PHYSICS 1-3
The texts for this course are:
1. H. D. Young & R. A. Freedman, UNIVERSITY
PHYSICS 10TH ed. 1999.
2. H. D. Young & R. A. Freedman, MODERN PHYSICS
11TH ed. 2003.
3. French, A.P. VIBRATIONS AND WAVES 1971.
4. Bekefi & Barrett, ELECTROMAGNETIC
VIBRATIONS, WAVES AND RADIATION 1977.
5. Asimov, I. Atom: JOURNEY ACROSS THE
SUBATOMIC COSMOS 1991.
6. JUST SIX NUMBERS, Martin Rees, 2000.
7. ? THE ASCENT OF SCIENCE OUP 2000.
1
Opening remarks: Welcome
Introductory class business:
Dr. BILL MILLS IS
•
•
•
•
The husband of one.
The father of 16 (including in-laws).
The grandfather of 8 so far.
A Christian Priest, Ecumenist, Theologian &
Apologist. A Physicist, and an International
Attorney.
• Committed to responsible epistemology.
• A positivist*
2
I am not
Inerrant, infallible, nor immune from
mere Scribner error.
3
IN OPPOSITION OR
IN HARMONY?
“Religion and science are
opposed…but only in the same sense
as that in which my thumb and
forefinger are opposed- and between
the two, one can grasp everything.”
Sir William Bragg
4
“Who can learn anything new and
not find it a shock?” John Wheeler
It is helpful to regularly review even
our most fundamental
understandings in light of our most
recent discoveries.
Religion and Science:
Two Sides Of One Coin
Warm summer evenings in Greece in the 4th century B.C.
Democritus¹: 460-370 B.C. “Atomic system” wandering
lights in the night sky, (GK. “planetes”, “wanderers”).
Stationary grains of sand on the sea shore, (“atomos”,
“atoms” meaning “indivisible” or “unbreakable).
Aristotle: 384-322 B.C. The father of science. Knowing
the physical world inexorable leads to knowing the
existence of God & His qualities. (“physika”, “physics”, Gk.
“of nature”, “to bring forth”). Four elements, each with
their unique place & duty in the universe² Everything held
in it’s place, whether fixed or in motion, by eternal
natural laws, ordained by God.
6
DARK MATTER & ENERGY OR
SPIRITUAL MATTER & ENERGY?
• Whatever one calls it, we now know that @ 96% of
the “Stuff”, mass¹ in the universe is not visible to us.
We only see the gravitational effects of 23%.
• Whatever one calls it, we now know that 73% is
energy¹ in the universe that is not visible to us. We
know that it is there because at scales larger than
galaxies it overcomes Gravity².
• It really is meaningless to try to distinguish between
physical & spiritual matter & energy. It is a
distinction without a difference. This makes them
the same⁴. It does not make either of them unreal.
7
Religion and Science:
Two Sides Of One Coin
A warm summer evening in Woolsthorpe,
Lincolnshire, England, 1665. Isaac Newton Jr. (1642 1727, noticed an apple fall from a tree. At arms length
the apple appeared about as big as the moon appeared
that evening¹. Newton wondered why the moon was not
also falling². His discoveries changed the world in many
ways! His discovery of the Gravitational Force ended the
age of materialism³ & randomness. There was more than
“atoms and the void.” God did not need myriad angels to
push the moon & planets around⁴. Similar natural laws
might govern everything, including mankind⁵.
Religion and Science:
Two Sides Of One Coin
1. Peter Abelard: 1079-1142 Si et non. The nature of
Canon, (Authority¹) & it’s limits.
2. William of Occam²: 1285-1349 Occam's two edged
Razor, (scalpel) : Canon + reason.
3. Galileo: 1564-1642 & Isaac Newton : (1642 -1727)
Canon + reason + Observation & experimentation.
4. Robert Boyle, 1627-1691: Experimental
epistemology.
5. John Locke: 1632-1704: Philosophical epistemology.
6. Immanuel Kant: 1724-1804: Pure reason.
9
Religion and Science:
Two Sides Of One Coin
1. 57 centuries vs. 3 centuries.
2. Special & Natural revelation*.
3. An apparent conflict between them about
“what and how” is resolved by Newton,
(1642-1727) before it became popular:
• The Principia: The Mathematical Principles of
Natural Philosophy, 1687: Discovering God’s
Laws neither limits Him, nor eliminates Him,
It gives us deep, profound insight into Him.
10
Religion and Science:
Two Sides Of One Coin
The division between physical objects & laws
and spiritual objects & laws is a myth,
unrecognized by God, & great scientists
throughout history! Notice how often symbols
of spiritual laws, i.e. “π”,(the compass) “²“, ”³”,
“r²”, etc. appear alone, and in combination,
within so many, so called “physical” laws,
“discovered” millennia after the “spiritual”
symbols and laws had been revealed!
11
Epistemology
What is Knowable?
• There are eternal, universal, unchanging,
objective Truths¹, (Facts)! Everywhere! Always!
• Three very different types of Truth (Facts):
1. Definitional: Bachelors are single because that is
how we define the word. Everywhere! Always!
2. Logical/Mathematical: 2 + 2 = 4! Everywhere!
Always!
3. Empirical/Existential: Water is H² O¹ & it’s triple
point is 0° C at one atmosphere of pressure!
Everywhere! Always!
12
Things aren't always
what they seem:
1. What goes up must come down?
2. The Bigger they are, the harder & faster they
fall?
3. Does the sun rise in the East & set in the
West?
4. Is the chair you are sitting on solid & still?
5. Are you sitting on it at all?
6. Are your feet on the floor?
7. Is grass green?
But there are eternal, universal, unchanging,
objective Truths, (Facts)! Everywhere! Always!
13
Objective vs. subjective truth:
Thinking, speaking & writing on this subject is often
muddled and/or unreasonable. Truth is not subjective if it
meets the criteria of slide # 11. Subjective truth arguments
are often the victim of circular reasoning. If Relativists claim
that all truth is subjective and therefore personal & relative,
than this set, “all truth” includes their own claims of universal
“subjective relativity” and the rest of humanity has no reason
to give any heed to it. Their arguments concerning their
universe being without objective truth says nothing at all
about my universe! If they have an argument about my
universe, (or our universe) that argument would need to be
objectively true. If they can objectively know this,
(Inductively reasoning from their subjectivity, first to mine,
then to universal subjectivity) at least one truth is objectively
14
knowable and other truth may also be knowable.
Objective vs. subjective truth:
This would defeat their argument of universal subjectivity! This
assertion is also demonstrably false! (see slide # 11) What I
know & how sure I am that I know it is the object as well as the
subject of epistemology. It is silly nonsense to dismiss as
“subjective truth,” truth claims that one has not yet subjected to
rigorous tests of epistemological responsibility: “Your belief that
a man walked on the moon is only your subjective truth because
I don’t know that it’s true? The Nazi holocaust was immoral is
only your subjective truth because not everyone agrees?” The
whole purpose of epistemology is to rigorously test and
determine if one can know things and how certain one can be.
To dismiss something as “subjective truth” is to beg the
question and to deprive oneself of both the process & the
product of knowing! This is surely one of the defining qualities
15
and one of the noblest attributes of humanity!
Epistemology
How can I know Truth?
“Some ideas are so bad, they are not even wrong.”
Enrico Fermi. “It is better to be wrong, than to be
vague.” Freeman Dyson.
