Units of Measurements
Conversion Factors
Dimensional Analysis
Unit Analysis
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The Most Basic Measurements
Base Quantities
• Base Quantities are physical measurements that
define a standard quantity.
• Often base quintiles can not be simplified into a simpler
set of quantities
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Seven (7) Base Measurements
1. length (L)
5. amount of substance (mole)
2. time (t)
6. electric current (I)
3. mass (m)
7. luminous intensity (candela)
4. temperature (Kelvin)
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Derived Quantities
• Derived Quantities are physical measurements
using combinations of base quantities.
• Examples:
1.
2.
3.
4.
5.
6.
7.
Speed or velocity (v); length/time (L/t)
Area (A); length x length (L2)
Volume (V); length x length x length (L3)
Acceleration (a); Δvelocity/time (L/t/t) (L/t2 )
Force (F); mass x acceleration (m∙ L/t2)
work & energy (joule)(J); force x distance (F∙L)
many many more
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Standard Units of Measurement
• Two widely accepted standard units of
measurement
1) BRITISH system : only used by 1 major
industrialized country USA)
2) METRIC system (SI system): used by the rest
of the industrialized world and Physists
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Systseme International (SI)
• Systseme International (SI) is the metric
system, it has its origins in the late 1700’s
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Systseme International (SI)
• Systseme International (SI) is the metric
system, it has its origins in the late 1700’s
• UNITS of MEASUREMENT for SI
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Systseme International (SI)
• Systseme International (SI) is the metric
system, it has its origins in the late 1700’s
• UNITS of MEASUREMENT for SI
• Base Quantities
Standard SI Units
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length
time
mass
electric current
temperature
amount of a substance
luminous intensity
meter
second
kilogram ≠ weight
ampere
Kelvin
mole
candela
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Systseme International (SI)
• Systseme International (SI) is the metric
system, it has its origins in the late 1700’s
• UNITS of MEASUREMENT for SI
• Base Quantities
Standard SI Units
• length
• time
• mass
meter
second
kilogram ≠ weight
• These three quantities are the units most often used in the 1st
semester of this course
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Systseme International (SI) MKS
• Systseme International (SI) is the metric
system, it has its origins in the late 1700’s
• UNITS of MEASUREMENT for SI
• Base Quantities
Standard SI Units
• length
• time
• mass
meter
second
kilogram ≠ weight
• This is the MKS measurement system of the SI
meter kilogram second are the standards for basic measurement
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Systseme International (SI) MKS
• Systseme International (SI) is the metric
system, it has its origins in the late 1700’s
• UNITS of MEASUREMENT for SI
• Base Quantities
Standard SI Units
• length
• time
• mass
meter
second
kilogram ≠ weight
• This is the MKS measurement system of the SI
•
meter kilogram second are the standards for basic measurement
We will be using the MKS measurements in this course
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Systseme International (SI) cgs
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•
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Base Quantities
Length
time
mass
Standard SI Units
centimeter
second
grams ≠ weight
Abbreviation
cm
s
g
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Systseme International (SI) cgs
•
•
•
•
Base Quantities
length
time
mass
Standard SI Units
centimeter
second
grams ≠ weight
Abbreviation
cm
s
g
• This is the cgs measurement system of the SI
Centimeter gram second are the standards for basic measurement
• We will NOT be using cgs measurements in this course
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Value of SI measurements
length (meter)
1/10,000,000 distance from equator to
North Pole along a meridian line running
through Paris
Distance traveled in 1/ 299,792,458 of a
second by light in a vacuum
Mass (kilogram)
1/1,000 of a cubic of pure water at 4oC
mass of a particular platinum- iridium
cylinder kept at the International Bureau of
Weights and Measurements in Paris
Time (second)
1/86,400 of a mean solar day
9,192,631,770 periods of radiation released
from cesium atoms
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Value of SI measurements
Other measurements will be introduced as
needed
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Prefixes; Measurement Modifiers
• In the British system different measurements
of the same base quantity have different
names
length: feet, inches, yards, miles, etc
weight: pounds, ounces, tons
time: seconds, minutes, hours, days, years, etc
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Prefixes; Measurement Modifiers
• In the SI system prefixes combined with a
common root are used to express different
quantities
length: meter, kilometer, centimeter, millimeter
mass: gram, milligram, kilogram, decagram,
time: second, millisecond, kilosecond, megasecond
hours, minutes, years
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standard base units in SI system
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• NOTICE THAT THE STANDARD BASE UNIT FOR
MASS IN THE METRIC SYSTEM IS A
KILOGRAM
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Prefixes; Measurement Modifiers
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Conversion Factors
• Often times a measured quantity in one set of units
must be converted to an equivalent quantity in
another set of units
• To make the conversion, a conversion factor is
required.
