Measurement
What is measurement?
Measurement is the process of comparing an unknown quantity with a known quantity.
Or,
Measurement is expressing characteristics or properties of an object in terms of number and unit. Like expressing length of a table as 1.5 meter, mass of a rice pack as 20 kg etc.
Or,
Measurement is expressing characteristics or properties of an object in terms of number and unit. Like expressing length of a table as 1.5 meter, mass of a rice pack as 20 kg etc.
Importance of measurement
- Standardization:- Measurement has made standardization of physical quantities in terms of predefined known quantities possible. This led to a revolution in field of science, technology, medicine, trade and commerce. In the absence of standard quantities the ways of expressing quantities were not uniform. Conficts used to arise while exchanging goods.
- Quantification:- Measurement helps to quantify unknown quantities. The measured values can be used for further calculation while estimitating, planning or replacing with similar quantity.
Applications of measurement
Every field uses measurement. Some sectors where measurement is used are as follows:-
- Physics
- Engineering and technology
- Medicine
- Agriculture
- Trade and commerce
- Sports and Entertainment
The use of knowledge of measurement and measurement techniques is very frequent in our daily life. Some usages of measurement in our daily life are as follows:-
- Selling or purchasing of goods,
- Offices, school and TV shows schedules,
- Expressing distance between two places,
- Taking size of apparel,
- Adjusting volume and brightness of electronic gadgets,
- Expressing age,
- To determine expiry date of groceries, medicine and documents,
- and so on.
Quantity
Quantities are characteristics or properties we are trying to measure, such as the length of an object.
Quantities can be classified into following categories:-
- Physical quantities
- Non-physical quantities
Physical quantities
Those quantities which can be measured are called physical quantities. Examples of physical quantities are time, length, mass, temperature, weight, area, height, speed, angle of elevation, angle of depression, etc.
Non-physical quantities
Those quantities which can't be measured are called non-physical quantities. Examples of non-physical quantities are love, anger, desire, lust, pain, happiness, etc.
Physical quantities vs non-physical quantities
| Physical quantity | Non-physical quantity |
|---|---|
| It can be measured. | It can't be measured. |
| It is expressed in terms of number and units. |
It can not be expressed in terms of number and units.
It is expressed in an abstract way using words like slight, severe, true etc. |
| Physical quantities of the same kind can be compared. | Non-physical quantities can’t be compared. |
|
Examples:-
Mass, Weight, Length, Luminous intensity, et cetera. |
Examples:-
Love, Anger, Lust, Anxiety, Pain, Happiness, Sadness, et cetera. |
Classification of physical quantities
- Fundamental quantity and
- Derived quantity
In any measurement system those physical quantities which are independent of other physical quantities are called base or fundamental or independent quantities.
There are 7 fundamental quantities in SI system and they are distance, mass, duration, luminous intensity, temperature, amount of substance and electric current.
There are 7 fundamental quantities in SI system and they are distance, mass, duration, luminous intensity, temperature, amount of substance and electric current.
Those physical quantities which dependen upon fundamental quantities and are expressed as algebric combinations of one or more fundamental quantities are called derived or dependent quantities.
Examples of derived quantities are area, volume, force, speed, weight, acceleration, power, energy, work, pressure, resistance, etc
Examples of derived quantities are area, volume, force, speed, weight, acceleration, power, energy, work, pressure, resistance, etc
Fundamental vs derived quantities :-
| Fundamental quantities | Derived quantities |
|---|---|
| Those physical quantities which are independent of other quantities are called fundamental or independent quantities. | Those physical quantities which dependen upon fundamental quantities for their expression in mathematical form are called derived or dependent quantities. |
| There are 7 fundamental quantities. |
There are numerous derived quantities.
Its hard to figure out exact number of derived quantities. |
| Fundamental quantities are elementary quantities so they can not be further broken down to other quantities. | Derived quantities are composite quantities so it can be broken down in terms of fundamental quantities. |
| All fundamental quantities have a unit associated with it. |
Some derived quantities are unitless as they are ratio of same physical quantities.
