Physics 121,Lecture 1,Pg 1
Physics 121,Sections,9,10,11,and 12
“General Physics”
Professor Robin C?té
Lecture 1
Agenda for Today
? Topic - Measurement and Units
?Fundamental units
?Systems of units
?Converting between systems of units
?Dimensional Analysis
?Significant digits
? Course Introduction
?Scope of the course
?Structure of the course
?what you have to do
Physics 121,Lecture 1,Pg 2
Announcements
? Homeworks posted on WedAssign
?You need to register (~ $10.00 by credit card)
?go to www.webassign.net and log in
? username,first letter of first name plus last name
e.g,John Fernando Lachance,jlachance
? institution,uconn
? password,your PeopleSoft ID #
? Homework will be posted on Friday.
Homework will be due by 1:00 AM the next Friday.
? Homework graded automatically (results known in class)
You can have up to 5 attempts per problem.
? Labs
?Begin next week
Physics 121,Lecture 1,Pg 3
Course Info
? Course has several components:
?Lecture,(me talking,demos and Active learning).
?Reading Assignments,from textbook.
?Homework Sets,mostly,context rich” problems.
?Tests,two midterms and a final.
?Questions on tests will look like those we do in the
rest of the class; in homework and during lectures.
?No surprises
?Labs,(group exploration of physical phenomena).
? More info on my website,www.phys.uconn.edu/~rcote
? Become familiar with the Physics Resource Center for
help in problem sets,Room P201.
Physics 121,Lecture 1,Pg 4
Lecture Organization
? Three main components:
?Lecturer discusses class material
?Topics from text
?Lecturer does demos/expts when possible
?Its not truth unless it makes a verifiable
prediction !
?You and I will interact with conceptual
“Active Learning” problems.
?Usually two or three per lecture
?Active Figures
?To illustrate concepts
Act
Physics 121,Lecture 1,Pg 5
Scope of Physics 121
? Classical Mechanics:
?Mechanics,How and why things work.
motion,balance,energy,vibrations
?Classical,
? Not too fast (v << c)
? Not too small (d >> atom)
? Most everyday situations can be described in these terms.
?Path of baseball
?Orbit of planets
?Vibrations of a piano wire
Physics 121,Lecture 1,Pg 6
Mechanics
? Motion in One and Two Dimension
? Laws of Motion
? Energy,Momentum and Collisions
? Rotational Motion and the law of Gravity
? Rotational Equilibrium and Dynamics
? Solids and Fluids
Physics 121,Lecture 1,Pg 7
Thermodynamics
? Thermal Physics
? Energy in Thermal Processes
? The Laws of Thermodynamics
Physics 121,Lecture 1,Pg 8
Vibrations and Waves
? Vibrations and Waves
? Sound
Physics 121,Lecture 1,Pg 9
Mathematical Notation
? Mathematical symbols
?????proportionality i.e,y ??x2
?<, is less than
?>, is greater than
?<<, is much less than
?>>, is much greater than
??, is approximately equal to
??, is defined as
Physics 121,Lecture 1,Pg 10
Scientific Notation
? Large number:
?100 = 1
?101 = 10
?102 = 100
? … etc
? Small numbers:
?10-1 = 0.1
?10-2 = 0.01
?10-3 = 0.001 … etc
Physics 121,Lecture 1,Pg 11
Scientific Notation
? The speed of light in vacuum
c ? 300 000 000 m/s
c ? 3.0 x 108 m/s
? The app,mass of a mosquito
m ? 0.00001 kg
m ? 10-5 kg
Physics 121,Lecture 1,Pg 12
Algebra
? Basic Rules
8x =32
8x/8 = 32/8
x = 4
x + 2 = 8
x + 2 - 2 = 8 – 2
x = 6
Physics 121,Lecture 1,Pg 13
Basic Rules
? Multiplying,(a/b)(c/d) = (ac)/(bd)
? Dividing,(a/b)/(c/d) = (ad)/(bc)
? Adding,a/b ± c/d = (ad ± bc)/(bd)
? Factoring:
ax + ay + az = a(x + y +z)
a2 + 2ab + b2 = (a + b)2
a2 - b2 = (a + b)(a –b)
Physics 121,Lecture 1,Pg 14
? The elements of substances and motion.
