General Physics
National Taichung University
Tsung-Wen Yeh
Content
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1. Physics, Mathematics, and the Real World
2. One Dimensional Kinematics
3. Two Dimensional Kinematics
4. Particle Dynamics I
5. Particle Dynamics II
6. Work and Energy
7. Conservation of Mechanical Energy
8. Linear Momentum
9. System of Particles
10. Rotational Motion
Content
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11.Gravitation
12. Solids and Fluids
13.Oscillations
14.Mechanical Waves
15. Sound
16. Temperature, Thermal Expansion, and Ideal Gas
Law
17. First Law of Thermodynamics
18. Kinetic Theory
19. Entropy and The Second Law of Thermodynamics
20. Electrostatics
21 The Electric Fields
Content
 22. Quantitative Treatment of Current and Circuit
Elements
 23. Quantitative Circuit Reasoning
 24. Magnetism and Magnetic Fields
 25. Electromagnetic Induction
 26. As the Twentieth Century Opens: The Unanswered
Questions
 27. Relativity
 28. Inroad into the Micro-Universe of Atoms
 29. The Concept of Quantization
 30. The Nucleus and Energy Technologies
 31. The Elementary Particles
 32. The Standard Model and 21st Century Physics
Text Books
 Main text book:
 Introductory Physics, building
understanding, Jerold Touger
 Reference books:
 University Physics, Harris Benson
 Principles of Physics, Serway & Jewett
 Fundamentals of Physic, Halliday,
Resnick, & Walker
Scores
 100 Excercises： 40％
 Final exam：20％
 4 tests：40％
What Is Physics ?
 Physics is the activity of trying to find
the rules by which nature plays.
 We Believe that
“There are rules, that nature is in some
sense orderly”
What Is Physics ?
 Physics is the activity of trying to find
the rules by which nature plays.
 We Believe that
“There are rules, that nature is in some
sense orderly”
What Is Physics ?
 Physics is the activity of trying to find
the rules by which nature plays.
 We Believe that
“There are rules, that nature is in some
sense orderly”
What Is Physics ?
 Physics is the activity of trying to find
the rules by which nature plays.
 We Believe that
“There are rules, that nature is in some
sense orderly”
Rules : Our Brain Can Imagine
What Is Physics ?
 Physics is the activity of trying to find
the rules by which nature plays.
 We Believe that
“There are rules, that nature is in some
sense orderly”
Order : In Lit., Soc., Math, Eco., Bio., etc. forms
In Words
 Physics is a fundamentally human
activity.
The most beautiful experience
we can have is the mysterious.
It is the fundamental emotion
that stands at the cradle of
true art and true science.
--Albert Einstein
In Words
 Science and the arts are somewhat
alike.
There is no science without fancy,
No art without facts.
--Vladimir Nabokov
In Words
 Physics, like all true science, require
collective understanding—not just
how I understand something but
reaching agreement on how we
understand it.
Art is I.
Science is we.
--Claude Bernard
緒論
 為何要學習科學？
1. 科學提供一種有力的工具使我們能瞭解周
遭的世界是如何運作，及我們又是如何與
環境產生互動。
2. 科學知識與日常生活息息相關。
科學方法
 科學方法由四個步驟所組成：
1. 觀察：瞭解大自然最直接的方法就是觀察
它是如何運作，及運作的原因。
2. 自眾多現象中尋找規律及規則性。
3. 設定假設及建立理論。
4. 預測及測試。
科學方法-四步驟循環
找出規律
觀察
實驗
數據
偏見
預測
假設
科學信條：
任何新實驗，
都可能改變一已成立的理論或定律。
科學定律
 科學定律的形成：
1. 假設：一種出於富有經驗的嘗試性猜測。
2. 理論：一種對物理世界的描述能同時涵蓋
自然現象及通過實驗的驗證。
3. 定律：當理論已經過相當多的驗證且此理
論應當在宇宙的任何一處皆成立。
科學的運作方法
1. 科學必須忠於實驗（觀察）所呈現的事實。
2. 由四步驟循環之任一步驟開始均應得到相同的結
論。
3. 科學結果必須是可複製的。
4. 四步驟循環是持續且沒有終點。
5. 科學與藝術或文學一樣，均是人類創造性活動的
結果，因此新發現常是充滿驚奇且沒有脈絡可尋。
分辨偽科學
 可以利用以下方法來檢驗某一學說是否屬
於偽科學：
1. 支持此學說的”事實”是否是事實？
2. 是否存在另一種解釋？
3. 其主張是否可證明為偽？
4. 其主張是否已經過嚴格檢驗？
5. 其主張是否與一些已被廣為接受的觀念之
間存在不合理的矛盾？
Chapter I Introduction
 What is Physics ?
 Who investigates the physics ? －
Physicists
 A physicist is a Scientist
 A Scientist retains childlike curiosity
and wonder about Nature
 Physics deals with the behavior and
composition of matter and its
interactions.