For example angle between two lines, efficiency, etc. |
|
Examples
Length, mass, time, amount of substance, temperature, luminous intensity and electric current. |
Examples
Speed, Frequency, plain angle, solid angle, force, pressure, energy, work, power, electric voltage, magnetic flux density, etc |
|
Examples of SI units associated with fundamental quantities :-
meter, kilogram, second, mole, kelvin, candela and current. |
Examples of SI units associated with derived quantities :-
meter per second(m/s), hertx(Hz), degree, newton(N), pascal(Pa), joule(J), watt(W), voltage(V), tesla(T), etc. |
Unit
A standard measuring value associated with a particular physical quantity which is used to express or quantify physical quantities of same type is called a unit.
For example 'meter' is unit associated with length so it can be used to quantify other similar quantities like distance, breadth, height, etc but not other dissimilar quantities like area, volume, weight, duration, etc.
Physical quantities are expressed in term of some standard quantity of same kind termed as unit. Without unit, a physical quantity is just a number which gives no sense about the standard quantity in terms of which the physical quantity is expressed. A physical quantity only has sense when expressed in some terms of standard units.
Or,
In any measurement system those units which are independent of other units are called fundamental units.
Examples of fundamental units are meter(m), kilometer(km), gram(g), kilogram(kg), millisecond(ms), degree centigrade(°C), kelvin(K), mole(mol), milliampere(mA), etc.
Or,
Those units which are expressed as algebric cominations of fundamental units are called derived units.
Examples of derived units are meter-squared(m²), hertz(Hz), newton(N), pascal(Pa), joule(J), calorie(cal), watt(W), horsepower(Hp), etc.
For example 'meter' is unit associated with length so it can be used to quantify other similar quantities like distance, breadth, height, etc but not other dissimilar quantities like area, volume, weight, duration, etc.
Physical quantities are expressed in term of some standard quantity of same kind termed as unit. Without unit, a physical quantity is just a number which gives no sense about the standard quantity in terms of which the physical quantity is expressed. A physical quantity only has sense when expressed in some terms of standard units.
Types of units
- Fundamental unit and
- Derived unit
Fundamental unit
Units associated with fundamental quantities are called fundamental units.
Or,
In any measurement system those units which are independent of other units are called fundamental units.
Examples of fundamental units are meter(m), kilometer(km), gram(g), kilogram(kg), millisecond(ms), degree centigrade(°C), kelvin(K), mole(mol), milliampere(mA), etc.
Derived unit
Units associated with derived quantities are called derived units.
Or,
Those units which are expressed as algebric cominations of fundamental units are called derived units.
Examples of derived units are meter-squared(m²), hertz(Hz), newton(N), pascal(Pa), joule(J), calorie(cal), watt(W), horsepower(Hp), etc.
Fundamental units vs Derived units
| Fundamental units | Derived units |
|---|---|
| In any measurement system those units which are independent of other units are called fundamental units. | Those units which are expressed as algebric cominations of fundamental units are called derived units. |
| Fundamental units are associated with fundamental quantities. | Derived units are associated with derived quantities. |
| There are 7 fundamental units in SI unit. |
There are numerous derived units.
Its hard to figure out exact number of derived units. |
| Fundamental units are elementary units so they can not be further broken down to other units. | Derived units are composite units so it can be broken down in terms of fundamental units. |
|
Examples :-
meter, kilogram, second, mole, kelvin, candela and current. |
Examples :-
meter per second(m/s), hertx(Hz), degree, newton(N), pascal(Pa), joule(J), watt(W), voltage(V), tesla(T), etc. |
Systems of measurement
Systems of measurement are standard which declares fundamental quantities to be considered for measurement.
Or,
Systems of measurement are defined as system which declares base physical quantities and units of measurement and all other physical quantities are expressed in some algebric expression of these base quantities.
SI, MKS, MKSA, CGS, FPS are some widely used measurement system.
Measurement systems are necessary as they draw a general consensus by declaring base quantities and units. In absence of such system conflicts would arise among different parties. Also measurement systems lead to formation of standard derived quantities.
Following types of systems of measurements are widely used:-
Or,
Systems of measurement are defined as system which declares base physical quantities and units of measurement and all other physical quantities are expressed in some algebric expression of these base quantities.
SI, MKS, MKSA, CGS, FPS are some widely used measurement system.
Measurement systems are necessary as they draw a general consensus by declaring base quantities and units. In absence of such system conflicts would arise among different parties. Also measurement systems lead to formation of standard derived quantities.
