A Brief Historical A Brief Historical IntroductionIntroduction

There are more things in Heaven and There are more things in Heaven and Earth, Horatio, than are dreamt of in Earth, Horatio, than are dreamt of in

your philosophies.your philosophies.

-- William Shakespeare, -- William Shakespeare, HamletHamlet

Long ago, humans gazed up at the night sky and Long ago, humans gazed up at the night sky and made up stories to help them make sense of the made up stories to help them make sense of the

world around them.world around them.

OrionOrion

Most early civilizations had a well developed Most early civilizations had a well developed astronomy before they had a written language.astronomy before they had a written language.

StonehengeStonehenge

The night sky contains amazing vistas …The night sky contains amazing vistas …

… … along with order and predictability.along with order and predictability.

The MoonThe Moon

Today, we still make up stories about the Today, we still make up stories about the heavens. They tell us about things that no eye heavens. They tell us about things that no eye

could ever see ...could ever see ...

Black HolesBlack Holes

QuarksQuarks

… … and of distances to vast to imagine.and of distances to vast to imagine.

Hubble Deep FieldHubble Deep Field((every point of light is a galaxyevery point of light is a galaxy))

The seeds of physics were The seeds of physics were planted back when astronomers planted back when astronomers first tried to unravel the mystery first tried to unravel the mystery

of planetary motion.of planetary motion.

Johannes KeplerJohannes Kepler

It was the marriage of mathematics with It was the marriage of mathematics with astronomy that marked the dawn of classical astronomy that marked the dawn of classical

physics.physics.

(1571-1630)(1571-1630)

The word The word PhysicsPhysics comes from the Latin comes from the Latin physicaphysica, , meaning ‘meaning ‘knowledge of natural thingsknowledge of natural things’.’.

PhysicsPhysics – – the study of matter and energy and the the study of matter and energy and the interactionsinteractions that govern their behavior that govern their behavior

** Physics is the discipline where man attempts to explain the ** Physics is the discipline where man attempts to explain the motion and behavior of the physical universe as completely and motion and behavior of the physical universe as completely and accurately as possible, accurately as possible, on scales that are very large (universe, galaxies…), very small (atoms, quarks…) and everywhere in between.

* Natural phenomena exists and has existed long before we observed them.* Natural phenomena exists and has existed long before we observed them. ((i.e. Newton did not discover gravity, he was the first to describe it quantitativelyi.e. Newton did not discover gravity, he was the first to describe it quantitatively ))

Traditional & Modern Fields of Study

Classical Mechanics [Newton] Quantum Mechanics [Schrödinger]

Thermodynamics [Gibbs] Relativity [Einstein]

Electromagnetism [Maxwell]

Geometric Optics [Galileo]

Acoustics Particle Physics

Solid State Physics

Atomic/Molecular Physics

Nuclear Physics

Cosmology

Engineering

1900 A.D.

Classical Physics Modern Physics F

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Applies to everyday sizes and speeds

Applies to extreme sizes and speeds

The Physics ProcessThe Physics Process

• ObservationObservation• Information about our universe comes from experiments and Information about our universe comes from experiments and

observation.observation.

• AnalysisAnalysis• Scientific experiments produce immense, confusing or even Scientific experiments produce immense, confusing or even

exciting data that must be carefully analyzed.exciting data that must be carefully analyzed.

• ModelingModeling• The physicists job is to produce a “story” or model that The physicists job is to produce a “story” or model that

accurately represents the observed phenomena.accurately represents the observed phenomena.

The Game of Physics

• Any number of individuals may playAny number of individuals may play

• The object of the game is to discover the The object of the game is to discover the Rules of NatureRules of Nature

• The playing field is the entire universeThe playing field is the entire universe

• Any device: physical, conceptual or computational may be usedAny device: physical, conceptual or computational may be used

• Players can score “Prestige” points while playing:Players can score “Prestige” points while playing:• Points for Discovering a Rule of NaturePoints for Discovering a Rule of Nature• Points for the each phenomena a Rule correctly explainsPoints for the each phenomena a Rule correctly explains• Bonus points if the Rule predicts previously unobserved phenomenaBonus points if the Rule predicts previously unobserved phenomena

• The game is never overThe game is never over

• Players can Players can nevernever win! win!