Classical Physics
 Physics developed in 1600~1900 are
called classical physics
 Classical Mechanics
 Thermodynamics
 Electromagnetism
Modern Physics
 After 1905, the lately developed
physics are called modern physics
 Special Relativity
 Quantum Mechanics
 General Relativity
The Goal of Physicists
 To Explain physical phenomena in
simplest and most economical
terms, i.e., elegant form
Classifications of physics
 Concept: a physical quantity can be used to
analyze natural phenomena
 Laws & Principles: math’s relationships－
laws； general statements－principles
 Models: a convenient representation of a
physical system
 Theories: a theory uses a combination of
priciples, a model, and initial assumptions to
deduce specific consequences or laws
Category of Physics
The Goal of Physicists
 Matter Hierarchy:
matter
atoms
nuclei
protons
2U quarks
1 D quark
neutrons
electrons
1 U quark
2 D quarks
The Goal of Physicists
Four
Basic
Interactions:
Forces
Strong
EM
Weak
ElectroWeak
Grand-Unified
Unified
Gravity
Measurement and Units
Distance Measurements
 Very Large distance
 Tiny distance
Very Large Objects
 10^21 meter
 10^42 Kilogram
Tiny Objects
 Each pits has
4x10^-7 meter
Systeme Internationale (SI Units)
Mass
Units
 SI – kilogram, kg
Defined in terms of kilogram,
based on a specific cylinder kept
at the International Bureau of
Weights and Measures
See table 1.2 for masses of various
objects
Time
Units
 Seconds, s
Historically defined in terms of a solar
day, as well as others
Now defined in terms of the
oscillation of radiation from a
cesium atom
See table 1.3 for some approximate
time intervals
Length
 Units
 SI – meter, m
 Historically length has had many definitions
 Length is now defined in terms of a
meter – the distance traveled by light in
a vacuum during a given time
 See table 1.1 for some examples of lengths
Systems of Measurements, SI
Summary
SI System
 Most often used in the text
Almost universally used in science and
industry
 Length is measured in meters (m)
 Time is measured in seconds (s)
 Mass is measured in kilograms (kg)
Number Notation
When writing out numbers with many
digits, spacing in groups of three will
be used
 No commas
Examples:
 25 100
 5.123 456 789 12
Reasonableness of Results
When solving problem, you need to
check your answer to see if it seems
reasonable
Reviewing the tables of approximate
values for length, mass, and time will
help you test for reasonableness
Significant Figures
 No mearsurement is completely
precise.
 Ex, you cannot read distance much
smaler than 0.001 m (1 mm) on a
meter stick.
 The number of places that you
can legitimately read with your
measuring instrument is called
the number of significant figures.
Significant Figures (cont.)
 A numerical value should always be
written to show the number of
significant figures.
 When you use your measured values
to calculate a result, you cannot claim
greater accuracy (more significant
figures) for your results than for the
measurements from which is came.
Example 1-2
Suppose A=2.000 m znd B=3.000 m are the measured lengths of
the two legs of a right triangle. You wish to calculate the length of
hypotenuse using the Pythagorean theorem:
 Rules:
A2  B 2  C 2
Prefixes
Prefixes correspond to powers of 10
Each prefix has a specific name
Each prefix has a specific abbreviation
Prefixes, cont.
 The prefixes can
be used with any
base units
 They are
multipliers of the
base unit
 Examples:
 1 mm = 10-3 m
 1 mg = 10-3 g
Fundamental and Derived
Quantities
 In mechanics, three fundamental quantities
are used
 Length
 Mass
 Time
 Will also use derived quantities
 These are other quantities that can be expressed
as a mathematical combination of fundamental
quantities
Density
Density is an example of a derived
quantity
It is defined as mass per unit volume
m

V
Units are kg/m3
Dimensional Analysis
 The basic quantities involved in the
definition of a derived quantity are
called its dimensions.
 Mass [M], Length [L], Time [T]
 Energy has a dimenion [MLT-2]
Dimensional Analysis
 Technique to check the correctness of an
equation or to assist in deriving an equation
 Dimensions (length, mass, time,
combinations) can be treated as algebraic
quantities
 Add, subtract, multiply, divide
 Both sides of equation must have the same
dimensions
Basic Quantities and Their
Dimension
Dimension has a specific meaning – it
denotes the physical nature of a
quantity
Dimensions are denoted with square
brackets
 Length – L
 Mass – M
 Time – T
Dimensional Analysis, cont.
