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-Lesson one : Physical Measurements. - Fulfilled learning outcomes. - Complete explanation. - Solved examples. - Exercises with no answers. -Lesson Two : Measurement Errors - Fulfilled learning outcomes. - Complete explanation. - Solved examples. - Exercises with no answers.
Typology: Lecture notes
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ST
Chapter
Lesson
Unknown
Quantity
Known Quantity (Length = 1 cm)
ST
Measurement is the process of comparing an unknown quantity with another
quantity of its kind (called the unit of measurement) to find out how many times the
first includes the second.
The measurement process has three key elements:
The quantities which can be measured by an instrument and by means of which we
can describe the laws of physics are called physical quantities.
Till class M3, we have studied many physical quantities. For example, length,
velocity, acceleration, force, time, pressure, mass, density etc.
Physical quantities are of THREE types:
First Physical Quantity
Measurement
ST
These are physical quantities which can be expressed in terms of basic quantities. In other
words, can be defined in terms of the fundamental physical quantities.
Derived
quantity
Symbol
Relationship with base
quantities
Derived
unit
Unit in SI
base unit
Area 𝑨 Length × Length 𝐦
𝟐
𝑚 × 𝑚
= 𝑚
2
Volume 𝑽 Length × Length × Length 𝐦
𝟑
𝑚 × 𝑚 × 𝑚
= m
3
Density 𝝆
Mass
Length × Length × Length
𝐤𝐠. 𝐦
−𝟑
kg
m
3
= kg. m
− 3
Velocity 𝒗
Displacement
Time
𝐦. 𝐬
−𝟏
m
s
= m. s
− 1
Acceleration 𝒂
Velocity
Time
𝐦. 𝐬
−𝟐
ms
− 1
s
= m. s
− 2
Force 𝑭 Mass × Acceleration 𝐤𝐠. 𝐦. 𝐬
−𝟐
kg × ms
− 2
= kg. m. s
− 2
Also called
NEWTON
ST
Man in ancient eras used parts of his
body and natural phenomena as
tools of measurement.
He used the arm, the hand span, and
the foot as tools to measure length.
Also, he benefited from the sunrise,
the sunset, and the moon phases in
devising a measure of time.
However, various measurement
systems originated and developed in
different countries.
The measuring tools have been
tremendously developed in the
context of the great industrial
evolution next to the Second World
War. Consequently, these tools were
very helpful to man in describing
phenomena accurately and exploring
facts.
Second
Measuring Tool
Historical Fact
King Henry I of England fixed the yard as
the distance from his nose to the thumb
of his out-stretched arm. Today it is 36
inches.
ST
Quantity Instrument Image To measure
ST
Two pan
balance
One pan
balance
Digital
balance
Golden Ring
or some
chemical
compounds
(powder)
ST
Without using measuring units, most operations we perform in everyday experience
become meaningless. For instance, when we say that the mass of an object is equal to
(5) without giving a unit of measurement,that makes us puzzled. Is it in grams,
kilograms,or tons?
On the other hand, saying that the mass of an object is equal to (5 kg), the quantity
would be fully clarified.
Scientists have tried to figure out the most accurate definition for each of the
standard units for LENGTH, MASS, and TIME. And here are some of these
definitions.
The French were the first who used the
meter as a standard unit for measuring
the length. This definition has been
changed aiming the most accurate
definition.
Third
Measuring Unit
1 - Standard Length Unit (THE METER)
ST
The Standard Meter is the distance
between two engraved marks at the ends
of a rod made of platinum and Iridium
alloy kept at 0
∘
C at the International
Bureau of Weights and Measures near
Paris.
The standard kilogram is the mass of a
cylinder made of platinum and iridium
alloy of specific dimensions kept at 0
∘
C ,
at the International Bureau of Weights and
Measures near Paris.
2 - Standard Mass Unit (THE KILOGRAM)
ST
Q01: What is the SI base unit of time?