1. Sense & Non Sense¹: “Canoes, pancake covered dog
houses, and ice cream that doesn’t have legs.”
2. Dogmatism & sorcery: Repeating things
authoritatively doesn’t make them true.
3. Magical/wishful thinking¹: Much of atheism and
materialism is magical and\or wishful thinking.
4. If you call a dog’s tail his leg²… your thoughts and
your words are muddled and wrong.
• Falsifiability: The truth claims of Christianity ³are
completely factual, testable, provable (Falsifiable).
16
Epistemology
How can I know Truth?
1. Can I appeal to authority? Relying on a source
that we trust is the oldest and still by far the
most common way of knowing or making sure.
2. Can I reason through it? Does 2+2=4?
3. Can I observe it?
4. Can I experiment and test it? (Can I make
certain it is true?)
5. Can I “feel it” or “know it in my heart”?
6. Can God tell me it is true? (Can He make me
certain It is true?)
17
Epistemology
How can I know Truth?
Can God tell me it is true?
Can I “feel it” or “know it
in my heart”?
Can I experiment and test
it? (Can I make certain it
is true?)
Can I observe it?
Can I reason through it?
Does 2+2=4?
Can I appeal to
authority¹?
18
Epistemology
How certain can I be?
Degrees of Certainty: Faith, Emotion, & Evidence.
1. Probable cause¹:
2. Preponderance of the evidence²:
3. Clear & Convincing:
4. Beyond a Reasonable doubt:
5. Beyond any doubt:
6. No genuine question of fact exists (Judicial notice):
Faith is not believing something or trusting some authority
against common sense or without evidence or some degree
of certainty. Faith is sticking to your evidence based
convictions, even when you are emotionally tempted to19
Epistemology
How certain can I be?
“Any measurement that you make (decision
that you come to) without knowledge of its
uncertainty is completely meaningless.” “A
measurement that doesn’t also indicate its
degree of accuracy is meaningless.”
“Knowing degrees of accuracy is critical to
so many things in our lives.” Dr. Walter
Lewin: FOR THE LOVE OF PHYSICS, 2011
pgs. x. ,8. (Parenthetical comment added.)
20
Epistemology
How certain can I be?
No genuine question of fact
exists
Beyond any doubt
Beyond a Reasonable doubt
Clear & Convincing
Preponderance of the
evidence
Probable cause
21
SET THEORY
•
•
•
•
Probabilities limited by the size of the set:
Is the denominator of the probability of x > N?
How long does each sample take?
Replacement vs. Non-replacement in
probability theory: Are the odds changing
with each sample, (drawing from a hat) or are
the odds staying the same, (flipping a coin)?
22
EPISTEMOLOGICAL
SET THEORY
WHAT IS
KNOWABLE
WHAT
HUMANITY
KNOWS
WHAT I
KNOW
23
EPISTEMOLOGICAL
SET THEORY
WHAT IS KNOWABLE
WHAT
HUMANITY
KNOWS
WHAT I
KNOW
24
EPISTEMOLOGICAL
SET THEORY
WHAT I DON’T
KNOW
WHAT
HUMANITY
DOES NOT
KNOW
WHAT IS
UNKOWABLE
(TERMINAL
COUNSELS)
25
EPISTEMOLOGICAL
SET THEORY
WHAT IS TRUE
WHAT IS MOSTLY
OR NEARLY TRUE
WHAT I
THINK
IS TRUE
WHAT IS MOSTLY
OF NEARLY FALSE
WHAT IS FALSE
26
THE EPISTEMOLOGICAL
PYRAMID
AUTHORITY
EXTERNAL
CONSISTENCY
INTERNAL CONSISTENCY
REASONABLENESS
SENSE VS. NON-SENSE
27
EPISTEMOLOGICAL SETS AS A PARLOR
GAME¹: Where did Bill get his education?
His
memories
are
accurate
His
memories
were
changed
slightly*
AUTHORITY
AUTHORITY
EXTERNAL
CONSISTENCY
INTERNAL
CONSISTENCY
REASONABLENE
SS
SENSE VS.
NON-SENSE
EXTERNAL
CONSISTENCY
INTERNAL
CONSISTENCY
He is from
another
planet
AUTHORITY
AUTHORITY
EXTERNAL
CONSISTENCY
INTERNAL
CONSISTENCY
EXTERNAL
CONSISTENCY
REASONABLENESS
INTERNAL
CONSISTENCY
REASONABLENESS
SENSE VS. NONSENSE
He was
tutored by
angles
REASONABLENESS
SENSE VS. NONSENSE
SENSE VS. NONSENSE
28
ANOTHER EPISTEMOLOGICAL
PYRAMID
WHAT I KNOW IS TRUE
WHAT I KNOW IS FALSE
WHAT I THINK IS TRUE
WHTAT I THINK IS FALSE
WHAT I THINK IS
KNOWABLE
WHAT I THINK IS
UNKNOWABLE
29
Can I reason through it?
TRUTH
• Deductive Reasoning: Large to small: •
• Example: All Mammals are warm
blooded. Humans are warm blooded,
•
therefore humans are mammals.
• Inductive Reasoning: Small to large:
• Example: . Humans are warm blooded.
All Mammals are warm blooded,
•
therefore humans are mammals.
• Sequential Reasoning:
• Example: Smoke is seen after fire. I see
smoke, therefore there has been fire.
• If the premise is false, the sentence is
non-sense, even if the conclusion
happens to be true².
ERROR
Example: Many men are
selfish. Bill is a man,
therefore Bill is selfish.
Example: I knew a kind
Christian. Bill is a
Christian, therefore Bill is
kind.
Post Hoc Reasoning¹:
Example: I saw a black cat.
Something bad happened,
therefore seeing a black
cat is bad luck. I went
outside when it was cold. I
got sick, therefore being
outside in the cold causes
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sickness.
STATISTICAL SIGNIFICENCE
• Small sample error: One type of error in
inductive reasoning: “Crocodile Dundee” TV
scene in NY motel: “Yep, that’s what I saw.”
• Galileo's experiments:
• The speed of light: How closely are we
looking?
• The spontaneous generation of flies: How
closely controlled is our experiment?
• Climate Change: How long will it take to
know?
31
Relying on authority
Almost everything we believe to be true, we
learned from some “Authority”. Generally we believe
because of authority. Most personal experience,
(observation, reasoning & experimentation) confirms
or disputes what we previously believed or doubted
because of authority. The Real question isn’t “Have we
faith in authority?” It is What or Which authority have
we faith in, how much faith do we have in it, and how
much additional research, reasoning and/or
experimentation will we do to test or verify what
“Authority” has said?
32
TOLSTOY & BACON
“I know that most men, including those at ease with
problems of the greatest complexity, can seldom accept
even the simplest and most obvious truth, if it be such
as would oblige them to admit the falsity of conclusions
which they have delighted in explaining to colleagues,
which they have proudly taught to others, and which
have been woven, thread by thread into the fabric of
our lives.” Tolstoy
“The human understanding when it has once adopted
an opinion…draws all things else to support and agree
with it. And though there be a greater number and
weight of instances to be found on the other side, yet
these it either neglects or despises.” Bacon
33
Types & Tokens
Type: A person or thing symbolizing or exemplifying the
ideal or defining characteristics of something.
Type: The ideal or defining characteristics of something.
