heating effect of this alternating current (I) is equal to the heating effect of a
direct current of value Irms . Joule’s law states W I2Rt, therefore
Ir ms2 Rt I 2Rt
heat produced by the d.c. equals heat produced by the a.c.
Ir ms2 t I 2 t
Ir ms2 t
dividing both sides by R
(I0 sin 2pft) t
2
subbing ‘I0 sin 2pft ’ for ‘I’
In order to equate these we can graph current squared against time for the a.c. and
the d.c. equivalent.
I2
I2
I02
I 2 = (I0 sin 2 ft) 2
Irms 2
0
t
Graph of square of d.c. against time
8
I N V E S T I G AT I N G P H YS I C S
0
t
Graph of square of a.c. against time.
The area under the curve in both graphs is equal to Irms2 t and (I0 sin 2pft)2 t respectively.
As these are equal, we get:
L
Ir ms2dt T
3
L
(I0 sin 2pft)2dt
the area under a curve is equal to its integral
(I0 sin 2pft)2 dt
equating one cycle by setting the limits as 0 to
T, where T is the periodic time
T
Ir ms2 dt
0
3
0
I2
I2
I 2 = (I0 sin 2␲ ft ) 2
I0
2
Irms
2
0
t
T
Graph of square of d.c. against time,
with one period highlighted
T
Ir ms2
3
dt I 02
3
(sin 2pft)2dt
0
T
3
Graph of square of a.c. against time,
with one period highlighted
T
0
Ir ms2
t
0
T
taking the constants outside the
integrals
T
dt I 02
0
1
(1 cos 2(2pft)) dt
32
0
T
using the trigonometric identity
sin2A T
I0 2
(1 cos (4pft)) dt
Ir ms2 dt 2 3
3
0
0
Ir ms2[t]T0 I 02
1
a [t]T0 [sin 4pft]T0 b
2
4pf
1
(1 cos 2A)
2
taking the constants outside the
integrals and simplifying the cosine
function
carrying out the integration
Ir ms2(T 0)
I 02
1
a(T 0) (sin 4pf T sin 0)b
2
4pf
Ir ms2(T ) I 02
1
aT (0 0)b
2
4pf
Ir ms2(T ) I0 2
(T )
2
Ir ms2 Irms I 02
2
I0
22
subbing in the limits
1
Q fT 1,
f
therefore sin 4pf T sin 4p 0.
Also sin 0 0
T
dividing both sides by T
square rooting both sides
By a similar argument it may be shown that the root mean squared value of alternating
V0
voltage is given by Vrms 22
D E R I VAT I O N S O F F O R M U L A E
9
ln 2
Derivation of Formula T1>2 l
Based on the law of radioactive decay we have:
dN
lN
dt
where N number of undecayed nuclei, l decay
constant, t time
1
dN ldt
N
rearranging the above equation
1
dN ldt
L
LN
integrating both sides
ln N lt C
where C constant of integration
ln N0 0 C
where N0 the number of nuclei present when t 0
Q C ln N0
ln N lt ln N0
subbing ‘ln N0’ for ‘C ’
ln N ln N0 lt
rearranging the above equation
ln
N
lt
N0
>2
N0
ln
ln
N0
lT1>2
1
lT1>2
2
ln 2 lT1>2
T1>2 10
I N V E S T I G AT I N G P H YS I C S
ln 2
l
x
using the laws of logs, log a a b log a x log a y
y
by definition of half-life, N 12N0 when t T1>2
Links
Links to Websites Related to Topics
in Investigating Physics
Chapter 2 – Linear Motion
1. Addition of vectors: p. 16
http://surendranath.tripod.com/Applets/Math/VectorAddition/
VectorAdditionApplet.html
2. Finding the resultant of two vectors: p. 17
http://www.walter-fendt.de/ph14e/equilibrium.htm
3. Difference between distance and displacement: p. 18
http://faraday.physics.utoronto.ca/GeneralInterest/Harrison/Flash/ClassMechanics/
DisplaceDistance/DisplaceDistance.html
4. Distance–time and velocity–time graphs: p. 26
http://www.walter-fendt.de/ph14e/acceleration.htm
Chapter 3 – Force and Momentum
5. Principle of Conservation of Momentum: p. 40
http://www.walter-fendt.de/ph14e/collision.htm
6. Demonstrating that F ⫽ ma : p. 43
http://www.walter-fendt.de/ph14e/n2law.htm
7. Illustration of the scale of the Earth to the Sun: p. 46
http://www.rense.com/general72/size.htm
8. Acceleration due to gravity: p. 48
http://www.seed.slb.com/uploadedFiles/Science/Laboratory/Air_and_Space/
Galileo_Drops_the_Ball/anim/en/index.html?width=740&height=570&popup=true