• A conversion factor is often expressed as a fraction
with the numerator and denominator having the
same quantity expressed in different units
• The quantity to be converted is then multiplied by
the conversion factor. The units to be changed must
cancel leaving only the desired unit(s).
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Examples of Conversion Factors
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12 inches/1 foot
1 foot/12 inches
36 inches/ 1 yard
1 yard/ 36 inches
60 seconds / 1 minute
1 minute/ 60 seconds
3600 seconds/ 1 hour
2.54 cm/1 inch
1000m/kilometer 1000m/km
1 m/1000mm
A conversion factor
must have a value of
1 (one).
In each example the quantity in the numerator
equals the quantity in the denominator
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Applicatin of Conversion Factors
1. Convert 18 inches into feet
18 inches (1 foot/12 inches) = 1.5 feet
2. Convert 1.33 hrs into seconds
1.33 hrs (3600 seconds/1 hr) = 4788 seconds
sig figs 4790 seconds
3. Convert 758 mm into meters
758 mm (1 m/1000mm) = 0.758 m
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Application of Conversion Factors
Sometimes two or more conversion factors must be
used.
4. Convert 26.7 m/s into kilometers/hr
26.7 m/s ( 1 km/1000m) ( 3600 s/1 hr) = 96.12 km/hr
sig figs 96.1 km/hr
5. Convert 4580 cm3 into m3
4580 cm3 (1 m/1000cm)3 = 0.000004580 m3
= 4.58 x 10-6 m3
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Conversion Factors
proper dimension
• When using conversion factors the original
measurement must have the same dimension
as the final measurement
• 60 km/minute (1 minute/60 sec) = 1 km/sec
• velocity dimension = velocity dimension
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Dimensions in Physics
A dimension in physics is a unit (base unit)
or a combination of units (derived units)
that are used to measure a quantity.
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Dimensions in Physics
Base dimensions
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Dimensions in Physics
Base Dimensions
length (L)
mass (M)
time (t)
temperature (K)
electric current (A) ampere
mole (mol)
luminous intensity (cd)
Derived Dimensions
speed or velocity (d/t)
acceleration (d/t2 )
force (m d/t2)
work (f x d) = (m d2/t2)
kinetic energy
potential energy
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Dimensional Analysis
Dimensional analysis: is a procedure that
determines if a mathematical equation will
produce the expected dimension.
Both sides of the equation must have the same
dimension
•If the equation is expected to produce the
dimension length, each number in the equation
should be a length
• 6m + 4m = 10 m
• L + L = L
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Dimensional Analysis
•For an equation to be dimensionally correct it
must have the same dimension on both sides of
the equation, but each number might have a
different unit for that dimension.
•6m + 6ft = ?
L + L = L
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Dimensional Analysis
•For an equation to be dimensionally correct it
must have the same dimension on both sides of
the equation, but each number might have a
different unit for that dimension.
•6m + 6ft = ?
L + L = L
dimensionally correct
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Dimensional Analysis
•For an equation to be dimensionally correct it
must have the same dimension on both sides of
the equation, but each number might have a
different unit for that dimension.
•6m + 6ft = ?
L + L = L dimensionally correct
To solve this equation one length must have its
units converted to match the other length
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Dimensional Analysis
•6m + 6ft = ?
• L + L = L
• dimensionally correct
• 3m/s(5s) + 6m = 21m
• L + L = L
• dimensionally correct
• 35m + 15 s = 50m
•
L + t ≠ L
• dimensionally incorrect
•Time can cont be added to length
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Dimensional Analysis
• To be mathematically correct an equation must be
dimensionally correct
• An equation that is dimensionally correct may not be
mathematically correct
• This will be demonstrated and explained further at a later
time
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Unit Analysis
In an equation, measurements may involve
units of time, length, mass, velocity, force etc.