Token: One specific example.
Token: One specific, distinct, physical, person or thing.
A chair is one type of furniture. A table is another type of
furniture. A stool is a type of chair. A recliner is another
type of chair; perhaps the perfect, ideal, or complete
“type” of chair.
The chair you are sitting in is a token chair. The chair next
to you may be a token of the exact same type.
34
INTRODUCTION
Measurement Standards & degrees of uncertainty:
VECTORS & SCALARS:
A scalar has only magnitude and no direction.
A vector is a physical quantity that requires the
specification of both direction and magnitude.
35
Ordinal Set Theory
Mohamed Ali and superlatives:
Someone is always “The Greatest”.
In any defined group or set, for every measureable quality,
one member of that group is “most” or “best”.
If qualities can be summed, someone is the overall “greatest.”
Of all beings currently conscious, one of them is the greatest,
(using the Laws, Constants, Forces, & Elements most effectively
to bless & serve others).
That being is God.
For Christians that living being is Jesus Christ!
Agnostics & Atheists have simply not been persuasively or
36
effectively introduced to Him, Yet!
Epistemology
How certain can I be?
“Any measurement that you make (decision
that you come to) without knowledge of its
uncertainty is completely meaningless.” “A
measurement that doesn’t also indicate its
degree of accuracy is meaningless.”
“Knowing degrees of accuracy is critical to
so many things in our lives.” Dr. Walter
Lewin: FOR THE LOVE OF PHYSICS, 2011
pgs. x. ,8. (Parenthetical comment added.)
37
ATOMIC THEORY
If one enlarged the baseball until it was about the
size of the earth, an average Carbon-12 atom in that
baseball would be about the size of a baseball. If
one enlarged the now baseball sized atom again,
until it was about 2 miles, (3.5km.) in diameter, the
nucleus would be the size of a golf ball in the center
and the electrons would be grains of sand, two miles
away with nothing, that we know of, except the
forces, in between.
ATOMS
• Ordinary matter is made of atoms which are
composed of electrons, protons, & neutrons.
• The nucleus contains between 99.945-99.975 of
the total mass of an atom.
• Atoms have an atomic number, Z = element =
protons in their nuclei.
• N = neutrons in their nuclei.
• Σ = The sum of N +Z = A = the mass number. There
are several mass numbers of each element. These
are called isotopes.
ATOMS
• Electrons almost balance out the protons to make
atoms electrically neutral in charge. (Electrons
appear to be without internal structure & are part
of the Lepton family within the particle zoo.)
• Most matter is slightly positively charged most of
the time. That is why we can sit on a chair, can’t
walk through walls & don’t fall through the floor &
the earth.
• Protons & neutrons each contain three quarks, (⁺⅔
+ ⁺⅔ + ⁻⅓ = 1).
• There are six kinds of quarks, two of which (up &
down) make protons & neutrons.
Uni-verse or Cosmos?
•
•
•
•
•
•
Are There Universal Laws, (Equations)?
Are There Universal Constants?
Are There Universal Elements?
Are There Universal Forces
We do not live in an (exclusively) material world!
We live in a Universe, with Eternal Laws,
Constants, Elements, (materials) and Forces.
• They are the Typical God: Eternal, unchanging,
omniscient, omnipotent, & omnipresent!
41
There Are many Universal
Laws, (Equations)!
The Five Equations that changed the world are a few
examples:
1. Gravity F = G x M₁ X M₂/d². Newton.
2. The 2nd Law of Thermodynamics: (Entropy)
ΔS ˃ 0. Clausius or ΔS = ΔQ/t.
3. Hydrodynamics: Constant = P/ρ + gz + v²/2. Bernoulli*.
4. Electromagnetic induction¹: (EM)
ΔX E = -∂B/∂T. Faraday-Maxwell. F = K x q₁ x q₂/d².
Coulomb.
5. Matter is energy: 𝑬 = 𝑴𝑪². Einstein
42
There Are Universal
Constants!
• There are hundreds of precise Fundamental
Constants in our universe. They must be EXACT:
• Never more. Never less.
• No where more. No where less.
• Never different. No where different.
• “Who can learn anything new and not find it a
shock?” John Wheeler
• It is helpful to regularly review even our most
fundamental understandings in light of our most
recent discoveries.
43
There Are Universal
Constants!
Just Six Numbers that control our universe! (Sir Martin Rees)
1. N = EM/G = @ 1x10³⁵: The strength of the electrical magnetic force that holds atoms in their places within molecules,
divided by the gravitational force pulling them together, =
1,000,000,000,000,000,000,000,000,000,000,000,000!
2. ε = 0.007*: Determines how firmly atomic nuclei bind
together, how atoms are made, which atoms & how many of
each atom are made, & it controls the sun’s power.
3. Ω = Σm\G = @ .3: The total amount of material in the universe, both what we can see, (stars, planets etc.) and the “spiritual” matter, (“Dark matter”) that we cannot see divided by the
gravitational force . This balances the gravity, (G) and expansion
44
energy of the universe, (Λ) .
There Are Universal
Constants!
Just Six Numbers that control our universe!
(Sir Martin Rees)
4. Λ = @ 0.7: The expansion energy of the universe
expressed in relationship to # 3¹. This results in a
slow steady expansion of 70.4 +/- 1.4 kilometers
per second per megaparsec.
5. Q = Σrme* /G: The gravitational force divided by
the expansion energy of the universe, Λ : @
1x10¯5 = 1/100,000.
6. D = 3. The number of dimensions in space-time.
45
There Are Universal
Constants!
Seven correlate to the Forces that control our universe.
7. Gravitational: G = 6.6725985 x 10¯¹¹m³kg¯¹s¯².
8. EM: Elementary Charge: ε = 1.6021773349 x 10¯¹⁹C.
1 eV = 1.6021892 x 10¯¹⁹ J & 1.7826759 x 10¯³⁶ kg.
9. Week: Ratio: mp/ mₑ = 1836.15152; E=MC²
10. Strong: Atomic mass unit: amu = 1.6605655 x
10¯²⁷kg. E=MC²
Λ: = The expansion energy of the universe. This results
in a slow steady expansion of 70.4 +/- 1.4 kilometers per
second per megaparsec.
11.Fc = Equation.
12.(Agape) = Equation.
46
There Are Universal
Constants!
13.Speed of Light: C = 2.99792458 x 10⁸ m s¯¹.
14.Plank’s: h = 6.626075540 x 10 ¯³⁴ Js, or J/Hz. The
ratio of the smallest possible unit, (A quantum) of
energy, to its frequency: E = hv.
15.Dirac’s ħ = h/2π = 1.0545887 x 10 ¯³⁴ Js. This
derivative of Plank’s Constant is helpful in physics.
16.Plank’s Length: Lp = √(Għ/C³) = @ 10¯³⁵m. The
distance at which quantum mechanics must
compliment classical gravity.
17.Plank’s Time: Tp= √(Għ/C⁵) = @ 10¯⁴³s. How long it
takes a photon to travel Plank’s Length.
47
There Are Universal
Constants!
18.Plank’s : Mass: Mp = √(ħc/G) = @ 10¯⁸kg. The mass of
a particle whose Compton wavelength is equal to
Planks length.
19.Permittivity of vacuum: Eo = 8.85418782 x 10¯¹² c²/Jm.
F = Q₁Q₂/r²4πεₒ. A ratio of electric displacement, used
with insulators.
