Ch.

1 Doing Physics

• SI unit system
– SI base units
Optional
– Dimension
• Numbers in physics calculations
- Scientific notation Important
- Accuracy and significant figures
Q… What is the volume of the soda cans/bottles?

355
mL 500
250 mL
mL 355
mL

Why 355 mL? Not 350 mL or 333 mL (=1/3 L)

12 oz = 354.882 mL
oz : US fluid ounce
“Ounce” in US and UK

8 oz=1 cup 10 oz=1 cup

16 oz=2 cup = 1 pint 20 oz=2 cup = 1 pint
32 oz=4 cup = 2 pint = 1 qurt 40 oz=4 cup = 2 pint = 1 qurt
128 oz=16 cup = 8 pint = 4 qurt = 1 gallon 160 oz=16 cup = 8 pint = 4 qurt = 1 gallon
Americano: espresso shots
1 2 3 4

8 oz 12 oz 16 oz 24 oz 31 oz
SI unit system
 Metric vs. US custom unit

• Science vs. industry standard

• International vs. regional standard
 Metric vs. US custom unit
Wrench set

Hex key (Allen wrench)

Large Hadron Collider
 Failure of Mars Climate Orbiter (1999)

$125 million
(~ \ 1800억)

current vaule
~$ 230M

• Due to complications arising from human error, the spacecraft encountered

Mars at a lower than anticipated altitude and disintegrated due to atmospheric
stresses.
• The primary cause of the discrepancy was that one piece of ground
software produced results in a “United States customary unit” , while a second
system, supplied by NASA, expected those results to be in SI units.
More reading at https://en.wikipedia.org/wiki/Mars_Climate_Orbiter
 SI unit
International System of Units
( Le Système International d'unités)
• 7 fundamental physical quantities (base units)
– Length: m (meter) Derived units (Combinations of SI units)
– Mass: kg (kilogram) N, J ? e.g. : N=kg m/s2
J = kg m2/s2
– Time: s (second)
˚C
– Electric current: A (ampere) Non-SI unit: mile, feet, pound, oz
– Temperature: K (kelvin)
– Amount of a substance: mol (mole)
Non-SI units accepted for use with the SI
– Luminous intensity: cd (candela) min, h, d (day), ˚ (angle) , L, ton (t), au, eV

• Supplementary units describing angles h, L, ˚ ?

– Plane angle: rad (radian)
– Solid angle: sr (steradian)

(See Appendix B in the textbook) Note: BTU, cal, atm also often used.
physics.nist.gov/cuu/Units/SIdiagram.html
 Q: Then how long is 1 m, and
who can tell you have an accurate ruler?
These institutes provide standards for measurements
 Metrology
: scientific study of measurement including 1) definition of
units of measurement, 2) realization of these units of
measurement in practice, 3) traceability, which is linking
measurements made in practice to the reference standards.
 Definitions of the meter
Date Basis of definition
1/10,000,000 part of the quadrant along the meridian, measurement
1795
by Delambre and Méchain
1799 First prototype Mètre des Archives platinum bar standard
1889 Platinum-iridium bar at melting point of ice (1st CGPM)
Platinum-iridium bar at melting point of ice, atmospheric pressure,
1927
supported by two rollers (7th CGPM)
Hyperfine atomic transition; 1650763.73 wavelengths of light from a
1960
specified transition in krypton-86 (11th CGPM)
Length of the path travelled by light in a vacuum in 1/2999792458
1983
second (17th CGPM) CGPM: Conférence Générale des Poids et Mesures
(The General Conference on Weights and Measures)

https://physics.nist.gov/cuu/Units/meter.html https://www.nist.gov/nist-museum/museum-collection/exhibits
 Definitions of the kilogram
Date Basis of definition
The gram, 1/1000 of a kilogram, was provisionally defined as the mass
1795
of one cubic centimeter of water at the melting point of ice
Kilogramme des Archives (Kilogram of the Archives) was built and the
1799 kilogram was defined as being equal to its mass. (equal to the mass of
one cubic decimeter of water at 4 °C.)
1889 International Prototype Kilogram (IPK) replaced the old standard.
The kilogram is defined by setting the Planck constant h exactly to
2019. 05 6.626070040×10−34 J⋅s (J = kg⋅m2⋅s−2), given the definitions of the
meter and the second (https://www.nist.gov/si-redefinition/kilogram)
 2019 redefinition of SI base units

- Redefinition of SI base units adopted at the 26th General

Conference on Weights and Measures (CGPM) on 16 November
2018 and become effective on 20 May 2019
https://en.wikipedia.org/wiki/2019_redefinition_of_SI_base_units
https://physicstoday.scitation.org/do/10.1063/PT.6.2.20181116a/full/
 Definitions of the SI base units
Unit of The meter is the length of the path travelled by light in vacuum during a time interval
meter
length of 1/299 792 458 of a second.