9. Terminal velocity: p. 51
http://www.waowen.screaming.net/revision/force&motion/skydiver.htm
Chapter 4 – Moments, Density and Pressure
10. Principle of the Lever: p. 67
http://www.walter-fendt.de/ph14e/lever.htm
11. Boyle’s law: p. 77
http://phet.colorado.edu/simulations/sims.php?sim=Gas_Properties
Chapter 5 – Work, Energy and Power
12. Newton’s cradle: p. 91
http://www.physics.org/article-interact.asp?id=32
LINKS
11
Chapter 6 – Circular Motion
13. Applet 6.2: illustrating centripetal acceleration: p. 100
http://phet.colorado.edu/simulations/sims.php?sim=Motion_in_2D
Chapter 7 – Simple Harmonic Motion and Hooke’s Law
14. Simple Harmonic Motion: p. 114
http://www.ngsir.netfirms.com/englishhtm/SpringSHM.htm
15. Simple pendulum: p. 116
http://phet.colorado.edu/sims/pendulum-lab/pendulum-lab_en.html
Chapter 8 – Temperature
16. Difference between heat and temperature: p. 122
http://www.yenka.com/freecontent/attachment.action?quick=ad&att=738
Chapter 9 – Heat
17. Explanation of conduction: p. 146
http://www.absorblearning.com/media/attachment.action?quick=s5&att=2016
18. Demonstration of convection currents: p. 148
http://www.absorblearning.com/media/attachment.action?quick=an&att=758
Chapter 10 – Waves
19. Transverse waves: p. 156
http://www.acoustics.salford.ac.uk/feschools/waves/wavetypes.htm
20. Longitudinal waves: p. 156
http://www.ngsir.netfirms.com/englishhtm/Lwave.htm
21. Electromagnetic waves: p. 157
http://micro.magnet.fsu.edu/primer/java/scienceopticsu/electromagnetic/
index.html
22. Reflection, refraction and diffraction: p. 160
http://www.lon-capa.org/~mmp/kap13/cd372.htm
23. Explanation of phase: p. 161
http://www.acoustics.salford.ac.uk/feschools/waves/super.htm
24. Polarisation: p. 163
http://www.ngsir.netfirms.com/englishhtm/Polarization.htm
25. Doppler Effect: p. 163
http://www.astro.ubc.ca/~scharein/a311/Sim/doppler/Doppler.html
Chapter 11 – Vibrations and Sound
26. Demonstrating the wave nature of sound: p. 171
http://phet.colorado.edu/simulations/sims.php?sim=Sound
27. Resonance: p. 173
http://www.absorblearning.com/media/attachment.action?quick=yy&att=2505
12
I N V E S T I G AT I N G P H YS I C S
28. Production of stationary waves: p. 175
http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/reflect.html
29. Harmonics in strings: p. 176
http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/
StandingWaves1.html
30. Stationary waves in pipes: p. 177
http://www.phys.unsw.edu.au/jw/flutes.v.clarinets.html
31. Notes from different instruments: p. 180
http://www.absorblearning.com/media/attachment.action?quick=14h&att=2903
32. Addition of waves: p. 180
http://www.eserc.stonybrook.edu/ProjectJava/WaveInt/index.html
33. Vernier callipers: p. 180
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=52
Chapter 12 – Reflection of Light
34. Applet 12.1 illustrating reflection in a plane mirror: p. 197
http://www.freezeray.com/flashFiles/planeMirror.htm
35. Ray diagrams for mirrors: p. 199
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=48.0
Chapter 13 – Refraction of Light
36. Snell’s law: p. 210
http://www.upscale.utoronto.ca/PVB/Harrison/Flash/Optics/Refraction/
Refraction.html
37. Total internal reflection and critical angle: p. 217 (attached to Demonstration 13.1)
http://www.freezeray.com/flashFiles/Refraction1.htm
38. Ray-tracing: p. 221
http://www.teachnet.ie/torourke/flashprojects/raydiagrams.html
39. The functioning eye: p. 229
http://www.freezeray.com/flashFiles/eyeDefects.htm
Chapter 14 – Wave Nature of Light
40. Young’s Double Slit Experiment: p. 236
http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/index.html