? All things in classical mechanics can be expressed in terms
of the fundamental quantities:
?Length L
?Mass M
?Time T
Standard Quantities
? Some examples of more complicated quantities:
?Speed has the quantity of L / T (i.e,miles per hour).
?Acceleration has the quantity of L/T2,
?Force has the quantity of ML/ T2 (as you will learn).
Physics 121,Lecture 1,Pg 15
Units
? SI (Système International) Units:
?mks,L = meters (m),M = kilograms (kg),T = seconds (s)
? British Units:
?L = inches,feet,miles,M = slugs (pounds),T = seconds
? We will use mostly SI units,but you may run across some
problems using British units,You should know how to convert
back & forth.
Physics 121,Lecture 1,Pg 16
Standards of Length
? Length is measured in Meters (m)
? The Meter is defined as the distance traveled by light in
1/299 792 458 second
? The speed of light is therefore 299 792 458 meters per
second.
? Used to be,one ten-millionth of the distance from the North
Pole to equator.
Physics 121,Lecture 1,Pg 17
Length:
Distance Length (m)
Radius of Visible Universe 1 x 1026
To Andromeda Galaxy 2 x 1022
To nearest star 4 x 1016
Earth to Sun 1.5 x 1011
Radius of Earth
Sears Tower 4.5 x 102
Football Field 1.0 x 102
Tall person 2 x 100
Thickness of paper
Wavelength of blue light
Diameter of hydrogen atom
Diameter of proton 1 x 10-15
6.4 x 106
1 x 10-4
4 x 10-7
1 x 10-10
Physics 121,Lecture 1,Pg 18
Order of Magnitude Calculations / Estimates
Earth’s radius?
? Need to know something from your experience:
?Flying from NYC to SF one accumulates ~ 3,500 miles
?NYC to SF spans about 1/6 of the Earth’s circumference
?So,the Earth’s circumference L = 3,500 x 6 ~ 20,000 mi
?Since circumference of a circle is, L = 2 ? r
?Estimate of Earth radius,
3x103 mi = 3x103 x 1.61 km ~ 5x103 km = 5x106 m??
r ? L2 ? ? 20,000 mi6 ? 3,000 mi
Physics 121,Lecture 1,Pg 19
Standards of Time
? Time is measured in Seconds (s)
? The Second in defined as 9 192 631 700 times the period
of radiation form a cesium atom.
? Used to be,(1/24)(1/60)/(1/60) of a average length of solar
day in 1900
Physics 121,Lecture 1,Pg 20
Time:
Interval Time (s)
Age of Universe 5 x 1017
Age of Grand Canyon 3 x 1014
Avg age of college student 6.3 x 108
One year
One hour
Light travel from Earth to Moon
One cycle of guitar A string 2 x 10-3
One cycle of FM radio wave 6 x 10-8
One cycle of visible light
Time for light to cross a proton 1 x 10-24
3.2 x 107
3.6 x 103
1.3 x 100
1 x 10-15
Physics 121,Lecture 1,Pg 21
Standards of Mass
? Mass is measured in Kilograms (Kg)
? The Kilogram is defined as the mass of a specific platinum-
iridium alloy cylinder kept at the International Bureau of
Weights and Measures at Sevres,France
? We are still using the,old” definition
Physics 121,Lecture 1,Pg 22
Mass:
Object Mass (kg)
visible universe ~ 1052
Milky Way galaxy 7 x 1041
Sun 2 x 1030
Earth 6 x 1024
Boeing 747 4 x 105
Car 1 x 103
Student 7 x 101
Dust particle 1 x 10-9
Bacterium 1 x 10-15
Proton 2 x 10-27
Electron 9 x 10-31
Physics 121,Lecture 1,Pg 23
The Building Blocks of Matter
? Atoms and Molecules
?Hydrogen atom ~ 10-10 m
? The Atomic Nucleus
?Atomic nucleus ~ 10-14 m
? Protons and neutrons
?Proton ~ 10-15 m
? Quarks,up,down,strange,
charmed,bottom,and top
Physics 121,Lecture 1,Pg 24
Some Prefixes for Power of Ten
Power Prefix Abbreviation
103 kilo k
106 mega M
109 giga G
1012 tera T
1015 peta P
1018 exa E
10-18 atto a
10-15 femto f
10-12 pico p
10-9 nano n
10-6 micro m
10-3 milli m
Physics 121,Lecture 1,Pg 25
Dimensional Analysis
? The word dimension has a special meaning in
Physics,It it the physical nature of a quantity.