 Cannot give numerical factors: this is its limitation
 Dimensions of some common quantities are given
below
Dimensional Analysis, example
Given the equation: x = 1/2 a t2
Check dimensions on each side:
L 2
L  2 T  L
T
The T2’s cancel, leaving L for the
dimensions of each side
 The equation is dimensionally correct
 There are no dimensions for the constant
Conversion of Units
When units are not consistent, you
may need to convert to appropriate
ones
Units can be treated like algebraic
quantities that can cancel each other
out
See Appendix A for an extensive list of
conversion factors
Conversion
Always include units for every quantity,
you can carry the units through the
entire calculation
Multiply original value by a ratio equal
to one
 The ratio is called a conversion factor
Example 15.0 in  ? cm
 2.54 cm 
15.0 in
  38.1 cm
 1 in 
Converting Units
 Different units are used in life
 Convert units into our favorite ones—
SI units
 Examples
 1 min = 60 s, 1 s = 1/60 min
 1 km = 1000 m
 1 kg = 1000 g
Example 1-1
A bus travels 110 km/h on open highway. What is this speed
in stand SI units ?
 Step 1: Choose SI units for answer
 Step 2: Write 110 km/h=110 km/1hr
 Step 3: Write the conversion relations:
 1 km = 1000 m, 1 h = 60 min,
 1 min =60s
 Step 4: In fractions
1km
1h
1min
 1,
 1,
1
1000m
60 min
60s
Example 1-1
A bus travels 110 km/h on open highway. What is this speed
in stand SI units ?
 Step 4: Multiply by 1 as many as
necessary
1km 1000m
1h
1min 110 000 m
110




 30.6 m/s
1h
1km 60 min 60s
3600 s
Order of Magnitude
 Approximation based on a number of
assumptions
 May need to modify assumptions if more precise
results are needed
 Order of magnitude is the power of 10 that
applies
 In order of magnitude calculations, the
results are reliable to within about a factor
of 10
Uncertainty in Measurements
There is uncertainty in every
measurement, this uncertainty carries
over through the calculations
 Need a technique to account for this
uncertainty
We will use rules for significant figures
to approximate the uncertainty in
results of calculations
Significant Figures
 A significant figure is one that is reliably
known
 Zeros may or may not be significant
 Those used to position the decimal point are not
significant
 To remove ambiguity, use scientific notation
 In a measurement, the significant figures
include the first estimated digit
Significant Figures, examples
 0.0075 m has 2 significant figures
 The leading zeroes are placeholders only
 Can write in scientific notation to show more
clearly: 7.5 x 10-3 m for 2 significant figures
 10.0 m has 3 significant figures
 The decimal point gives information about the
reliability of the measurement
 1500 m is ambiguous
 Use 1.5 x 103 m for 2 significant figures
 Use 1.50 x 103 m for 3 significant figures
 Use 1.500 x 103 m for 4 significant figures
Operations with Significant
Figures – Multiplying or Dividing
When multiplying or dividing, the
number of significant figures in the
final answer is the same as the
number of significant figures in the
quantity having the lowest number of
significant figures.
Example: 25.57 m x 2.45 m = 62.6
m2
 The 2.45 m limits your result to 3
significant figures
Operations with Significant
Figures – Adding or Subtracting
When adding or subtracting, the
number of decimal places in the result
should equal the smallest number of
decimal places in any term in the sum.
Example: 135 cm + 3.25 cm = 138
cm
 The 135 cm limits your answer to the
units decimal value
Operations With Significant
Figures – Summary
 The rule for addition and subtraction are
different than the rule for multiplication and
division
 For adding and subtracting, the number
of decimal places is the important
consideration
 For multiplying and dividing, the number
of significant figures is the important
consideration
Rounding
 Last retained digit is increased by 1 if the
last digit dropped is 5 or above
 Last retained digit is remains as it is if the
last digit dropped is less than 5
 If the last digit dropped is equal to 5, the
retained should be rounded to the nearest
even number
 Saving rounding until the final result will
help eliminate accumulation of errors
More examples
 Addition/Subtraction
3.75 10  5.2 10  3.75 10  0.52 10  4.27 10
6
5
6
6
6
 Multiplication/Division
(3.0 108 m / s)(2.11010 s)  (3.0)(2.1) 108( 10) m  6.3 102 m
 Powers/Roots
(3.61104 )3  3.613 10(3)(4)  (47.04 1012 )1/ 2
 47.02 10(12)(1/ 2)  6.86 106
More examples
 Addition/Subtraction
 The answer should have the same number of digits
to the right of the decimal point as the term in the
sum or difference that has the smallest number of
digits to right of the decimal points.
 Multiplication/Division
 The answer should have the same number of
significant figures as the least accurate of the
quantity entering the calculation.
 Powers/Roots
 Raise the digits to the given power and multiply
the exponent by the power.
Exercises
1. (3.6  105 m)  (2.1 103 km) 
( m)
2. (4.2  103 m / s )  (0.57 ms)  ( m / s 2 )
3.[(5.1 102 cm)  (6.8  103  m)]  (1.8  104 N )
4. 3 (6.4  1019 )
5. (1.46 m)  (2.3 cm)
6. A 3.6-cm-long radio antenna is added to the front of an airplane
41 m long. What is the overall length ?
7. Repeat the Exercise 6 given that the airplane's length is 41.05 m.