Chapter 1
Introduction
Theories and Experiments
? The goal of physics is to develop
theories based on experiments
? A theory is a,guess,” expressed
mathematically,about how a system
works
? The theory makes predictions about
how a system should work
? Experiments check the theories’
predictions
? Every theory is a work in progress
1.1 Fundamental Quantities
and Their Dimension
? Length [L]
? Mass [M]
? Time [T]
? other physical quantities can be
constructed from these three
Units
? To communicate the result of a
measurement for a quantity,a unit
must be defined
? Defining units allows everyone to
relate to the same fundamental
amount
Systems of Measurement
? Standardized systems
? agreed upon by some authority,usually a
governmental body
? SI -- Systéme International
? agreed to in 1960 by an international
committee
? main system used in this text
? also called mks for the first letters in the
units of the fundamental quantities
Systems of Measurements,
cont
? cgs – Gaussian system
? named for the first letters of the units
it uses for fundamental quantities
? US Customary
? everyday units
? often uses weight,in pounds,instead
of mass as a fundamental quantity
Length
? Units
? SI – meter,m
? cgs – centimeter,cm
? US Customary – foot,ft
? Defined in terms of a meter – the
distance traveled by light in a
vacuum during a given time
Mass
? Units
? SI – kilogram,kg
? cgs – gram,g
? USC – slug,slug
? Defined in terms of kilogram,
based on a specific cylinder kept at
the International Bureau of
Weights and Measures
Standard Kilogram
Time
? Units
? seconds,s in all three systems
? Defined in terms of the oscillation
of radiation from a cesium atom
Approximate Values
? Various tables in the text show
approximate values for length,
mass,and time
? Note the wide range of values
? Lengths – Table 1.1
? Masses – Table 1.2
? Time intervals – Table 1.3
Prefixes
? Prefixes correspond to powers of
10
? Each prefix has a specific name
? Each prefix has a specific
abbreviation
? See table 1.4
1.2 the building blocks of
matter
Structure of Matter
? Matter is made up of molecules
? the smallest division that is
identifiable as a substance
? Molecules are made up of atoms
? correspond to elements
More structure of matter
? Atoms are made up of
? nucleus,very dense,contains
? protons,positively charged,“heavy”
? neutrons,no charge,about same mass
as protons
? protons and neutrons are made up of quarks
? orbited by
? electrons,negatively charges,“light”
? fundamental particle,no structure
Structure of Matter
1.3 Dimensional Analysis
? Technique to check the correctness
of 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
Dimensional Analysis,cont,
? Cannot give numerical factors,this
is its limitation
? Dimensions of some common
quantities are listed in Table 1.5
1.4 uncertainty in measurement and
significant figures
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
? All non-zero digits are significant
? Zeros are significant when
? between other non-zero digits
? after the decimal point and another
significant figure
? can be clarified by using scientific notation
Operations with Significant
Figures
? Accuracy – number of significant figures
? When multiplying or dividing two or
more quantities,the number of
significant figures in the final result is
the same as the number of significant
figures in the least accurate of the
factors being combined
Operations with Significant
Figures,cont,
? When adding or subtracting,round the
result to the smallest number of
decimal places of any term in the sum
? If the last digit to be dropped is less
than 5,drop the digit
? If the last digit dropped is greater than
or equal to 5,raise the last retained
digit by 1
1.5 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
? See the inside of the front cover for an
extensive list of conversion factors
? Example,
2.5 415,0 38,1
1
cmin c m
in??
Examples of various units
measuring a quantity
1.6 estimates and order-
of-magnitude calculations
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
1.7 Coordinate Systems
? Used to describe the position of a
point in space
? Coordinate system consists of
? a fixed reference point called the
origin
? specific axes with scales and labels
? instructions on how to label a point
relative to the origin and the axes
Types of Coordinate
Systems
? Cartesian
? Plane polar
Cartesian coordinate
system
? Also called
rectangular
coordinate
system
? x- and y- axes
? Points are labeled
(x,y)
Plane polar coordinate
system
? Origin and
reference line are
noted
? Point is distance r
from the origin in
the direction of
angle ?,ccw from
reference line
? Points are labeled
(r,?)
1.8 trigonometry
Trigonometry Review s in
c o s
ta n
opp os ite s ide
hy pot enu s e
adj ac ent s ide
hy pot enu s e
opp os ite s ide
adj ac ent s ide
?
?
?
?
?
?
More Trigonometry
? Pythagorean Theorem
? To find an angle,you need the
inverse trig function
? for example,
? Be sure your calculator is set
appropriately for degrees or
radians
2 2 2r x y??
1s in 0,7 0 7 4 5? ?? ? ?
1.9 Problem Solving Strategy
Problem Solving Strategy
? Read the problem
? Identify the nature of the problem
? Draw a diagram
? Some types of problems require very
specific types of diagrams
Problem Solving cont,
? Label the physical quantities
? Can label on the diagram
? Use letters that remind you of the quantity
? Many quantities have specific letters
? Choose a coordinate system and label it
? Identify principles and list data
? Identify the principle involved
? List the data (given information)
? Indicate the unknown (what you are looking
for)
Problem Solving,cont,
? Choose equation(s)
? Based on the principle,choose an
equation or set of equations to apply
to the problem
? Substitute into the equation(s)
? Solve for the unknown quantity
? Substitute the data into the equation
? Obtain a result
? Include units
Problem Solving,final
? Check the answer
? Do the units match?
? Are the units correct for the quantity
being found?
? Does the answer seem reasonable?
? Check order of magnitude
? Are signs appropriate and meaningful?