Unit analysis is a procedure to ensure each of
these measurements is using the same unit
5 min + 10 min = 15 min
units are correct-- same time unit thru out the
equation
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Unit Analysis
5 min + 600 sec = ?
Seconds can not be added to minutes
•Dimensionally correct
• Units of time are not the same
•Equation can not be solved in this form
•Requires a conversion factor
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Unit Analysis
5 min + 600 sec = ?
•5 min ( 60 sec/min) = 300 sec
300 sec + 600 sec = 900 sec
•Dimensionally correct
• Units of time are the same
•Equation can be solved in this form
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• Order of magnitude could also be
considered a type of measurement
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Problem Solving
6 steps
38
Problem Solving
6 steps
1) Study/analyze problem carefully
39
Problem Solving
6 steps
1) Study/analyze problem carefully
 determine what you are solving for
40
Problem Solving
6 steps
1) Study/analyze problem carefully
 determine what you are solving for
 determine what is given
41
Problem Solving
6 steps
1) Study/analyze problem carefully
 determine what you are solving for
 determine what is given
2) When appropriate draw a simple diagram
42
Problem Solving
6 steps
1) Study/analyze problem carefully
 determine what you are solving for
 determine what is given
2) When appropriate draw a simple diagram
 Projectile motion, buoyancy, -----
43
Problem Solving
6 steps
1) Study/analyze problem carefully
 determine what you are solving for
 Determine what is given
2) When appropriate draw a simple diagram
 Projectile motion, buoyancy, ----3) Write down
44
Problem Solving
6 steps
1) Study/analyze problem carefully
 determine what you are solving for
 Determine what is given
2) When appropriate draw a simple diagram
 Projectile motion, buoyancy, ----3) Write down
 what you are solving for
45
Problem Solving
6 steps
1) Study/analyze problem carefully
 determine what you are solving for
 Determine what is given
2) When appropriate draw a simple diagram
 Projectile motion, buoyancy, ----3) Write down
 what you are solving for
t= ? v= ? a = ?
46
Problem Solving
6 steps
1) Study/analyze problem carefully
 determine what you are solving for
 Determine what is given
2) When appropriate draw a simple diagram
 Projectile motion, buoyancy, ----3) Write down
 what you are solving for
t= ? v= ? a = ?
 What information is given to solve the problem
47
Problem Solving
6 steps
1) Study/analyze problem carefully
 determine what you are solving for
 Determine what is given
2) When appropriate draw a simple diagram
 Projectile motion, buoyancy, ----3) Write down
 what you are solving for
t= ? v= ? a = ?
 What information is given to solve the problem
4) What principles & equation(s) will be needed to solve the problem
48
Problem Solving
6 steps
1) Study/analyze problem carefully
 determine what you are solving for
 Determine what is given
2) When appropriate draw a simple diagram
 Projectile motion, buoyancy, ----3) Write down
 what you are solving for
t= ? v= ? a = ?
 What information is given to solve the problem
4) What principles & equation(s) will be needed to solve the problem
5) Substitute data into the equations & perform calculations
49
Problem Solving
6 steps
1) Study/analyze problem carefully
 determine what you are solving for
 Determine what is given
2) When appropriate draw a simple diagram
 Projectile motion, buoyancy, ----3) Write down
 what you are solving for
t= ? v= ? a = ?
 What information is given to solve the problem
4) What principles & equation(s) will be needed to solve the problem
5) Substitute data into the equations & perform calculations
6) Check your results
50
Problem Solving
6 steps
1) Study/analyze problem carefully
 determine what you are solving for
 Determine what is given
2) When appropriate draw a simple diagram
 Projectile motion, buoyancy, ----3) Write down
 what you are solving for
t= ? v= ? a = ?
 What information is given to solve the problem
4) What principles & equation(s) will be needed to solve the problem
5) Substitute data into the equations & perform calculations
6) Check your results
 do they seem reasonable
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