20.Permeability of vacuum: µₒ= 1/EoC² = 1.2566370614 x
10¯⁶ H/m = 4π x 10¯⁷ H m ¯¹. A ratio of magnetic flux.
21.Avogadro’s¹ NA = 6.022136736 x 10²³ mol¯¹. The
number of atoms or molecules in one mole of
substance.
There Are Universal
Constants!
22. Electron Mass at rest: mₑ = 9.109389754 x 10 ¯³¹ kg.
23.Proton Mass¹ at rest: mp = 1.6726485 x 10¯²⁷ kg.
24.Neutron Mass¹ at rest: mn = 1.6749286 x 10¯²⁷ kg.
25.Atomic mass Constant: mg = 1.6605402 x 10¯²⁷ kg.
26. Electron charge to mass ratio: ε/mₑ = 1.7588047 x
10¹¹ C/kg.
27.Bohr Radius: aₒ = 4πεₒh²/ mₑe² = 0.52917706 x 10¯¹⁰
m. A unit of length to measure atoms.
28. Faraday Constant: ₣ = Nₐε = 9.648530929 x 10⁴ C/mol.
The electric charge carried by one mole of electrons.
49
There Are Universal
Constants!
29.Coulomb Constant: C = k = 8.9875 x 10⁹ N x m²/C².
30.Fine-structure Constant: [μ₀c²/ 4π](e²ħc) = a¯' =
137.0360411.
31.Muon mass: m μ = 1.8825327 x 10¯²⁸ kg.
32.Ratio of muon mass to electron mass: 206.7686547.
33.Bohr magneton: μB = eħ/2mε
= 9.274078 x 10¯²⁴
J/T. A unit for measuring very small magnetism.
34.Molar Gas Constant: R = 8.31451070 JK¯¹ mol¯¹.
Relating to the relationship between
temperature, pressure, and volume of a gas.
There Are Universal
Constants!
35.Boltzmann constant: kB = 1.38065812 x 10¯²³ j/k¯¹.
The ratio of the gas constant to #20.
36. Gas Volume: Vm = 8.31441 J/mol K.
37. Nuclear magneton: μN = eħ/2mp = 5.0508248 x
10¯²⁷ J/T. Another unit for measuring very small
magnetism.
38.Free electron g factor: gₑ = 2 x 1.0011596567.
Relating to qualities of metals.
39. Classical electron radius: [μ₀c²/ 4π](e²/ mₑc²) = a³/ 4π
R∞.
51
There Are Universal
Constants!
40. Rydberg: R∞ = 1.0973731 x 10⁷m¯¹, = µₒ²me⁴c³/8h³.
Related to the atomic spectra and the binding energy
between an electron and a nucleon & related to other
Constants.
41. Loschmidt: L = NA /Vm = 2.68676323 x 10²⁵m¯³. The
number of particles per mm³ of an ideal gas at sea level.
42. Stefan-Boltzmann: σ = 5.6705119 x 10¯⁸ W m¯² K¯⁴.
Related to the total amount of radiated heat energy
excluding light. E = σT⁴.
43. Thomson cross section: (8/3)πrₑ² = σₑ = 0.665244833 x
10¯²⁸m².
44-227 for the 184 Elemental Constants, (Atomic weight &
52
number for the 92 natural elements) Etc. Ad infinitum.
There Are Universal
Elements!
• There are 92 natural elements, distinct
atoms, in our universe. They each have
their own distinct atomic number and their
own distinct atomic weight.
• Never more. Never less.
• No where more. No where less.
• Never different. No where different.
53
There Are Universal
Elements!
• Paley¹ observed that if one discovered a watch among
iron ore, correctly set & keeping proper time, one
would know that a watchmaker had created it. (1802)
• Now that we know how God made the elements, 90 of
92 forged in the furnace of giant stars, not only are the
“creations” “Paley’s Watch”, but the ingredients used to
build the “Watch” are also “Paley’s Watch”.
• To discover something brilliantly, even exquisitely
designed, creatively and skillfully constructed, currently
operating with minutely tuned precision, and think it
had no Creator, is as Schopenhauer observed, “Not
merely mistaken, but stupid.” (1860)
54
A few useful equations:
The famous mathematician Euler as asked by
Catherine the Great to refute Diderot’s atheism.
“Sir, (𝒂 + 𝒃ᴺ)/n = x. Hence God Exists. Reply.” The
beauty and the Elegance of nature & truth as a
argument for God’s existence is even more plainly
seen in: E = MC², Libnez’s famous equation for Π:
𝟒
𝟏
𝟏
𝟏
𝟏
𝜫 = − + − + … Lp = √(Għ/C³) = @ 10¯³⁵m,
𝟏
𝟑
𝟓
𝟕
𝟗
per Plank’s Time: Tp= √(Għ/C⁵) = @ 10¯⁴³s. Etc.
55
There Are Universal
Forces!
The True meaning of Omnipotence: Beyond passive
Laws that cannot be broken¹, there are powerful Laws,
Forces, that literally, physically force their influence upon
us! This is A fundamental misunderstanding of
disobedience! We do not ever break God’s laws, we
sometimes break ourselves against them! “Obedience” is
from a Greek word, ”hpakono”² through Latin, (ob oedire
“toward + hearing”) meaning “to listen”.
1. Gravitational: Newton: G.F. = G x M₁ X M₂ \d².
2. Electromagnetic ³: Faraday/Maxwell: EM= Δ x E = ∂B/∂T.
56
There Are Universal
Forces!
3. WEAK: Einstein, Curies, et. al. : Δm = (mp + mn) –
md. X C².
4. STRONG: Einstein, Oppenheimer, et. al. : ¹₁H + ¹₁H →
²₁H + °₁e + v. ¹₁H + ²₁H → ³₂He + ϒ. (followed by either)
¹₁H + ³₂He → ⁴₂He + °₁e + v x C², or ³₂He + ³₂He → ⁴₂He
+ ¹₁H + ¹₁H x C².
5. LAMBDA: Λ = @ 0.7: The expansion energy of the
universe. This results in a slow steady expansion of
70.4 +/- 1.4 kilometers per second per megaparsec.
6. FEIGENBAUM’s Constant of Chaos: (Fc = Equation).
7. AGAPE (LOVE OF GOD-LIGHT OF CHRIST): (Equation).
57
Gravitational Force
F = G x M₁ X M₂ \d².
• God uses gravity to hold many things in the universe in their
exact proper places, in a very complex interdependent dance.
• Man uses gravity to hold satellites in orbit with great skill &
exact calculations for a few years. To believe God did not
place the earth and moon into a much more precise orbit for
billions of years: Now that is an act of Blind faith*!
• Where did Newton get this knowledge? According to his
testimony, The Christian God revealed this to him! And a great
deal more! Newton was perhaps the greatest scientist who
ever lived. His Christian devotion is second to none. His
discoveries changed the world. Shall we ignore other things
he learned, and how he learned them? Is it better to have one
article, or continuing access to the Internet?
58
Gravitational Force
F = G x M₁ X M₂ \d².
G = 6.6725985 x 10¯¹¹m³kg¯¹s¯².
• Sometimes we rebel and disobey gravity, injuring or killing
ourselves and/or others.
• Sometimes our disobedience makes our burdens greater and
our lives harder.
• The ‘Thou Shalt not’s’ in scripture protect us from these
errors¹.