? The dimension of a distance is Length,whether
we measure it in yards or meters.
? The dimension of Area A is [A] = L2
? The dimension of velocity v is written
[v] = L/T
Physics 121,Lecture 1,Pg 26
Dimensional Analysis
? Dimensions can be treated as algebraic
quantities
? They can be added or subtracted only if they
have the same dimensions.
? Both sides of and equation must have the same
dimensions.
? Dimensional analysis helps to determine whether
or not an expression has the correct form.
Physics 121,Lecture 1,Pg 27
? This is a very important tool to check your work
?It’s also very easy!
? Example:
Doing a problem you get the answer for distance
d = v t 2 ( velocity x time2 )
Quantity on left side = L
Quantity on right side = L / T x T2 = L x T
? Left units and right units don’t match,so answer must be
wrong !!
Dimensional Analysis
Physics 121,Lecture 1,Pg 28
Lecture 1,ACT 1
Dimensional Analysis
? The force (F) to keep an object moving in a circle
can be described in terms of the velocity (v,
dimension L/T) of the object,its mass (m,
dimension M),and the radius of the circle (R,
dimension L).
?Which of the following formulas for F could be correct?
Remember,Force has dimensions of ML/T2
R
mvF 2?2?
?
??
?
??
R
vmF(a) (b) (c)F = mvR
Physics 121,Lecture 1,Pg 29
Lecture 1,ACT 2
? There is a famous Einstein's equation connecting energy
and mass (relativistic),Using dimensional analysis find
which is the correct form of this equation,
Solution -> (b)
? Note,
?c is speed of light (L/T)
?E is energy (M L2 / T2)
??
E ? mc 3
??
E ? mc 2(a) (b) (c)
??
E ? mc
Physics 121,Lecture 1,Pg 30
Converting between different systems of units
? Useful Conversion factors:
?1 inch = 2.54 cm
?1 m = 3.28 ft
?1 mile = 5280 ft
?1 mile = 1.61 km
? Example,convert miles per hour to meters per second:
s
m
s
m
s
hr
ft
m
mi
ft
hr
mi
hr
mi
2
1447.0
3 6 0 0
1
28.3
15 2 8 011 ??????
Physics 121,Lecture 1,Pg 31
Lecture 1,ACT 3
Converting between different systems of units
? When on travel in Europe you rent a small car which consumes 6
liters of gasoline per 100 km,What is the MPG of the car?
? Useful Conversion factors:
?1 gallon = 4 liters
?1 mile = 1.61 km
??
100 km
6l ?
??
100 km
6 l ?
1 mi
1, 61 km ?
4 l
1 g a llo n
??
? 41 migallon
Solution
= 41 MPG !
Physics 121,Lecture 1,Pg 32
Significant Figures
? The number of digits that matter in a measurement or calculation,
? When writing a number,all non-zero digits are significant.
? Zeros may or may not be significant.
?those used to position the decimal point are not significant.
?those used to position powers of ten ordinals may or may not be
significant.