Unit of The kilogram is defined by setting the Planck constant h exactly to 6.62607015×10−34 J⋅s (J =
kilogram
mass kg⋅m2⋅s−2), given the definitions of the meter and the second

Unit of The second is the duration of 9 192 631 770 periods of the radiation corresponding to the
second
time transition between the two hyperfine levels of the ground state of the cesium 133 atom.

Unit of
The ampere is expected to be defined by setting the fixed numerical value of the elementary
electric ampere
charge e to 1.602176634×10−19 C (C = A⋅s), given the definition of the second.
current

Unit of The kelvin is expected to be defined by setting the fixed numerical value of the Boltzmann
thermodynamic kelvin constant k to 1.380649×10−23 J⋅K−1, (J = kg⋅m2⋅s−2), given the definition of the kilogram, the
temperature meter and the second.

Unit of The amount of substance of exactly 6.02214076×1023 elementary entities. This number is
amount of mole the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1
substance and is called the Avogadro number.

Unit of It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic
luminous candela radiation of frequency 540×1012 Hz, Kcd, to be 683 when expressed in the unit lm/W, which
intensity is equal to cd sr/W
 Unit check up & Dimensional analysis
m 𝐿𝐿
Length: m  [L] Speed: = = [L][T]–1
s 𝑇𝑇
Mass: kg  [M]
Time: s  [T] Force (N : kg m/s2 ); [M] [L][T] –2
Energy (J : kg m2/s2 ); [M] [L]2[T] –2
1
𝐹𝐹𝐹𝐹, 𝑚𝑚𝑚𝑚𝑚, 𝑚𝑚𝑣𝑣 2 , 𝑝𝑝𝑝𝑝
2

Suppose the position of a particle as a function of time is

given by
The dimensions of the coefficient c are
–1 –1 –3 –1 3
A) [L] [T] B) [L][T] C) [L] [T]
3 –1
D) [L][T] E) [L] [T]
 Numbers in Science
Scientific notation & SI prefix
Realms of physics
 Realms of physics

• Classical mechanics
• Thermodynamics and statistical mechanics
• Electromagnetism and electronics
• Relativity
• Quantum mechanics
• Optics,
• Atomic and molecular physics
• Condensed matter physics
• High energy/particle physics and nuclear physics
• Cosmology (astrophysics)
• Interdisciplinary fields (biophysics, chemical physics, econophysic
s, etc.)
 Basic domains of physics
What do you study within Physics?

10-9 m

109 m

Size of
Nucleus: ~ 10-14 m
Atom: ~ 10-10 m
Solar system : 1.5 x 1011 m
Universe: ~ 1026 m

wikipedia.org
 Scientific notation
• Best expressed with ordinary-sized numbers multiplied by powers
of 10.
– 31415.9 = 3.14159×104
– 0.002718 = 2.718×10–3

• SI prefixes describe powers of 10:

e.g.) 1.6×10–8 m = 16×10–9 m
= 16 nm

110 KM/h ????  110 km/h

http://htwins.net/scale2/
 What we study in Physics
1026 m

String theory: 10-35 m http://htwins.net/scale2/

Range of Mass (kg) Range of Time (s)

Mass of observable
1052 Age of the universe 1017
universe

Mass of the Sun 1030 Typical human life span 109

Mass of proton 10-27 1 year 107
Mass of electron 10-30 Light pass across atom 10-19

* Photon: No mass
 Number and measurement
• Measures of physical quantities are within the limits of “the
experimental uncertainty”
 Number and measurement
Example #1:
From the entrance gate of KAIST to E11 building is 1.2 km. The
distance from the front door to the class room is 45 m. Then the
distance from the front gate to class room is 1245 m??

Example #2:
You measured the width and length of a object as 16.3 cm and 4.5
cm, then what is the area?
 Area = Length × Width = 16.3 cm × 4.5 cm = 73.35 cm2 ???