• The lever, pulley & Wheel-barrow are examples of simple
obedience to God’s law of gravity that makes our lives easier².
• Satellites are an example of a higher order of obedience to
gravity, making possible many ‘miracles’ that seem magical to
those who do not know these laws or refuse to obey them³.
59
Gravitational Force
F = G x M₁ X M₂ \d².
G = 6.6725985 x 10¯¹¹m³kg¯¹s¯².
• Experiment between two people. Obtain mass * various
distances. Calculate gravitational attraction. What is margin of
uncertainty?. Might other massive objects or other forces be
effecting this experiment?
60
UNIVERSAL LAW OF
GRAVITATION: PLANETARY ORBITS
F = G x M₁ X M₂ \d².
G = 6.6725985 x 10¯¹¹m³kg¯¹s¯².
ESCAPE VELOCITY:
𝑽ₑ = 𝟐𝑮𝑴ₑ/𝑹ₑ.
61
ENERGY: UNIVERSAL
GRAVITATION &
PLANETARY ORBITS
Compare & contrast artificial satellites & natural
planets & moons.
EXTRA CREDIT: NEWTONS’ 3RD BODY EQUATONS:
62
UNITS & DIMENSIONS
INTRODUCTION & OVERVIEW
FUNDAMENTAL UNITS OF THE S.I.
1.
2.
3.
4.
5.
6.
7.
LENGTH = METER¹.
MASS = KILOGRAMME².
TIME = SECOND³.
ELECTRIC CURRENT = AMPERE⁴.
THERMODYNAMIC TEMPERATURE = °KELVIN⁵.
AMOUNT OF SUBSTANCE = MOLE⁶.
LUMINOUS INTENSITY = CANDELA⁷; cd.
63
UNITS & DIMENSIONS
INTRODUCTION & OVERVIEW
DERIVED UNITS OF THE S.I.
8. °Celsius¹.
9. 2D & 3D Angle: Radian; rad & Steradian; st.
10.Area & Volume: Metre squared; M² & cubed; M³.
11.Velocity: Metre/second; m/s⁻¹.
12.Acceleration: Metre/second²; m/s⁻².
13.Density: Kilogramme/metre³; kgm⁻³.
14.Mass rate of flow: Kilogramme/sec; kgs⁻¹.
15.Volume rate of flow: Cubic metre/sec; m³s⁻¹.
16.Moment of inertia: kg m².
17. Momentum & Angular: kg m s⁻¹ & kg m² s⁻¹ .
64
UNITS & DIMENSIONS
INTRODUCTION & OVERVIEW
DERIVED UNITS OF THE S.I.
18. Force: Newton; kg m s⁻².
19. Torque (Moment of Force): Newton Metre; NM.
20. Work (Energy Heat): Joule; 1J = 1NM = 1kg m²s⁻².
21. Power: Watt; 1w = 1J s⁻¹.
22.Frequency: Hertz; Hz= waves/s⁻¹.
23.Electric Charge: Coulomb; C = A s.
24.Pressure: Pascal; Pa = kg/m s² = N/m² = J/m³.
25. Pressure & Surface Tension: NM.
26. Luminous flux: Lumen; lm = cd sr.
27.Illumination: Lux; lx = lm m⁻².
65
UNITS & DIMENSIONS
INTRODUCTION & OVERVIEW
DERIVED UNITS OF THE S.I.
28.Electric potential difference: Volt;
V = kg m²/s³ A = J/A s = J/C
29. Electric resistance: Ohm; Ω = kg m²/s³A² = V/A.
30.Electric conductance: Siemens; S = s³A²/kg m² = Ω⁻¹.
31.Electric capacitance: Farad;
F = A₂s⁴/kg m² = A s/V = C/V.
32.Magnetic flux: Weber; Wb = kg m²/s²A V s.
33.Inductance: Henry; H = kg m²/s²A² = V s/A = Wb/A.
34.Magnetic flux density (magnetic induction) :
Tesla; T = kg/s²A = V s/m².
66
UNITS & DIMENSIONS
INTRODUCTION & OVERVIEW
VARIATIONS OF THE S.I.
35. Energy: Erg; erg = g cm²/s² = 10⁻⁷ J.
36. Force: Dyne; dyn = g cm/s² = 10⁻⁵ N.
37. Viscosity: Poise; P = g/cm s = 10⁻¹ Pa s.
38. Kinetic¹ Viscosity: Stokes; St = cm²/s = 10⁻⁴m²/s.
39. Length: Micron; μ = 10⁻⁴ cm = 10⁻⁶m.
40. Length: Angstrom: Å = 10⁻⁸cm = 10⁻¹⁰m.
41. Volume: Liter; l = 10³ cm³ = 1 dm³ = 10⁻³ m³.
42. Mass: Tonne; t = 10⁶g = 10³kg.
43. Pressure: Bar; bar = 10⁶ dyn/cm² = 10⁵ Pa.
44. Concentration (Molarity):
M = 10⁻³ mol/cm³ = mol/liter = mol/dm³.
67
MEASURING IN 3
DIMENSTIONS IN METERS:
Distance from earth to most remote known quasar: 1 * 10²⁶.
“
“
“ “ “
“
“ Galaxy: 4 * 10²⁵.
“
“
“ “ nearest galaxy (m-31):
2 * 10²².
“
“
“ to nearest star:
4 * 10¹⁶.
One light-year:
9 * 10¹⁵.
Our Solar System:
1 *10¹⁵.
Mean orbital radius of the earth:
2 * 10¹¹.
A view of our earth & moon:
1 *10¹⁰.
Mean distance from earth to moon:
4 * 10⁸.
Mean radius of the earth:
6 * 10⁶.
68
Typical altitude of orbiting satellite:
2 * 10⁵.
MEASURING IN 3
DIMENSTIONS IN METERS:
Length of a football field:
A Human:
Length of a housefly:
Smallest dust particles:
Most cells in most living organisms:
Diameter of A water molecule:
Diameter of A hydrogen atom:
Diameter of an atomic nucleus:
Diameter of An Electron & a proton:
Diameter of SuperStrings:
9 * 10¹.
2 X .3 X .3.
5 * 10⁻³.
1 * 10⁻⁴.
1 * 10⁻⁵.
1 * 10⁻⁸.
1 * 10⁻¹⁰.
1 * 10⁻¹⁴.
1 * 10⁻¹⁵.
1 * 10⁻²⁰.
69
MEASURING IN THE 4TH
DIMENSTION: THE
STREAM OF TIME IN SECONDS:
Lifetime of a proton:
Age of the Observable Universe:
Age of the earth:
Age of the Pyramid of Cheops:
U.S. Human Life Expectancy:
Average age of a college student:
One year:
Length of a day:
Interval between human heartbeats:
Period of audible sound waves:
1 * 10³⁹.
5 * 10¹⁷.
1 * 10¹⁷.
1 * 10¹¹.
2 * 10⁹.
6 * 10⁸.
3 * 10⁷.
9 * 10⁴.
8 * 10⁻¹.
1 * 10⁻³.
70
MEASURING IN THE 4TH
DIMENSTION: THE
STREAM OF TIME IN SECONDS:
Period of concert-A tuning fork:
2 * 10⁻³.
Period of typical radio waves:
1 * 10⁻⁶.
Lifetime of a Muon:
2 * 10⁻⁶.