? in scientific notation all digits are significant
? Examples:
?2 1 sig fig
?40 ambiguous,could be 1 or 2 sig figs
?4.0 x 101 2 sig figs
?0.0031 2 sig figs
?3.03 3 sig figs
Physics 121,Lecture 1,Pg 33
Significant Figures
? When multiplying or dividing,the answer should have the
same number of significant figures as the least accurate of
the quantities in the calculation.
? When adding or subtracting,the number of digits to the
right of the decimal point should equal that of the term in
the sum or difference that has the smallest number of digits
to the right of the decimal point.
? Examples:
?2 x 3.1 = 6
?3.1 + 0.004 = 3.1
?4.0 x 101 ? 2.04 x 102 = 1.6 X 10-1
Physics 121,Lecture 1,Pg 34
Adding or Subtracting
? When numbers are added or subtracted,the
number of decimal places in the result equal the
smallest number of decimal places of any term in
the sum.
x = 123; y = 5.35
123.xxx
+ 5.35x
128.xxx
Physics 121,Lecture 1,Pg 35
Order-of Magnitude Calculations
? Sometimes it is necessary to know a quantity
only within a factor of 10
? This is know as an order of magnitude
? For example that is the total mass of everyone in
this class?
mass of a person m ~ 75 kg
Number of people n ~ 75
mTotal ~ 75 ′ 75 kg = 5625 kg ~ 6 ′ 103 kg
Physics 121,Lecture 1,Pg 36
Coordinate Systems
? A fixed reference point O,called the origin
? A set of specified axes,or direction,with an appropriate scale and labels
on the axes
? The Cartesian coordinate system,AKA the rectangular coordinate
system.
Physics 121,Lecture 1,Pg 37
Coordinate Systems
? Plane polar coordinates,(r,q)
Physics 121,Lecture 1,Pg 38
Recap of today’s lecture
? Measurement and Units (Chapter 1)
?Systems of units
?Density
?Converting between systems of units
?Dimensional Analysis
? Reading for today’s class:
?Chapter 1
? Reading for Thursday
?Chapter 2
? Homework #1,on Web at www.webassign.net
Physics 121,Sections,9,10,11,and 12
“General Physics”
Professor Robin C?té
Lecture 1
Agenda for Today
? Topic - Measurement and Units
?Fundamental units
?Systems of units
?Converting between systems of units
?Dimensional Analysis
?Significant digits
? Course Introduction
?Scope of the course
?Structure of the course
?what you have to do
Physics 121,Lecture 1,Pg 2
Announcements
? Homeworks posted on WedAssign
?You need to register (~ $10.00 by credit card)
?go to www.webassign.net and log in
? username,first letter of first name plus last name
e.g,John Fernando Lachance,jlachance
? institution,uconn
? password,your PeopleSoft ID #
? Homework will be posted on Friday.
Homework will be due by 1:00 AM the next Friday.
? Homework graded automatically (results known in class)
You can have up to 5 attempts per problem.
? Labs
?Begin next week
Physics 121,Lecture 1,Pg 3
Course Info
? Course has several components:
?Lecture,(me talking,demos and Active learning).
?Reading Assignments,from textbook.
?Homework Sets,mostly,context rich” problems.
?Tests,two midterms and a final.
?Questions on tests will look like those we do in the
rest of the class; in homework and during lectures.
?No surprises
?Labs,(group exploration of physical phenomena).
? More info on my website,www.phys.uconn.edu/~rcote
? Become familiar with the Physics Resource Center for
help in problem sets,Room P201.
Physics 121,Lecture 1,Pg 4
Lecture Organization
? Three main components:
?Lecturer discusses class material
?Topics from text
?Lecturer does demos/expts when possible
?Its not truth unless it makes a verifiable
prediction !
?You and I will interact with conceptual
“Active Learning” problems.
?Usually two or three per lecture
?Active Figures
?To illustrate concepts
Act
Physics 121,Lecture 1,Pg 5
Scope of Physics 121
? Classical Mechanics:
?Mechanics,How and why things work.
motion,balance,energy,vibrations
?Classical,
? Not too fast (v << c)
? Not too small (d >> atom)
? Most everyday situations can be described in these terms.