41. Illustration of path difference: p. 238
http://galileo.phys.virginia.edu/classes/109N/more_stuff/flashlets/youngexpt4.htm
42. Measurement of wavelength of light: p. 240
http://schools.matter.org.uk/Content/Interference/gratings.html
43. Factors affecting distance between fringes: p. 242
http://www.surendranath.org/Applets/Optics/Slits/DoubleSlit/DblSltApplet.html
LINKS
13
44. Addition of colours of light: p. 247
http://www.colorado.edu/physics/2000/tv/colortv.html
45. Colours in soap bubbles: p. 252
http://www.microscopy.fsu.edu/primer/java/interference/soapbubbles/index.html
Chapter 15 – Static Electricity
46. Illustrating electric field: p. 271
http://phet.colorado.edu/simulations/sims.php?sim=Charges_and_Fields
47. Illustrating electric field lines: p. 271
http://lectureonline.cl.msu.edu/~mmp/kap18/RR447app. htm
Chapter 16 – Voltage and Capacitance
48. Factors affecting the capacitance of a parallel plate capacitor: p. 284
http://micro.magnet.fsu.edu/electromag/java/capacitance/index.html
49. Charging a capacitor: p. 286
http://micro.magnet.fsu.edu/electromag/java/capacitor/index.html
Chapter 17 – Current Electricity
50. Heating effect of an electric current: p. 294
http://micro.magnet.fsu.edu/electromag/java/filamentresistance/index.html
Chapter 18 – Resistance
51. Colour Coded Resistance Calculator: p. 305
http://www.ese.upenn.edu/rca/calcjs.html
52. Rheostat as a variable resistor: p. 305
http://www.absorblearning.com/media/attachment.action?quick=118&att=2669
53. Ohm’s law: p. 306
http://micro.magnet.fsu.edu/electromag/java/ohmslaw/index.html
54. Building a circuit with resistors in series and parallel: p. 308
http://www.walter-fendt.de/ph14e/combres.htm
55. Potentiometer: p. 312
http://www.walter-fendt.de/ph14e/potentiometer_e.htm
56. Resistivity: p. 313
http://phet.colorado.edu/sims/resistance-in-a-wire/resistance-in-a-wire_en.html
57. Micrometer: p. 314
http://www.upscale.utoronto.ca/PVB/Harrison/Micrometer/Flash/
MicSimulation.html
58. Metre bridge: p. 325
http://www.walter-fendt.de/ph14e/wheatstone_e.htm
14
I N V E S T I G AT I N G P H YS I C S
Chapter 19 – Semiconductors
59. Semiconductor diode: p. 335
http://www-g.eng.cam.ac.uk/mmg/teaching/linearcircuits/diode.html
Chapter 20 – Electromagnetism
60. Magnetic fields around a bar magnet: p. 347
http://www.walter-fendt.de/ph14e/mfbar.htm
61. Magnetic fields due to a straight wire, loop and solenoid: p. 349
http://schools.matter.org.uk/Content/MagneticFields/fields_3.html
62. Force on a current-carrying conductor in a magnetic field: p. 352
http://www.walter-fendt.de/ph14e/lorentzforce.htm
63. d.c. motor: p. 354
http://www.walter-fendt.de/ph14e/electricmotor.htm
64. Force between currents: p. 356
http://web.mit.edu/8.02t/www/802TEAL3D/visualizations/magnetostatics/
ParallelWires/Parallel_Wires_640.mpg
65. Faraday’s Electromagnetic Lab: p. 357
http://phet.colorado.edu/simulations/sims.php?sim=Faradays_Electromagnetic_Lab
66. Faraday’s law: p. 358
http://phet.colorado.edu/sims/faraday-mx/faraday-mx.swf
67. Lenz’s law: p. 359
http://micro.magnet.fsu.edu/electromag/java/lenzlaw/index.html
68. a.c. generators: p. 363
http://www.walter-fendt.de/ph14e/generator_e.htm
69. Building a circuit: p. 364
http://phet.colorado.edu/simulations/sims.php?sim=Circuit_Construction_Kit_
ACDC
70. Transformers: p. 367
http://micro.magnet.fsu.edu/electromag/java/transformer/index.html
71. Inductance: p. 369
http://www.magnet.fsu.edu/education/tutorials/java/inductivereactance/index.html
Chapter 21 – The Electron
72. Crookes’Tube: p. 381
http://micro.magnet.fsu.edu/electromag/java/crookestube/index.html