Period of vibration of an atom in a solid:
1 * 10⁻¹³.
Period of visible light waves:
2 * 10⁻¹⁵.
Duration of a nuclear collision:
1 * 10⁻²².
Time for light to cross a proton:
3 * 10⁻²⁴.
Lifetime of most unstable particle (1989): 1 *10⁻²³.
Plank’s Epoch:
1 *10⁻⁴³.
71
MEASURING MASS IN KG:
OUR OBSERVABLE UNIVERSE:
OUR MILKYWAY GALAXCY:
OUR SUN:
EARTH:
OUR MOON:
AN AVERAGE SHARK:
AN AVERAGE HUMAN:
AN AVERAGE FROG:
AN AVERAGE MOSQUITO:
AN AVERAGE BACTERIUM:
A HYDROGEN ATOM:
AN ELECTRON:
1 * 10⁵².
7 * 10⁴¹.
2 * 10³⁰.
6 * 10²⁴.
7 * 10²².
1 * 10².
7 * 10¹.
1 * 10⁻¹.
1 * 10⁻⁵.
1 * 10⁻¹⁵.
1 * 10⁻²⁷.
1 * 10⁻³¹.
72
MEASURING ENERGY & POWER
OUTPUT IN JOULES¹ & WATTS²:
SUNLIGHT IN ONE YEAR:
SUNLIGHT IN ONE YEAR:
EARTH’S ROTATIONAL KINETIC ENERGY:
EARTH’S DAILY INPUT OF SOLAR ENERGY:
AN AVERAGE H BOMB
100% CONVERSION OF 1 GRAMOM MATTER 𝐄 = 𝐌𝐂² :
WORLD’S CURRENT ENERGY CONSUMPTION:
ONE BARREL OF OIL:
ONE AVERAGE POWER PLANT:
ONE MEDIUM PIZZA:
ONE D CELL BATTERY:
ONE MOSQUITO PUSHUP:
FISSION OF ONE ATOM OF U-235:
ONE PERSON:
10³⁴ J.
10²⁶ W.
10²⁹ J.
10²² J.
10¹⁷ J.
10¹⁴ J.
10¹³ W.
10¹⁰ J.
10⁹. W.
10⁷ J.
10⁴ J.
10⁻⁷ J.
10⁻¹¹ J.
10073W.
LARGE NUMBERS
& DIVERSE SCALES
“We are each made up of between 10²⁸ and 10²⁹
atoms. This ‘human scale’ is, in a numerical sense,
poised midway between the masses of atoms and
stars. It would take roughly as many human bodies
to make up the mass of the Sun as there are atoms
in each of us. But our Sun is just an ordinary star in
the galaxy that contains a hundred billion stars
altogether. There are at least as many galaxies in our
Observable Universe as there are stars in a galaxy.
More than 10⁷⁸ atoms lie within range of our
telescope.” There are @ 3 * 10²⁷ stars.
74
LARGE NUMBERS
& DIVERSE SCALES
“Living organisms are configured into layer
upon layer of complex structure. Atoms are
assembled into complex molecules; these
react, via complex pathways in every cell, and
indirectly lead to the entire interconnected
structure that makes up a tree, an insect or a
human. We straddle the cosmos and the
microworld-intermediate in side between the
Sun, at a billion metres in diameter, and a
molecule at a billionth of a metre.
75
LARGE NUMBERS
& DIVERSE SCALES
It is actually no coincidence that nature attains
its maximum complexity on this intermediate
scale: Anything larger, if it were a habitable
planet, would be vulnerable to breakage or
crushing by gravity.”
“ We are vulnerable to viruses a millionth of a
metre in length, and the minute DNA doublehelix molecule encodes our total genetic
heritage. And it‘s just as obvious that we
depend on the Son for its power.
76
KINEMATICS: 1D MOTION.
VELOCITY & ACCELERATION
a = v - v₀ /t.
v = v₀ + at
𝑿−𝑿𝒊
.
𝑻−𝑻𝒊
𝑽=
Where v = constant velocity, X = position, T
= time & i = initial or beginning. Δ = “the change in”.
For non-uniform motion, (not constant velocity):
Δ𝑿
𝑽=
& Δ𝑿 = 𝑽 ∗ Δ𝑻.
Δ𝑻
Δ𝑿
Δ𝑻
𝒅𝒙
.
𝒅𝒕
is also represented as
In this case, this does
not mean d * x or d * t. ≡ = is identical to.
77
WORK & KINETIC ENERGY
𝑾=𝑭∗𝒅
Work equals force times distance.
78
KINEMATICS¹: 1D MOTION.
DISPLACEMENT & VELOCITY
Work, W, by a constant force, F, is the product of the
component of the force along the direction of
displacement and the magnitude of the
displacement:
𝑾 = 𝑭 𝒄𝒐𝒔 𝝷 𝒔.
Free fall: 𝒙 =
𝒂𝒕2
.
𝟐
Where a = acceleration & t = time.
Acceleration near the surface of the Earth, @ 45th
parallel ≈ 9.80 m per s² = 9.8m/s².
79
CONSERVATION OF
MECHANICAL ENERGY
Kinetic is from a Greek word meaning movement.
KE = Kinetic Energy: 𝑲𝑬 = ½𝒎𝒗².
Where m = mass, & v = velocity.
Kinematics, (motion) in 2, or 3 dimensions is simply
a matter of adding additional vector variables.
Because motion is often described through time a 4th
dimension is unnecessary. Horizontal = X. Vertical =
Y, Depth = Z. Time is always T.
80
NEWTON’S LAWS:
GRAVITAION & WEIGHT,
PROJECTILES
𝒘 = 𝒎𝒈
Where w = weight, m = mass & g = the acceleration
due to gravity.
81
VECTORS, NEWTON’S LAWS
OF MOTION FORCE, MASS
& ACCELERATION
NEWTON’S 1ST LAW:
“An object at rest will remain at rest and an object in
motion will continue in motion with a constant
velocity.” (a constant speed in a straight line).
When Σ𝑭 = 𝟎, 𝒕𝒉𝒆𝒏 𝒂 = 𝟎.
Where,
Σ = “the sum of”.
F = Force.
A = Acceleration.
82
NEWTON’S 2ND LAW:
LINEAR MOMENTUM
& IMPULSE
ρ = 𝒎𝒗. Where the Greek letter ρ = momentum, m
= mass & v = velocity.
83
CONSERVATION LAWS
& POTENTIAL ENERGY
Energy is always conserved, ergo one can say that
when one picks up a massive object one has
conserved the potential energy, PE of it falling back
down.
This is also gravitational potential energy: 𝑷𝑬 =
𝒎𝒈𝒚. Where m = mass, g = gravity & y = height.
84
NEWTON’S LAWS OF
MOTION FORCE, MASS
& ACCELERATION
As a vector equation, Σ𝑭 = 𝒎𝒂. =
Σ𝑭ₓ = 𝒎𝒂ₓ
Σ𝑭y = 𝒎𝒂𝒚
Σ𝑭𝒛 = 𝒎𝒂𝒛
Σ𝑭𝒕 = 𝒎𝒂𝒕
The SI unit of force is the newton, which is the force
that accelerates one kg. of mass one meter per
second squared: 𝟏 𝑵 = 𝟏 𝒌𝒈 ∗ /s².