?Path of baseball
?Orbit of planets
?Vibrations of a piano wire
Physics 121,Lecture 1,Pg 6
Mechanics
? Motion in One and Two Dimension
? Laws of Motion
? Energy,Momentum and Collisions
? Rotational Motion and the law of Gravity
? Rotational Equilibrium and Dynamics
? Solids and Fluids
Physics 121,Lecture 1,Pg 7
Thermodynamics
? Thermal Physics
? Energy in Thermal Processes
? The Laws of Thermodynamics
Physics 121,Lecture 1,Pg 8
Vibrations and Waves
? Vibrations and Waves
? Sound
Physics 121,Lecture 1,Pg 9
Mathematical Notation
? Mathematical symbols
?????proportionality i.e,y ??x2
?<, is less than
?>, is greater than
?<<, is much less than
?>>, is much greater than
??, is approximately equal to
??, is defined as
Physics 121,Lecture 1,Pg 10
Scientific Notation
? Large number:
?100 = 1
?101 = 10
?102 = 100
? … etc
? Small numbers:
?10-1 = 0.1
?10-2 = 0.01
?10-3 = 0.001 … etc
Physics 121,Lecture 1,Pg 11
Scientific Notation
? The speed of light in vacuum
c ? 300 000 000 m/s
c ? 3.0 x 108 m/s
? The app,mass of a mosquito
m ? 0.00001 kg
m ? 10-5 kg
Physics 121,Lecture 1,Pg 12
Algebra
? Basic Rules
8x =32
8x/8 = 32/8
x = 4
x + 2 = 8
x + 2 - 2 = 8 – 2
x = 6
Physics 121,Lecture 1,Pg 13
Basic Rules
? Multiplying,(a/b)(c/d) = (ac)/(bd)
? Dividing,(a/b)/(c/d) = (ad)/(bc)
? Adding,a/b ± c/d = (ad ± bc)/(bd)
? Factoring:
ax + ay + az = a(x + y +z)
a2 + 2ab + b2 = (a + b)2
a2 - b2 = (a + b)(a –b)
Physics 121,Lecture 1,Pg 14
? The elements of substances and motion.
? All things in classical mechanics can be expressed in terms
of the fundamental quantities:
?Length L
?Mass M
?Time T
Standard Quantities
? Some examples of more complicated quantities:
?Speed has the quantity of L / T (i.e,miles per hour).
?Acceleration has the quantity of L/T2,
?Force has the quantity of ML/ T2 (as you will learn).
Physics 121,Lecture 1,Pg 15
Units
? SI (Système International) Units:
?mks,L = meters (m),M = kilograms (kg),T = seconds (s)
? British Units:
?L = inches,feet,miles,M = slugs (pounds),T = seconds
? We will use mostly SI units,but you may run across some
problems using British units,You should know how to convert
back & forth.
Physics 121,Lecture 1,Pg 16
Standards of Length
? Length is measured in Meters (m)
? The Meter is defined as the distance traveled by light in
1/299 792 458 second
? The speed of light is therefore 299 792 458 meters per
second.
? Used to be,one ten-millionth of the distance from the North
Pole to equator.
Physics 121,Lecture 1,Pg 17
Length:
Distance Length (m)
Radius of Visible Universe 1 x 1026
To Andromeda Galaxy 2 x 1022
To nearest star 4 x 1016
Earth to Sun 1.5 x 1011
Radius of Earth
Sears Tower 4.5 x 102
Football Field 1.0 x 102
Tall person 2 x 100
Thickness of paper
Wavelength of blue light
Diameter of hydrogen atom
Diameter of proton 1 x 10-15
6.4 x 106
1 x 10-4
4 x 10-7
1 x 10-10
Physics 121,Lecture 1,Pg 18
Order of Magnitude Calculations / Estimates
Earth’s radius?