A Instant B second C Moment D day
Q02: Can the quantity “mass” be defined by multiplying or dividing fundamental quantities?
A Yes B No
Q03: Can the quantity “speed” be defined by multiplying or dividing fundamental quantities?
A No B Yes
Q04: Which of the following is the symbol for the SI unit of absolute temperature?
A
∘
C B
∘
C
∘
F D K E C
Q05: Can the quantity “length” be defined by multiplying or dividing fundamental quantities?
A No B Yes
Q06: Which of the following is not an SI base quantity?
A Electric current B Electric charge
Q07: Which of the following is the SI base unit of luminous intensity?
A candela B watt per square meter
Q08: What is the SI base unit of length?
A degree B meter C centimeter
ST
Q09: Which of the following most correctly describes the difference between fundamental and
derived physical quantities?
A Fundamental quantities can have more than one unit, but derived quantities can only have
one unit.
B Derived quantities can have more than one unit, but fundamental quantities can only have
one unit.
C Fundamental quantities can be defined in terms of derived quantities.
D Derived quantities can be defined in terms of fundamental quantities.
E Fundamental quantities were proposed before derived quantities were proposed.
Q10: Which of the following physical quantities has the SI unit mole?
A Volume B Mass C Energy D Amount of substance
Q11: Which of the following is not an SI base quantity?
A Luminous intensity B Sound intensity
Q12: What is the SI base unit of mass?
A mole B kilogram C gram
Q13: Which of the following is equivalent to 15 seconds?
A 15+seconds B 15×seconds C seconds D 15
Q14: Which of the following is a unit of distance?
A Kilogram B Second C Meter D Kelvin
ST
Two bus stations
ST
Q01: A human hair is approximately 50 𝜇m in diameter. Express this diameter in
meters.
Q0 2 : If a radio wave has a period of 1 𝜇s, what is the wave's period in seconds?
Q0 3 : A hydrogen atom has a diameter of about 10 nm.
a. Express this diameter in meters.
b. Express this diameter in millimeters.
c. Express this diameter in micrometers.
Q0 4 : The distance between the sun and Earth is about 1. 5 × 10
11
m. Express this
distance with an SI prefix and in kilometers.
Q0 5 : The average mass of an automobile in the United States is about 1. 440 ×
6
g. Express this mass in kilograms.
ST
Scientists agreed to give a specific definition for each physical quantity. This
definition is applied everywhere in the world. The symbol we use in this book to
specify the dimension of :
⇒ Mass is " 𝑀
′′
⇒ Length is " 𝐿
′′
⇒ Time is "𝑇
′′
Accordingly, most of the derived physical quantities can be expressed in terms of the
fundamental physical quantities which are Length, Mass and Time. Each of them has
a particular exponent. Thus, we obtain the following general formula:
±𝑎
±𝑏
±𝑐
Where A is the physical quantity and a, b, and c are the dimensions of L, M, and T
respectively.
Dimensional Formula
ST
their dimension is [𝐿]
[Displacement] here [Height] can be read as "Dimension of Height"
= [ Length ] × [ Width ]
2
2
2
2
2
time so 𝜋 shouldn't affect the dimension of
Area.
[Volume] = [ Length ] × [Area ]
3
For sphere Volume =
4
3
3
[Volume ] = [
3
3
3
So dimension of volume will be always
3
whether it is volume of a cuboid or
volume of sphere.
mass
volume
[ Density ] =
[mass]
[ volume ]
𝑀
𝐿
3
1
− 3
Remember
Anything to the power zero equals one
X
0
=
So , M
0
=1 , L
0
=1 and T
0
=
Which means : It is NOT in the formula
Hint
For any mathematical constant, its
dimension should be 1 (𝑀
0
𝐿
0
𝑇
0
) and we
can say that it is dimensionless. From
similar logic we can say that all the
numbers are dimensionless.
