IntroductionChapter 1
Getting prepared!!!
Chapter 1,Introduction
Measurement,Models,
Theories and Laws
Vector and Scalar
IntroductionChapter 1
1-1 Models,theories,and laws (P3)
Model,is a kind of mental image of the
phenomena in terms of something are familiar
with.
Theory,is broader,more detailed,and
attempts to solve a set of phenomena.
Law,are general statements about how nature
behaves,The statement takes the form of a
relationship or equation ( 方程 ) between
quantities (量 ).
IntroductionChapter 1
1-2 Measurement and Uncertainty;
Significant Figures(P3-5)
Physics is based on measurement of physical
quantities (物理量 ),P3
Significant Figures(有效数字 ),The number of
reliably known digits in a number is called the
number of significant figures,P4
IntroductionChapter 1
Mass of the Earth:
5,980,000,000,000,000,000,000,000kg
or 5.98x1024kg
Diameter of proton（质子）,
0.000000000000001m
or 10-15m (or 1 E-15 on computers)
The advantage is that it allows the number of
significant figures to be clearly expressed.
Scientific notation (科学记数法 (p4)
Write numbers in,powers of ten”.
IntroductionChapter 1
1-4 Units,Standards,and the SI System (P5-7)
Unit (单位 ):
We measure each physical quantity in its own
units(单位 ) by comparison with a standard,P5
SI System (国际单位制 ),There are so many
physical quantities that it is a problem to
organize them,Fortunately,they are not all
independent （ 独立 ）,P7
IntroductionChapter 1
In 1971,the 14th General Conference onWeights and Measures,The SI (International
System) was adopted.
It is based on meter,second and kilogram.
It is also called Metric System (公制 ） or MKSsystem.
Many SI (System International) derived units
are defined in terms of these base units,such as:
1 watt = 1 W = 1 kg ·m 2 / s3
The second metric system is CGS(P7),in which
the centimeter,gram,and second are the
standard units of length,mass and time.
IntroductionChapter 1
exa E 1018
peta P 1015
tera T 1012
giga G 109
Mega M 106
kilo k 103
Hecto h 102
deka da 101
deci d 10-1
centi c 10-2
milli m 10-3
Micro? 10-6
nano n 10-9
pico p 10-12
femto f 10-15
atto a 10-18
Shorthand and some commonly used units (P7)
IntroductionChapter 1
Base quantities(基本量 ),length,time,mass.
Base units(基本单位 ),meter,second,kilogram.
Derivative quantities( 导 出 量 ),The
quantities derived from base quantities
such as,velocity,acceleration,
Derivative units( 导 出 单 位 ),The units
derived from base units such as,m/s m/s2.
Consistent set of units
IntroductionChapter 1
One meter is the length of path traveled by light
in a vacuum during a time interval（ 间隔 ） of
1/299792458 of a second,P5
One second is the time taken by 9192631770
oscillations(振动 ) of the light emitted by a cesium（ 铯 ）
-133 atom.
One kilogram is defined in terms of(根据、按照）
a particular platinum-iridium（铂铱） cylinder（柱体） kept near Paris,France,
For measurements on an atomic scale,the atomic
mass unit,defined in terms of the atom carbon-12,is
usually used,1u=1.6605402x10-27 kg
（ 1） Length （长度 P5）,
（ 2） Time（时间 P6）,
（ 3） Mass（质量 P6）,
IntroductionChapter 1
Some scalars are always positive,whereas others
such as electric charge can be positive or negative.
Fa n davr,,
Scalar (标量 ),A ordinary algebraic (代数的 )
quantity that has no direction,(mass,time,
temperature,… )
Vector (矢量 ),A quantity that has both direction
(方向 ) and magnitude (大小 ) it (displacement 位移,velocity速度,acceleration加速度,force力 ).
3-1 Vectors and Scalars (P44-45)
IntroductionChapter 1
Presentation of vector,
On a diagram,each vector is represented by an
arrow.
C?
Symbol,boldface type,(In handwritten work,the
symbol for a vector can be indicated by putting
an arrow over it.
.),...,,( et cFa n davr
IntroductionChapter 1
Vectors follow certain vector rules of combination.
A?
C?
B?