? Need to know something from your experience:
?Flying from NYC to SF one accumulates ~ 3,500 miles
?NYC to SF spans about 1/6 of the Earth’s circumference
?So,the Earth’s circumference L = 3,500 x 6 ~ 20,000 mi
?Since circumference of a circle is, L = 2 ? r
?Estimate of Earth radius,
3x103 mi = 3x103 x 1.61 km ~ 5x103 km = 5x106 m??
r ? L2 ? ? 20,000 mi6 ? 3,000 mi
Physics 121,Lecture 1,Pg 19
Standards of Time
? Time is measured in Seconds (s)
? The Second in defined as 9 192 631 700 times the period
of radiation form a cesium atom.
? Used to be,(1/24)(1/60)/(1/60) of a average length of solar
day in 1900
Physics 121,Lecture 1,Pg 20
Time:
Interval Time (s)
Age of Universe 5 x 1017
Age of Grand Canyon 3 x 1014
Avg age of college student 6.3 x 108
One year
One hour
Light travel from Earth to Moon
One cycle of guitar A string 2 x 10-3
One cycle of FM radio wave 6 x 10-8
One cycle of visible light
Time for light to cross a proton 1 x 10-24
3.2 x 107
3.6 x 103
1.3 x 100
1 x 10-15
Physics 121,Lecture 1,Pg 21
Standards of Mass
? Mass is measured in Kilograms (Kg)
? The Kilogram is defined as the mass of a specific platinum-
iridium alloy cylinder kept at the International Bureau of
Weights and Measures at Sevres,France
? We are still using the,old” definition
Physics 121,Lecture 1,Pg 22
Mass:
Object Mass (kg)
visible universe ~ 1052
Milky Way galaxy 7 x 1041
Sun 2 x 1030
Earth 6 x 1024
Boeing 747 4 x 105
Car 1 x 103
Student 7 x 101
Dust particle 1 x 10-9
Bacterium 1 x 10-15
Proton 2 x 10-27
Electron 9 x 10-31
Physics 121,Lecture 1,Pg 23
The Building Blocks of Matter
? Atoms and Molecules
?Hydrogen atom ~ 10-10 m
? The Atomic Nucleus
?Atomic nucleus ~ 10-14 m
? Protons and neutrons
?Proton ~ 10-15 m
? Quarks,up,down,strange,
charmed,bottom,and top
Physics 121,Lecture 1,Pg 24
Some Prefixes for Power of Ten
Power Prefix Abbreviation
103 kilo k
106 mega M
109 giga G
1012 tera T
1015 peta P
1018 exa E
10-18 atto a
10-15 femto f
10-12 pico p
10-9 nano n
10-6 micro m
10-3 milli m
Physics 121,Lecture 1,Pg 25
Dimensional Analysis
? The word dimension has a special meaning in
Physics,It it the physical nature of a quantity.
? The dimension of a distance is Length,whether
we measure it in yards or meters.
? The dimension of Area A is [A] = L2
? The dimension of velocity v is written
[v] = L/T
Physics 121,Lecture 1,Pg 26
Dimensional Analysis
? Dimensions can be treated as algebraic
quantities
? They can be added or subtracted only if they
have the same dimensions.
? Both sides of and equation must have the same
dimensions.
? Dimensional analysis helps to determine whether
or not an expression has the correct form.
Physics 121,Lecture 1,Pg 27
? This is a very important tool to check your work
?It’s also very easy!
? Example:
Doing a problem you get the answer for distance
d = v t 2 ( velocity x time2 )
Quantity on left side = L
Quantity on right side = L / T x T2 = L x T
? Left units and right units don’t match,so answer must be
wrong !!
Dimensional Analysis
Physics 121,Lecture 1,Pg 28
Lecture 1,ACT 1
Dimensional Analysis
? The force (F) to keep an object moving in a circle
can be described in terms of the velocity (v,
dimension L/T) of the object,its mass (m,
dimension M),and the radius of the circle (R,
dimension L).