85
VECTORS, NEWTON’S LAWS
OF MOTION FORCE, MASS
& ACCELERATION
THE CONCEPT OF FORCE:
Galileo's discovery aboard ship.
• “Who can learn anything new and not find it a
shock?” John Wheeler
• It is helpful to regularly review even our most
fundamental understandings in light of our most
recent discoveries.
86
VECTORS, NEWTON’S LAWS
OF MOTION FORCE, MASS
& ACCELERATION
NEWTON’S 2ND LAW:
“The acceleration of an object is directly proportional
to the resultant force acting on it and inversely
proportional to its mass. The direction of the
acceleration is in the direction of the resultant force.”
Σ𝑭 = 𝒎𝒂. Or 𝑭 =
Δρ
.
Δ𝒕
Where, Σ = “the sum of”, F = Force, m = mass, A =
Acceleration, Δ = the change in, ρ = momentum & t =
time,
87
NEWTON’S 2ND LAW:
MOMENTUM &
CENTER OF MASS
Center of mass is important because the net external
force, Fₑ acting on a system equals the total mass of
the system multiplied by the acceleration of the
center of mass, maₒ: 𝑭ₑ = 𝒎𝒂ₒ.
88
VECTORS, NEWTON’S LAWS
OF MOTION FORCE, MASS
& ACCELERATION
NEWTON’S 3RD LAW:
“If two bodies exert forces on each other, the force
exerted by body 2 on body 1 is equal in magnitude
and opposite in direction to the force exerted by
body 1 on body 2.”
In other words: For every action there is an equal
and opposite reaction.
89
NEWTON’S LAWS:
NORMAL FORCES & FRICTION
ƒ𝘀 ≤ 𝞵𝘀𝚗.
Where ƒ is friction, either static or kinetic (ƒk), 𝞵 is
the coefficient of static friction, and n is the normal
force.
ƒk ≤ 𝞵k𝚗.
90
NEWTON’S LAWS:
SPRING FORCES & TENSION
For now, think of springs & tension as potential
kinetic energy.
91
NEWTON’S 2ND LAW:
COLLISIONS &
KINETIC ENERGY
An inelastic collision is one in which momentum is
conserved but kinetic energy is not.
An elastic collision is one in which both are
conserved.
They are exactly what they sound like. Energy is
always conserved. When it is not in the equations,
where does it go?
92
NEWTON’S 2ND LAW:
MOMENTUM &
COLLISIONS
In a perfectly inelastic collision:
𝒎₁ 𝒗₁ +m₂ v₂ = (m₁ + m₂) Vf.
v₁ = ⇨, v₂ = ⇦, Vf = the new direction both are now
taking.
93
ROTATIONAL DYNAMICS
𝟏 𝒓𝒂𝒅 = 𝟑𝟔𝟎°/2π ≈57.3°.
π
Θ 𝒓𝒂𝒅 =
°Θ 𝒅𝒆𝒈 .
𝟏𝟖𝟎
ω = (𝝷₂-𝝷₁) / (t₂ - t₁) = Δ𝝷/Δt.
Where ω is angular velocity, 𝝷 is the angle measured
in radians, t is time, Δ𝝷 is the angular displacement.
Generally Δ refers to “change in”.
Angular acceleration, α = (ω₂ - ω₁) /(t₂ - t₁) =
Δω/Δt.
94
ANGULAR VELOCITY &
UNIFORM CICULAR MOTION
Imagine a satellite in a nearly circular orbit @ 160
km above the Earth. What is it’s minimum speed &
how long would each orbit take?
𝒈=
𝒗2
.
𝒓
Where r is the radius of the orbit.
𝒗 = 𝒓𝒈. V= 7.9 km/s.
𝟐π𝒓
𝑻=
= 𝟖𝟓 𝒎𝒊𝒏.
𝒗
Sputniks’s¹ orbits were not circular & lasted 96 min.
Sputnik 10’s orbits in 1961² were within @ 1%
(altitude 175km-247km.) & lasted 85 min. 42 s.
95
ND
2
NEWTON’S
LAW:
ANGULAR KINETICS,
TORQUE, RIDGID BODIES &
MOMENT OF INERTIA
NEWTON’S 2ND LAW:
“The acceleration of an object is directly
proportional to the resultant force acting on it and
inversely proportional to its mass. The direction of
the acceleration is in the direction of the resultant
force.”
Σ𝑭 = 𝒎𝒂.
Where, m = mass.
96
NEWTON’S 2ND LAW:
MOMENT OF INERTIA
& ANGULAR MOMENTUM
𝟏 𝒓𝒂𝒅 = 𝟑𝟔𝟎°/2π ≈57.3°.
π
Θ 𝒓𝒂𝒅 =
°Θ 𝒅𝒆𝒈 .
𝟏𝟖𝟎
ω = (𝝷₂-𝝷₁) / (t₂ - t₁) = Δ𝝷/Δt.
Where ω is angular velocity, 𝝷 is the angle measured
in radians, t is time, Δ𝝷 is the angular displacement.
Generally Δ refers to “change in”.
Angular acceleration, α = (ω₂ - ω₁) /(t₂ - t₁) =
Δω/Δt.
97
ANGULAR DYNAMICS:
TRANSLATION & ROTATION
𝟏 𝒓𝒂𝒅 = 𝟑𝟔𝟎°/2π ≈57.3°.
π
Θ 𝒓𝒂𝒅 =
°Θ 𝒅𝒆𝒈 .
𝟏𝟖𝟎
ω = (𝝷₂-𝝷₁) / (t₂ - t₁) = Δ𝝷/Δt.
Where ω is angular velocity, 𝝷 is the angle measured
in radians, t is time, Δ𝝷 is the angular displacement.
Generally Δ refers to “change in”.
Angular acceleration, α = (ω₂ - ω₁) /(t₂ - t₁) =
Δω/Δt.
98
mechanics
• Mechanics is concerned with the motion of
material objects.
• A baseball thrown at 60 MPH has a kinetic energy
of @ 53 joules.
• An average passenger car traveling at 60 MPH has
a kinetic energy of 600,000 Joules.
99
LEVERS, STATICS & TORQUE
1.
2.
3.
4.
5.
6.
LEVERS:
PULLEYS:
WHEEL & AXLE:
INXLINWS PLANE:
WEDGE:
SCREW
100
LEVERS, STATICS & TORQUE
The turning moment exerted by a tangential force
acting at a distance from the axis of rotation. It is
measured in newton-metres.
𝒕 = 𝒓𝑭𝒔𝒊𝒏Φ.
Where t = torque & the directions r & f create angle
Φ.
101
SOLID STATE Φ.
• A subsection of atomic Φ, Solid state Φ addresses
the electrical, magnetic, optical, & elastic
properties of atoms and subatomic particles when
in a solid or nearly solid condensed state.
• Solids are either crystalline or amorphous.
LIQUID STATE Φ.
• The property of atoms and subatomic particles
that allows translational motion & lack fixed
position. These qualities are temperature &
pressure dependent and relative to time.
• The distinction between a liquid & a gas is not
exact, but generally involves movement in the 3rd
dimension at constant temperature.
GASEOUS STATE Φ.
• The property of atoms and subatomic particles
that allows translational motion & lack fixed
position. These qualities are temperature &
pressure dependent and relative to time.
• The distinction between a liquid & a gas is not
exact, but generally involves movement in the 3rd
dimension at constant temperature.