Adding Vectors Graphically
The vector sum is the vector that extends from
the tail of one vector to the head of the other
vector------tail-to-tip method of adding
vectors.(p46)
3-2 Addition of Vectors (P45-46)
IntroductionChapter 1
A?
C?
B?
Parallelogram Method,(P46)
Is fully equivalent to the tail-to-tip method,
The two vectors are drawn starting from a
common origin,and a parallelogram is
constructed using these two vectors as adjacent
sides.
IntroductionChapter 1
)( BABAC
C
A?
B
1 Subtracting Vectors Graphically(p46)
B?
C
A?
B?
The difference between two vectors is the
vector that extends from the head of the 2nd
vector to the head of the 1st vector.
3-3 Subtraction of Vectors,
Mulitiplication of a Vector (P46-47)
IntroductionChapter 1
zzyyxx BBBC AAA
A?
B?
c o sB
A?
B?
c o sA
(1) The Scalar (Dot) Product (点积 ):
2 Multiplying a Vector by a Vector
CBA
c o sABC?
IntroductionChapter 1
CBA
(2) The Vector (Cross) Product (叉积 )
zyx
zyx
BBB
kji
C AAA
kBB
jBBiBBC
xyyx
zxxzyzzy
)AA(
)AA(?)AA(
CAB C?
B?
A?
C
Direction is as the figure showing.
,s i n?ABBA
IntroductionChapter 1
A component of a vector is the
projection of the vector on an
axis,This component may be in
two or three dimensional
coordinate system.
x
yyx vvvvvtan an d 22
is resolved to and,v? xv yv
s i n a n d c o s vvvv yx jvivv yx
v?
o
y
x
yv
xv
3-4 Components of Vectors (P47-51)
IntroductionChapter 1
For a fixed Cartesian system,Unit vectors,
Unit Vector is defined to have a magnitude (数量 )
exactly equal to one,
In the coordinate system,
Coordinate system can be chosen freely (arbitrary).
kAjAiAA zyx
kji,,
—— unit magnitude,only indicate directions
3-5 Unit Vectors (P51)
IntroductionChapter 1
P69:11
IntroductionChapter 1
Summary for Chapter One
See P12
Getting prepared!!!
Chapter 1,Introduction
Measurement,Models,
Theories and Laws
Vector and Scalar
IntroductionChapter 1
1-1 Models,theories,and laws (P3)
Model,is a kind of mental image of the
phenomena in terms of something are familiar
with.
Theory,is broader,more detailed,and
attempts to solve a set of phenomena.
Law,are general statements about how nature
behaves,The statement takes the form of a
relationship or equation ( 方程 ) between
quantities (量 ).
IntroductionChapter 1
1-2 Measurement and Uncertainty;
Significant Figures(P3-5)
Physics is based on measurement of physical
quantities (物理量 ),P3
Significant Figures(有效数字 ),The number of
reliably known digits in a number is called the
number of significant figures,P4
IntroductionChapter 1
Mass of the Earth:
5,980,000,000,000,000,000,000,000kg
or 5.98x1024kg
Diameter of proton（质子）,
0.000000000000001m
or 10-15m (or 1 E-15 on computers)
The advantage is that it allows the number of
significant figures to be clearly expressed.
Scientific notation (科学记数法 (p4)
Write numbers in,powers of ten”.
IntroductionChapter 1
1-4 Units,Standards,and the SI System (P5-7)
Unit (单位 ):
We measure each physical quantity in its own
units(单位 ) by comparison with a standard,P5
SI System (国际单位制 ),There are so many
physical quantities that it is a problem to
organize them,Fortunately,they are not all
independent （ 独立 ）,P7
IntroductionChapter 1
In 1971,the 14th General Conference onWeights and Measures,The SI (International
System) was adopted.
It is based on meter,second and kilogram.
It is also called Metric System (公制 ） or MKSsystem.
Many SI (System International) derived units
are defined in terms of these base units,such as:
1 watt = 1 W = 1 kg ·m 2 / s3
The second metric system is CGS(P7),in which
the centimeter,gram,and second are the
standard units of length,mass and time.