?Which of the following formulas for F could be correct?
Remember,Force has dimensions of ML/T2
R
mvF 2?2?
?
??
?
??
R
vmF(a) (b) (c)F = mvR
Physics 121,Lecture 1,Pg 29
Lecture 1,ACT 2
? There is a famous Einstein's equation connecting energy
and mass (relativistic),Using dimensional analysis find
which is the correct form of this equation,
Solution -> (b)
? Note,
?c is speed of light (L/T)
?E is energy (M L2 / T2)
??
E ? mc 3
??
E ? mc 2(a) (b) (c)
??
E ? mc
Physics 121,Lecture 1,Pg 30
Converting between different systems of units
? Useful Conversion factors:
?1 inch = 2.54 cm
?1 m = 3.28 ft
?1 mile = 5280 ft
?1 mile = 1.61 km
? Example,convert miles per hour to meters per second:
s
m
s
m
s
hr
ft
m
mi
ft
hr
mi
hr
mi
2
1447.0
3 6 0 0
1
28.3
15 2 8 011 ??????
Physics 121,Lecture 1,Pg 31
Lecture 1,ACT 3
Converting between different systems of units
? When on travel in Europe you rent a small car which consumes 6
liters of gasoline per 100 km,What is the MPG of the car?
? Useful Conversion factors:
?1 gallon = 4 liters
?1 mile = 1.61 km
??
100 km
6l ?
??
100 km
6 l ?
1 mi
1, 61 km ?
4 l
1 g a llo n
??
? 41 migallon
Solution
= 41 MPG !
Physics 121,Lecture 1,Pg 32
Significant Figures
? The number of digits that matter in a measurement or calculation,
? When writing a number,all non-zero digits are significant.
? Zeros may or may not be significant.
?those used to position the decimal point are not significant.
?those used to position powers of ten ordinals may or may not be
significant.
? in scientific notation all digits are significant
? Examples:
?2 1 sig fig
?40 ambiguous,could be 1 or 2 sig figs
?4.0 x 101 2 sig figs
?0.0031 2 sig figs
?3.03 3 sig figs
Physics 121,Lecture 1,Pg 33
Significant Figures
? When multiplying or dividing,the answer should have the
same number of significant figures as the least accurate of
the quantities in the calculation.
? When adding or subtracting,the number of digits to the
right of the decimal point should equal that of the term in
the sum or difference that has the smallest number of digits
to the right of the decimal point.
? Examples:
?2 x 3.1 = 6
?3.1 + 0.004 = 3.1
?4.0 x 101 ? 2.04 x 102 = 1.6 X 10-1
Physics 121,Lecture 1,Pg 34
Adding or Subtracting
? When numbers are added or subtracted,the
number of decimal places in the result equal the
smallest number of decimal places of any term in
the sum.
x = 123; y = 5.35
123.xxx
+ 5.35x
128.xxx
Physics 121,Lecture 1,Pg 35
Order-of Magnitude Calculations
? Sometimes it is necessary to know a quantity
only within a factor of 10
? This is know as an order of magnitude
? For example that is the total mass of everyone in
this class?
mass of a person m ~ 75 kg
Number of people n ~ 75
mTotal ~ 75 ′ 75 kg = 5625 kg ~ 6 ′ 103 kg
Physics 121,Lecture 1,Pg 36
Coordinate Systems
? A fixed reference point O,called the origin
? A set of specified axes,or direction,with an appropriate scale and labels
on the axes
? The Cartesian coordinate system,AKA the rectangular coordinate
system.
Physics 121,Lecture 1,Pg 37
Coordinate Systems
? Plane polar coordinates,(r,q)
Physics 121,Lecture 1,Pg 38
Recap of today’s lecture
? Measurement and Units (Chapter 1)
?Systems of units
?Density
?Converting between systems of units
?Dimensional Analysis
? Reading for today’s class:
?Chapter 1
? Reading for Thursday
?Chapter 2
? Homework #1,on Web at www.webassign.net