Example #3:
You measured the width of the objects three times: 4.5 cm, 4.7 cm,
4.7 cm. Average width of the object is: 4.6333333…………cm ?? or
46333333 nm?
You need to consider the significant figures !
 Scientific notation and significant figures
Significant figures : Digits that carry meaningful contributions to its
measurement resolution
Zeros may or may not be significant figures
4 zeros for positioning the decimal point
0.00075
2 significant figures
3 zeros as significant figures

0.00075000
5 significant figures

Thus, it is convenient to have ordinary-sized numbers multiplied by

powers of 10.
0.002718 = 2.718×10–3
0.00075 = 7.5×10–4
0.00075000 = 7.5000×10–4
 Significant figures Rule #1
The number of significant figures
Length = 16.3 cm Width = 4.5 cm
3 significant figures 2 significant figures

Rule#1: when multiply or divide, the number of significant

figures in the final answer should be the same as the lowest
number of significant figures used

 Area = Length × Width = 16.3 cm × 4.5 cm = 73.35 cm2 (X)

 Area = Length × Width = 16.3 cm × 4.5 cm = 73.35 cm2  73 cm2 (O)

2 significant figures
 Significant figures Rule #2

Rule#2: when add or subtract, the number of decimal place in

the result should be the same as the smallest number of decimal
places of any term in the sum
Example,

123 m + 5.65 m = 128.65 m (X)

123 m + 5.65 m = 128.65 m  129 m (O)

Round up
 Significant figures Rule #2

Rule#2: when add or subtract, the number of decimal place in

the result should be the same as the smallest number of decimal
places of any term in the sum
Example,

123 m + 5.65 m = 128.65 m (X)

123 m + 5.65 m = 128.65 m  129 m (O)

Round up

https://en.wikipedia.org/wiki/Significant_figures
 Precision & accuracy
•Precision is a description of random errors, a measure
of statistical variability
•Accuracy is a description of systematic errors, a measure
of statistical bias; as these cause a difference between a
result and a "true" value, ISO calls this trueness.
 Converting Units
Conversion of unit: handle the units like parameters.
𝐹𝐹 = 𝑚𝑚𝑚𝑚, 1 𝑁𝑁 = 1 𝑘𝑘𝑘𝑘 � (1 𝑚𝑚/𝑠𝑠 2 ) N=kg∙m/s2

Example 1 : 5280 ft (1 mi) is equal to m. (1 ft = 0.3048 m)

0.3048 m
5280 ft = 5280 ft ⋅ 1 = 5280 ft ⋅ = 1609 m
1 ft

5280 × 0.3048 = 1609.3440

Example 2 : 343 kWh is equal to J. (1 kWh=3.60 MJ)

3.60 MJ
343 kWh = 1.23 × 103 MJ = 1.23 GJ
1 kWh

343 × 3.60 = 1.2348

The density of aluminum is about
𝝆𝝆 = 𝟐𝟐. 𝟕𝟕𝟕𝟕 𝒈𝒈/𝒄𝒄𝒄𝒄𝟑𝟑 in SI units, this is equal to
a. 2.70 × 103 kg m3 .
b. 2.70 kg m3 .
c. 2.70 × 102 kg m3 .
d. 2.70 × 106 kg m3 .
e. 2.70 × 105 kg m3 .
 Estimation
• What’s the United States’ yearly gasoline
consumption?

1. There are about 300 million people in the U.S., so perhaps

about 100 million cars (108 cars).
2. A typical car goes about 10,000 miles per year (104 miles).
3. A typical car gets about 20 miles per gallon.
4. So in a year, a typical car uses (104 miles)/(20 miles/gallon) =
500 gal.
5. So the United States’ yearly gasoline consumption is about
(500 gal/car)(108 cars) = 5×1010 gallons.

 That’s about 20×1010 L or 200 GL.

A reasonable order-of-magnitude estimate
of the mass of a small raindrop is
a. 10−1 kg.
b. 10−3 kg.
c. 10−6 kg.
d. 10−9 kg.
e. 10−12 kg.
 Chapter summary
• SI unit system
7 fundamental physical quantities:
– Length: m (meter)
– Mass: kg (kilogram)
– Time: s (second)
– Electric current: A (ampere)
– Temperature: K (kelvin)
– Amount of a substance: mol (mole)
– Luminous intensity: cd (candela)
• Numbers in physics calculations
Scientific notation: 0.002718 = 2.718×10–3
Accuracy and significant figures (Addition & Multiplication)
• Remember the significant figures rules !
 Announcement
• No class on this Wed (2/26)
• Next Mon (3/3): Holiday
• Assigned seat for attendance check.
The seat you pick on Next Wed (3/5) will be
Your Assigned Seat until the midterm exam.