IntroductionChapter 1
exa E 1018
peta P 1015
tera T 1012
giga G 109
Mega M 106
kilo k 103
Hecto h 102
deka da 101
deci d 10-1
centi c 10-2
milli m 10-3
Micro? 10-6
nano n 10-9
pico p 10-12
femto f 10-15
atto a 10-18
Shorthand and some commonly used units (P7)
IntroductionChapter 1
Base quantities(基本量 ),length,time,mass.
Base units(基本单位 ),meter,second,kilogram.
Derivative quantities( 导 出 量 ),The
quantities derived from base quantities
such as,velocity,acceleration,
Derivative units( 导 出 单 位 ),The units
derived from base units such as,m/s m/s2.
Consistent set of units
IntroductionChapter 1
One meter is the length of path traveled by light
in a vacuum during a time interval（ 间隔 ） of
1/299792458 of a second,P5
One second is the time taken by 9192631770
oscillations(振动 ) of the light emitted by a cesium（ 铯 ）
-133 atom.
One kilogram is defined in terms of(根据、按照）
a particular platinum-iridium（铂铱） cylinder（柱体） kept near Paris,France,
For measurements on an atomic scale,the atomic
mass unit,defined in terms of the atom carbon-12,is
usually used,1u=1.6605402x10-27 kg
（ 1） Length （长度 P5）,
（ 2） Time（时间 P6）,
（ 3） Mass（质量 P6）,
IntroductionChapter 1
Some scalars are always positive,whereas others
such as electric charge can be positive or negative.
Fa n davr,,
Scalar (标量 ),A ordinary algebraic (代数的 )
quantity that has no direction,(mass,time,
temperature,… )
Vector (矢量 ),A quantity that has both direction
(方向 ) and magnitude (大小 ) it (displacement 位移,velocity速度,acceleration加速度,force力 ).
3-1 Vectors and Scalars (P44-45)
IntroductionChapter 1
Presentation of vector,
On a diagram,each vector is represented by an
arrow.
C?
Symbol,boldface type,(In handwritten work,the
symbol for a vector can be indicated by putting
an arrow over it.
.),...,,( et cFa n davr
IntroductionChapter 1
Vectors follow certain vector rules of combination.
A?
C?
B?
Adding Vectors Graphically
The vector sum is the vector that extends from
the tail of one vector to the head of the other
vector------tail-to-tip method of adding
vectors.(p46)
3-2 Addition of Vectors (P45-46)
IntroductionChapter 1
A?
C?
B?
Parallelogram Method,(P46)
Is fully equivalent to the tail-to-tip method,
The two vectors are drawn starting from a
common origin,and a parallelogram is
constructed using these two vectors as adjacent
sides.
IntroductionChapter 1
)( BABAC
C
A?
B
1 Subtracting Vectors Graphically(p46)
B?
C
A?
B?
The difference between two vectors is the
vector that extends from the head of the 2nd
vector to the head of the 1st vector.
3-3 Subtraction of Vectors,
Mulitiplication of a Vector (P46-47)
IntroductionChapter 1
zzyyxx BBBC AAA
A?
B?
c o sB
A?
B?
c o sA
(1) The Scalar (Dot) Product (点积 ):
2 Multiplying a Vector by a Vector
CBA
c o sABC?
IntroductionChapter 1
CBA
(2) The Vector (Cross) Product (叉积 )
zyx
zyx
BBB
kji
C AAA
kBB
jBBiBBC
xyyx
zxxzyzzy
)AA(
)AA(?)AA(
CAB C?
B?
A?
C
Direction is as the figure showing.
,s i n?ABBA
IntroductionChapter 1
A component of a vector is the
projection of the vector on an
axis,This component may be in
two or three dimensional
coordinate system.
x
yyx vvvvvtan an d 22
is resolved to and,v? xv yv
s i n a n d c o s vvvv yx jvivv yx
v?
o
y
x
yv
xv
3-4 Components of Vectors (P47-51)
IntroductionChapter 1
For a fixed Cartesian system,Unit vectors,
Unit Vector is defined to have a magnitude (数量 )
exactly equal to one,
In the coordinate system,
Coordinate system can be chosen freely (arbitrary).
kAjAiAA zyx
kji,,
—— unit magnitude,only indicate directions
3-5 Unit Vectors (P51)
IntroductionChapter 1
P69:11
IntroductionChapter 1
Summary for Chapter One
See P12