The Game of Physics, Cont.

• An untested candidate for a Rule of Nature is called a An untested candidate for a Rule of Nature is called a hypothesishypothesis

• When a hypothesis has successfully described many phenomena, it When a hypothesis has successfully described many phenomena, it may achieve the status of may achieve the status of theorytheory

• Well tested theories that successfully explain a large number of Well tested theories that successfully explain a large number of events, by agreement of the players, may be awarded the exulted events, by agreement of the players, may be awarded the exulted status of status of lawlaw..

• Any hypothesis, theory or law may be challenged by any player at Any hypothesis, theory or law may be challenged by any player at any timeany time

• All disputes will be settled by experiments as agreed upon by the All disputes will be settled by experiments as agreed upon by the playersplayers

• The decisions of Nature, as revealed through experiments, are final!The decisions of Nature, as revealed through experiments, are final!

This part of the game is known as the This part of the game is known as the Scientific MethodScientific Method

How can scientific information (or a scientific “story”) be How can scientific information (or a scientific “story”) be presented so that other people can understand it?presented so that other people can understand it?

DEMO:DEMO: What’s in the bag? What’s in the bag?

ANSWER:ANSWER:AnalogiesAnalogiesModelsModels

RequiresRequires individuals to share some individuals to share some common reference pointscommon reference points and and a a common languagecommon language..

The Communication The Communication ProblemProblem

A. The standard reference problem is solved by using:

MeasurementsMeasurements

B. The language problem is solved by using:

the “Symbolic” Language of Mathematicsthe “Symbolic” Language of Mathematics

The SolutionThe Solution

* Whenever words, rather than math, must used to * Whenever words, rather than math, must used to express a physical principle, the words used are very express a physical principle, the words used are very specific and well crafted to avoid any confusion or miss-specific and well crafted to avoid any confusion or miss-understanding.understanding.

Solution A – Common References

Every scientific measurement always consists of 2 parts:Every scientific measurement always consists of 2 parts:

a numbera number ((which represents magnitude or sizewhich represents magnitude or size))

a unita unit

What are What are likelike measurements? measurements?

distance, time, mass, temperaturedistance, time, mass, temperature……

Numbers in Physics are meaningless without units!

Units provide the reference point to which all like measurements are compared.

Fundamental Properites

• Any physical property in the universe that can be Any physical property in the universe that can be measured can be described by using 1 of 4 fundamental measured can be described by using 1 of 4 fundamental

physics properties or by some combination of the 4.physics properties or by some combination of the 4.

4 Fundamental Physics Properties4 Fundamental Physics Properties::LengthLength (a measure of the amount of space in a given direction)

MassMass (a measure of the amount of matter an object contains)

TimeTime (a measure of the interval between events)

ChargeCharge

• What fundamental property would you use to describe the size of What fundamental property would you use to describe the size of this room?this room?

LengthLength area area oror volume volume

• What color is the sky? What color is the sky? What fundamental property would you use to describe the What fundamental property would you use to describe the

color blue?color blue?

Length or timeLength or time wavelength wavelength oror frequencyfrequency

Different colors have different wavelengths or Different colors have different wavelengths or frequencies.frequencies.

Examples

The unit associated with each fundamental The unit associated with each fundamental property depends on the choice of measurement property depends on the choice of measurement system.system.

• 2 Types of Measurement Systems2 Types of Measurement Systems

• Imperial (English/British) SystemImperial (English/British) System• ft-lb-sft-lb-s

• SI or Metric SystemSI or Metric System• mksmks**

• Length – meter (m)Length – meter (m)• Mass – kilogram (kg)Mass – kilogram (kg)• Time – seconds (s)Time – seconds (s) **standardstandard

• cgscgs

The metric system is based on powers of The metric system is based on powers of 1010 for quick & for quick & easy conversions using easy conversions using prefixesprefixes

ExEx..