Problem Solving Summary
? Equations are the tools of physics
? Understand what the equations mean
and how to use them
? Carry through the algebra as far as
possible
? Substitute numbers at the end
? Be organized
Introduction
Theories and Experiments
? The goal of physics is to develop
theories based on experiments
? A theory is a,guess,” expressed
mathematically,about how a system
works
? The theory makes predictions about
how a system should work
? Experiments check the theories’
predictions
? Every theory is a work in progress
1.1 Fundamental Quantities
and Their Dimension
? Length [L]
? Mass [M]
? Time [T]
? other physical quantities can be
constructed from these three
Units
? To communicate the result of a
measurement for a quantity,a unit
must be defined
? Defining units allows everyone to
relate to the same fundamental
amount
Systems of Measurement
? Standardized systems
? agreed upon by some authority,usually a
governmental body
? SI -- Systéme International
? agreed to in 1960 by an international
committee
? main system used in this text
? also called mks for the first letters in the
units of the fundamental quantities
Systems of Measurements,
cont
? cgs – Gaussian system
? named for the first letters of the units
it uses for fundamental quantities
? US Customary
? everyday units
? often uses weight,in pounds,instead
of mass as a fundamental quantity
Length
? Units
? SI – meter,m
? cgs – centimeter,cm
? US Customary – foot,ft
? Defined in terms of a meter – the
distance traveled by light in a
vacuum during a given time
Mass
? Units
? SI – kilogram,kg
? cgs – gram,g
? USC – slug,slug
? Defined in terms of kilogram,
based on a specific cylinder kept at
the International Bureau of
Weights and Measures
Standard Kilogram
Time
? Units
? seconds,s in all three systems
? Defined in terms of the oscillation
of radiation from a cesium atom
Approximate Values
? Various tables in the text show
approximate values for length,
mass,and time
? Note the wide range of values
? Lengths – Table 1.1
? Masses – Table 1.2
? Time intervals – Table 1.3
Prefixes
? Prefixes correspond to powers of
10
? Each prefix has a specific name
? Each prefix has a specific
abbreviation
? See table 1.4
1.2 the building blocks of
matter
Structure of Matter
? Matter is made up of molecules
? the smallest division that is
identifiable as a substance
? Molecules are made up of atoms
? correspond to elements
More structure of matter
? Atoms are made up of
? nucleus,very dense,contains
? protons,positively charged,“heavy”
? neutrons,no charge,about same mass
as protons
? protons and neutrons are made up of quarks
? orbited by
? electrons,negatively charges,“light”
? fundamental particle,no structure
Structure of Matter
1.3 Dimensional Analysis
? Technique to check the correctness
of 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
Dimensional Analysis,cont,
? Cannot give numerical factors,this
is its limitation
? Dimensions of some common
quantities are listed in Table 1.5
1.4 uncertainty in measurement and
significant figures
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
? All non-zero digits are significant
? Zeros are significant when
? between other non-zero digits
? after the decimal point and another
significant figure
? can be clarified by using scientific notation
Operations with Significant
Figures
? Accuracy – number of significant figures
? When multiplying or dividing two or
more quantities,the number of
significant figures in the final result is
the same as the number of significant
figures in the least accurate of the
factors being combined
Operations with Significant
Figures,cont,
? When adding or subtracting,round the
result to the smallest number of
decimal places of any term in the sum
? If the last digit to be dropped is less
than 5,drop the digit
? If the last digit dropped is greater than
or equal to 5,raise the last retained
digit by 1
1.5 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
? See the inside of the front cover for an
extensive list of conversion factors
? Example,
2.5 415,0 38,1
1
cmin c m
in??
Examples of various units
measuring a quantity
1.6 estimates and order-
of-magnitude calculations
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
1.7 Coordinate Systems
? Used to describe the position of a
point in space
? Coordinate system consists of
? a fixed reference point called the
origin
? specific axes with scales and labels
? instructions on how to label a point
relative to the origin and the axes
Types of Coordinate
Systems
? Cartesian
? Plane polar
Cartesian coordinate
system
? Also called
rectangular
coordinate
system
? x- and y- axes
? Points are labeled
(x,y)
Plane polar coordinate
system
? Origin and
reference line are
noted
? Point is distance r
from the origin in
the direction of
angle ?,ccw from
reference line
? Points are labeled
(r,?)
1.8 trigonometry
Trigonometry Review s in
c o s
ta n
opp os ite s ide
hy pot enu s e
adj ac ent s ide
hy pot enu s e
opp os ite s ide
adj ac ent s ide
?
?
?
?
?
?
More Trigonometry
? Pythagorean Theorem
? To find an angle,you need the
inverse trig function
? for example,
? Be sure your calculator is set
appropriately for degrees or
radians
2 2 2r x y??
1s in 0,7 0 7 4 5? ?? ? ?
1.9 Problem Solving Strategy
Problem Solving Strategy
? Read the problem
? Identify the nature of the problem
? Draw a diagram
? Some types of problems require very
specific types of diagrams
Problem Solving cont,
? Label the physical quantities
? Can label on the diagram
? Use letters that remind you of the quantity
? Many quantities have specific letters
? Choose a coordinate system and label it
? Identify principles and list data
? Identify the principle involved
? List the data (given information)
? Indicate the unknown (what you are looking
for)
Problem Solving,cont,
? Choose equation(s)
? Based on the principle,choose an
equation or set of equations to apply
to the problem
? Substitute into the equation(s)
? Solve for the unknown quantity
? Substitute the data into the equation
? Obtain a result
? Include units
Problem Solving,final
? Check the answer
? Do the units match?
? Are the units correct for the quantity
being found?
? Does the answer seem reasonable?
? Check order of magnitude
? Are signs appropriate and meaningful?
Problem Solving Summary
? Equations are the tools of physics
? Understand what the equations mean
and how to use them
? Carry through the algebra as far as
possible
? Substitute numbers at the end
? Be organized