73. Deflection of a charged particle in a magnetic field: p. 382
http://www.surendranath.org/Applets/Electricity/MovChgMag/
MovChgMagApplet.html
74. Photoelectric effect: p. 389
http://phet.colorado.edu/simulations/photoelectric/photoelectric.jnlp
LINKS
15
Chapter 22 – The Nucleus
75. Rutherford’s Gold Foil Experiment: p. 394
http://www.absorblearning.com/media/item.action?quick=bf
76. Emission line spectra: p. 395
http://jersey.uoregon.edu/vlab/elements/Elements.html
77. Bohr model and the production of emission line spectra: p. 396
http://www.upscale.utoronto.ca/PVB/Harrison/BohrModel/Flash/BohrModel.html
78. Ionisation by an alpha particle: p. 400
http://www.absorblearning.com/media/item.action?quick=187
79. G-M tube: p. 403
http://chemistry.binghamton.edu/ilc/labs/radiochem/moviepop/
geiger-counter-sim.htm
80. Solid state detector: p. 404
http://micro.magnet.fsu.edu/primer/java/digitalimaging/avalanche/index.html
81. Half-life graph: p. 406
http://lectureonline.cl.msu.edu/~mmp/applist/decay/decay.htm
82. Decay chains: p. 407
http://www.walter-fendt.de/ph14e/decayseries.htm
83. Fission reactions: p. 410
http://phet.colorado.edu/simulations/sims.php?sim=Nuclear_Fission
Chapter 23 – Particle Physics (Option 1)
84. (Cockroft and Walton Experiment: p. 428 attached to heading ‘Cockroft and
Walton Experiment’)
http://www-outreach.phy.cam.ac.uk/camphy/cockcroftwalton/
cockcroftwalton11_1.htm
85. (Quark Model: p. 441 Attached to Table 23.4)
http://www.lon-capa.org/~mmp/applist/q/q.htm
86. (The Particle Adventure: p. 443 attached to STS Box ‘We’re all just empty space’)
http://www.particleadventure.org/modern_atom.html
87. (Building atoms: p. 443 attached to Table 23.5)
http://www.pbs.org/wgbh/aso/tryit/atom/builder.html
88. (Building hadrons: p. 443 attached to Table 23.5)
http://www.lon-capa.org/~mmp/applist/q/q.htm
Chapter 24 – Applied Electricity (Option 2)
89. Force on a current-carrying conductor in a magnetic field: p. 448
http://www.walter-fendt.de/ph14e/lorentzforce.htm
90. d.c. motor: p. 449
http://www.walter-fendt.de/ph14e/electricmotor.htm
16
I N V E S T I G AT I N G P H YS I C S
91. a.c. generators: p. 454
http://www.walter-fendt.de/ph14e/generator_e.htm
92. Transformers: p. 455
http://micro.magnet.fsu.edu/electromag/java/transformer/index.html
Links to Websites with Applets
(Interactive Animations) Relevant
to the Leaving Cert. Syllabus
You should note that many of these sites provide far more information than is required
at Leaving Cert. level.They can be a useful support to textbook and classroom learning,
but should not be viewed as a means to learning the definitive answers for the Leaving
Cert. examination. These sites do provide an opportunity to gain a deeper understanding of various topics and can aid a teacher’s classroom teaching.
http://www.walter-fendt.de/ph14e/
http://phet.colorado.edu/simulations/index.php?cat=Physics
http://www.ngsir.netfirms.com/englishVersion.htm
http://www.surendranath.org/Applets.html
http://www.absorblearning.com/physics/contents.html
http://micro.magnet.fsu.edu/electromag/java/index.html
http://www.freezeray.com/physics.htm
The list of sites below relates to interesting areas of physics. The material on the sites
does not relate to the syllabus, but may be of interest to physics students.
http://www.pbs.org/wgbh/nova/elegant/
http://www.pbs.org/wgbh/nova/time/
http://www.particleadventure.org/
http://superstringtheory.com/index.html
http://www.bbc.co.uk/iplayer/categories/factual/science_and_nature/
LINKS
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