10,000 meters = 10 10,000 meters = 10 kilokilometersmeters

0.001 meter = 1 0.001 meter = 1 millimillimetermeter

When the magnitudes get too large or small, scientific notation is usedWhen the magnitudes get too large or small, scientific notation is used

• Always use the base SI unit when adding a prefixAlways use the base SI unit when adding a prefix• Exception: Mass (grams)Exception: Mass (grams)

Units of Convenience

ExEx. .

AreaArea ((lengthlength * *lengthlength)) m*m = m*m = mm22

VolumeVolume ((lengthlength * *length length **lengthlength)) m*m*m = m*m*m = mm33

??? Density??? Density (() ) ((??? / Volume??? / Volume))

mass density (mass density (=m/V)=m/V) kg/mkg/m33

Fundamental units can be combined with themselves or other fundamental units to help describe or represent other physical phenomena. Units formed by a combination of the fundamental SI units are called units of convenience or derived units.

• Importance of UnitsImportance of Units

Units are extremely important because they will always be Units are extremely important because they will always be associated with a unique property or concept.associated with a unique property or concept.

• Unit ConversionsUnit Conversions

At times, it may become necessary to switch between measurement At times, it may become necessary to switch between measurement systems.systems.

ExEx. . Length Length

English SystemEnglish System mksmks

feetfeet metermeter

ButBut 1 1 ftft ≠≠ 1 1 mm

1 1 ftft = .3048 = .3048 mm or or 1 1 mm = 3.281 = 3.281 ftft

• What is 34 What is 34 mm in in ft ft ??

• Write down what you start w/ followed by a set of big Write down what you start w/ followed by a set of big parenthesis w/ a line in themparenthesis w/ a line in them

34 m34 m

• Place the number 1 & the current unit on bottom & the Place the number 1 & the current unit on bottom & the destination unit on topdestination unit on top

34 m34 m

• Insert the appropriate conversion factor on top & then Insert the appropriate conversion factor on top & then multiplymultiply

34 m34 m = = 111.554 ft111.554 ft

1 m1 mftft

1 m1 m

3.281 ft3.281 ft

What is 100 km/hr in mph (mi/hr)?

100 km/hr100 km/hr

100 km/hr100 km/hr

100 km/hr100 km/hr = = 62.5 mph 62.5 mph

1 km/hr1 km/hrmphmph

1 km/hr1 km/hr0.625 mph0.625 mph

The Dangers of Incorrect The Dangers of Incorrect Measurements or ConversionsMeasurements or Conversions

• [Magnitude][Magnitude]Ex.Ex. Prescription Drugs Prescription Drugs

How much of a cancer curing pill would you take if more How much of a cancer curing pill would you take if more than 750 than 750 mg mg was fatal?was fatal?

100.0 100.0 mgmg1000 1000 mgmg

• [Units][Units] Ex.Ex. SalarySalary

Suppose you are to be paid 100,000 a month. Would you Suppose you are to be paid 100,000 a month. Would you rather be paid:rather be paid:

100,000 100,000 centscents100,000 100,000 dollarsdollars

Magnitudes are important!Magnitudes are important!

Missing units create confusion!Missing units create confusion!

Why Mathematics?Why Mathematics?

Mathematics is very precise. Mathematics is very precise.

Mathematics and mathematical symbols can be used as Mathematics and mathematical symbols can be used as shorthand ways of representing physical quantities.shorthand ways of representing physical quantities.

Mathematical equations can convey relationships, theories, Mathematical equations can convey relationships, theories, data, concepts… quickly and efficiently.data, concepts… quickly and efficiently.

Mathematics is Universal.Mathematics is Universal.