• For purposes of the hydraulics & fluid dynamics of
flight, atmosphere is a liquid & it’s density &
temperature make dichotomous life & death
differences.
PLASMA STATE Φ.
• The vast majority of matter in our universe is in an
electronically balanced state of highly ionized gas
called Plasma. This is the condition of stars. This
is the typical condition of matter.
• Why is their a tiny exception?
• What is the result, consequence or purpose of this
exception?
ENERGY TRANSFORMATIONS:
THE LAWS OF THERMODYNAMICS
Benjamin Thompson’s Apple pies & Fahrenheit’s
saltwater.
0⁰F, 0⁰C, 0⁰K (⁻273.15⁰C).
The equation for the expansion of solids:
Δ𝑳 = α𝑳0 Δ𝑻.
Or 𝑳 − 𝑳₀ = αL₀(T-T₀).
In 1900 Max Plank discovers that energy like matter
comes in discreet indivisible units that he called
quanta. First particles have wave-like qualities, now
energy has particle like qualities!
106
ENERGY
TRANSFORMATIONS: HEAT
1 food calorie = 4.186 J.
1 food calorie = 10³ cal. S.I.
Specific heat is: 𝒄 =
𝑸
.
𝒎Δ𝑻
Inversely: 𝑸 = 𝒎𝒄Δ𝑻.
107
ENERGY TRANSFORMATIONS:
THE LAWS OF THERMODYNAMICS
1. THE CONSERVATION OF ENERGY: THE TOTAL
ENERGY OF A CLOSED SYSTEM REMAINS CONSTANT
ALTHOUGH IT MAY BE TRANSFORMED FROM ONE
FORM TO ANOTHER.
The quantity Q-W = the change in the internal energy
of the system. Δ𝑼 = 𝑼ƭ − 𝑼𝒊 = 𝑸 − 𝑾.
Where all the quantities must have the same units of
energy.
On the atomic level this includes the kinetic &
potential energies of the molecules in the system.
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ENERGY TRANSFORMATIONS:
THE LAWS OF THERMODYNAMICS
2. HEAT CAN NEVER PASS SONTAINEOUSLY FROM A
BODY AT A LOWERE TEMPRATURE TO ONE AT
HIGHER TEMPRATURE. (CLAUSIUS), OR LOSS OF
ENERGY & WORK IS NEVER EQUAL (KELVINPLANK.) ΔS ˃ 0. Clausius or ΔS = ΔQ/t. Or
𝑾 = 𝑸𝒉 − 𝑸𝒄.
“The Second Law of Thermodynamics- which in
simple terms just states that energy tends to flow
from where there is more to whew there is less.”¹
109
ENERGY TRANSFORMATIONS:
THE LAWS OF THERMODYNAMICS
3. THE ENTROPY OF A SUBSTANCE APPROACHES ZERO
AS ITS TEMPRATURE APPROACHES ABSOLUTE ZERO
110
Φ OF WAVES I.
“The impetus is much quicker than the water, for it
often happens that the wave flees the place of its
creation, while the water does not; like the waves
made in a field of grain by the wind, Where we see
the waves running across the field while the grain
remains in place.” Leonardo da Vinci.
Φ OF WAVES I.
“ A bit of gossip starting in Washington reaches New
York very quickly, even though not a single individual
who takes part in spreading it travels between these
two cities. There are two quite different motions
involved, that of the rumor, Washington to New York,
and that of the persons who spread the rumor. The
wind, passing over a field of grain, sets up a wave
which spread out across the whole field. Here again
we must distinguish between the motion of the wave
and the motion of the separate plants, which undergo
only small oscillations…
Φ OF WAVES I.
“ …The particles constituting the medium perform
only small vibrations, but the whole motion is that of
a progressive wave. The essentially new thing here is
that for the first time we consider the motion of
something which is not matter, but energy
propagated through matter.”
Einstein & Infeld, The Evolution of Physics, 1961.
Φ OF WAVES I.
• Hooke’s Law: Fs = −kx.
Where k = spring constant & x is the displacement
from its unstretched position.
De Broglie’s hypothesis: λ =
h
.
ρ
Where ρ is the momentum of the particle.
Φ OF WAVES I.
• Mechanical vibrations & waves: Eternal principles
remain the same regardless of the mediums.
Φ OF WAVES I.
• Simple harmonic motion: When the net force is
proportional to the displacement and in the
opposite direction.
• A Transverse wave or traveling wave is one in
which the particles of the disturbed medium move
perpendicular to the wave velocity such as EM
waves including light.
• Longitudinal waves are parallel.
Φ OF WAVES I.
• Normal modes:
𝟐π
k=
= 𝒂𝒏𝒖𝒍𝒂𝒓 𝒘𝒂𝒗𝒆 𝒏𝒖𝒎𝒃𝒆𝒓.
λ
λ = wave length.
𝟏
λ
K = wave number =
k
.
𝟐π
The Law of Conservation of energy allows us to
express velocity as a function of position:
𝒗=±
𝒌
𝒎
𝑨2
−
𝒙2
.
Φ OF WAVES I.
• Forced vibrations & resonance: Crystal shattered
by a human voice: In a tube open at both ends he
natural frequencies of vibration form a series in
which all harmonics are present and are equal to
𝒗
integral multiples of the fundamental: ƒn = 𝒏 .
𝟐𝑳
Where v = the speed of sound in air.
Coupled Oscillations:
Driven Coupled Oscillators:
Φ OF WAVES I.
• Vibrations of continuous systems:
If two or more waves are moving through a
medium the resultant wave equals the sum of
the displacements of the waves point by point.
Φ OF SOUND WAVES.
The limits of hearing are dependent on the
frequency of the tone & usually vary between 50Hz12,000Hz with 3300Hz being easiest to hear.
Φ OF SOUND WAVES.
• Ultrasound & other digital sound technologies:
The process of converting mechanical energy (sound)
into electrical energy & vice versa is called the
Piezoelectric effect.
Φ OF SOUND WAVES.
• The speed of sound in medium B & density ρ is:
• 𝒗=
𝑩
.
ρ
• Velocity also depends on the temperature of the
medium. In air it is: 𝒗 =
𝒎
𝟑𝟑𝟏
𝒔
𝟏+
𝑻
.
𝟐𝟕𝟑
• The intensity of a sound wave in decibels is:
• Β = 𝟏𝟎 𝒍𝒐𝒈
𝑰
𝑰₀
.
Φ OF SOUND WAVES.
• The intensity of a spherical wave: 𝑰 =
′
𝒗₀
±
𝒗
𝑷𝒂𝒗
.
2
𝟒π𝒓
• The Doppler effect is: Ƒ = ƒ(𝒗
). Where + is
used when the observer is moving toward the
source.
Φ OF QUANTUM MECHANICS.
THE Φ OF MUSICAL INSTUMENTS.
• Those who are musically gifted might consider
developing equations of symphonic harmonies
that could turn an art into a science!
WEB SITES OF INTEREST
1. The Electronic Nobel Museum Project:
www.nobel.se/prize/index.html.
2. www.aip.org.
3. http://physics.nist.gov/euu/Constants/
CODA recommended values of the fundamental
physical constants
4. www.isinet.com/.
5. http://Webbook.nist.gov/.
6. www.nist.gov/srd/jperd.htm. Cumulative index
to the Journal of physical and Chemical Reference
Data.
7. Most college & university libraries.
125