Solution BSolution B – The Common Language – The Common Language

Symbols

Ex. - the ratio of the circumference of a circle to its diameter

- refers to an angle

Subscripts on symbols or letters can also be used to help Subscripts on symbols or letters can also be used to help identify or label a particular quantityidentify or label a particular quantity

Ex. Timet = timeti = (i)nitial timetf = (f)inal time

Symbols stand for or represent a very specific property or concept

Identifiable Symbols

$

Average vs. Instantaneous Values

AverageAverage [Big Picture]

Average ??? – total quantity divided by the total elapsed time

** Average values tell us nothingnothing about fluctuations or values at specific points in time (unless the value was constant the whole time)

ExEx. Class Test Grades. Class Test GradesThe class test average tells how the class did as a The class test average tells how the class did as a

whole, but does not indicate how any one individual whole, but does not indicate how any one individual did on the test.did on the test.

InstantaneousInstantaneous [Snap Shot]

Instantaneous ??? – value of a quantity at a specific instant in time

** Instantaneous values tell us nothingnothing about general trends or the total process over time (unless the value was constant the whole time)

ExEx. Individual Test Grades. Individual Test GradesAn individual test grade tells how a student did on An individual test grade tells how a student did on

the test, but does not indicate how they did compared the test, but does not indicate how they did compared to to the rest of the class.the rest of the class.

Dangers of interchanging Avg. and Inst. Values

When information from one type of time measurement is extended to gain information about the other, chances are it will be wrong!

Ex. The average daily temp. in Hawaii is 84o

Today it will be 84o in Hawaii

One bag of 100 M&M’s has 70 reds The average # of red M&M’s per bag is 70

Graphing

Graphs are a visual representation of the relationships between quantities

Graphs can come in many different forms:Graphs can come in many different forms:

Graphs are one of Graphs are one of the quickest and the quickest and easiest methods to easiest methods to convey convey information, information, butbut they can also be they can also be one of the most one of the most deceptive!deceptive!

TablesAnother quick method to display data is to use tablestables.

Correct labeling of graphs and tables is Correct labeling of graphs and tables is criticalcritical if any useful if any useful information is to be learned or derived from them.information is to be learned or derived from them.

Examples of Mathematical EfficiencyExamples of Mathematical Efficiency

• Which would you rather use? Why?Which would you rather use? Why?A:A: The length of a football field is one hundred yards The length of a football field is one hundred yards

B:B: ll = 100 = 100 ydsyds

A:A: 32,738 32,738

B:B: Thirty Two Thousand, Seven Hundred Thirty Eight Thirty Two Thousand, Seven Hundred Thirty Eight

• What does this mean?What does this mean?

4 4 inin

16 16 inin

A = 64 A = 64 inin22

Information can be transmitted withoutInformation can be transmitted withoutusing any words at all!using any words at all!

What if you can’t speak the What if you can’t speak the language?language?

You will You will NOTNOT be able to understand the thoughts or be able to understand the thoughts or information being presented, which will likely cause information being presented, which will likely cause

confusion and/or frustration.confusion and/or frustration.

ExEx.. SpanishSpanish

El chocolate es regalo del dios a la humanidadEl chocolate es regalo del dios a la humanidad

** With a common reference system and language, it is ** With a common reference system and language, it is much easier to develop analogies or models that much easier to develop analogies or models that others can understand.others can understand.

SummarySummary

• StoriesStories were used by ancient civilizations to explain were used by ancient civilizations to explain the workings of the natural world.the workings of the natural world.

• PhysicsPhysics is the discipline where man attempts to is the discipline where man attempts to explain the motion and interactions of the physical explain the motion and interactions of the physical universe as completely and accurately as possible.universe as completely and accurately as possible.

• Scientists communicate their models to others using Scientists communicate their models to others using the language of mathematics and a reference system the language of mathematics and a reference system built around a set of established built around a set of established unitsunits..

In the beginning you laid In the beginning you laid the foundations of the the foundations of the earth, and the heavens are earth, and the heavens are the work of your hands.the work of your hands.

Psalms 102:25Psalms 102:25