Following types of systems of measurements are widely used:-
- SI (système international)
- MKS system
- MKSA system
- CGS system
- FPS system
SI units
To bring uniformity in measurement system and make trade and commerce convenient across the borders some global metric system was needed. To answer this SI was intoduced in 1960.
The system of measurement approved by the General Conference on Weights and Measures in 1960 AD is called SI system.
Or,
SI system is a metric system having 7 fundamental units viz meter(m) for length, kilogram(kg) for mass, second(s) for time, ampere(A) for electric current, Candela(cd) for luminous intensity, kelvin(K) for temperature and mole(mol) for amount of substance.
SI stans for système international (System of international).
The base units approved by the General Conference on Weights and Measures in 1960 AD and all other units derived from these base units are called SI units.
Or,
SI system is a metric system having 7 fundamental units viz meter(m) for length, kilogram(kg) for mass, second(s) for time, ampere(A) for electric current, Candela(cd) for luminous intensity, kelvin(K) for temperature and mole(mol) for amount of substance.
SI stans for système international (System of international).
The base units approved by the General Conference on Weights and Measures in 1960 AD and all other units derived from these base units are called SI units.
| Base quantities | Base units |
|---|---|
| Length or distance | Meter(m) |
| Mass | Kilogram(kg) |
| Time | Second(s) |
| Electric current | Ampere(A) |
| Temperature | Kelvin(K) |
| Luminous intensity | Candela(cd) |
| Amount of substance | Mole(mol) |
MKS
MKS stands for meter, kilogram and second.
MKS system is a metric system having 3 fundamental units viz meter(m) for distance, kilogram(kg) for mass and second(s) for time.
MKSA
MKSA stands for meter, kilogram, second and ampere.
MKSA system is a metric system having 4 fundamental units viz meter(m) for distance, kilogram(kg) for mass, second(s) for time and ampere for electric current.
CGS
CGS stands for centimeter, gram and second.
CGS system is a metric system having 3 fundamental units viz centimeter(cm) for distance, gram(g) for mass and second(s) for time.
FPS
FPS stands for foot, pound and second.
FPS system is a metric system having 3 fundamental units viz foot for distance, pound for mass and second for time. It is also called British or English system of measurement.
MKS vs SI
| MKS system | SI system |
|---|---|
| MKS stands for meter kilogram and second. | SI stands for "Système International" in French which means International system. |
| MKS system has 3 fundamental units. | S.I. has 7 fundamental units. |
|
MKS units are:-
Meter, Kilogram and Second |
SI units are:-
Meter, Kilogram, Second, Ampere, Candela, Kelvin and Mole |
| It is the basis for the development of the S.I. system. |
SI system is an extended version of MKS system.
Some base units were added to SI system time to time. The last added unit is mole. |
| It has only units for mechanical quantities. |
It has units for mechanical quantities along with electromagnetics, themodynamics and optical quantities.
It has the Avogadro constant as mole unit. |
| It was adopted as international metric system in May 20, 1875. | It was adopted as international metric system in 1960. |
Definition of SI units
1 second :-
One second is defined as the reciprocal of the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, which is 9,192,631,770 Hz.
In short:-
One second is defined as the reciprocal caesium frequency.
One second is defined as the reciprocal of the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, which is 9,192,631,770 Hz.
In short:-
One second is defined as the reciprocal caesium frequency.
1 meter :-
Before November 2018, one meter is defined as the length of the international prototype of platinum-iridium bar kept at International Bureau of Weights and Measures (BIPM) in Sèvres, France.
The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m/s, where the second is defined in terms of ΔνCs.
Before November 2018, one meter is defined as the length of the international prototype of platinum-iridium bar kept at International Bureau of Weights and Measures (BIPM) in Sèvres, France.
The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m/s, where the second is defined in terms of ΔνCs.
1 kg :-
Before November 2018 1 kg mass was defined as the mass of the platinum-iridium cylinder kept at International Bureau of Weights and Measures (BIPM) in Sèvres, France.
One kilogram is defined as the taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10–34 when expressed in the unit J s, which is equal to kg m2 s–1, where the metre and the second are defined in terms of c and ΔνCs.
Before November 2018 1 kg mass was defined as the mass of the platinum-iridium cylinder kept at International Bureau of Weights and Measures (BIPM) in Sèvres, France.
One kilogram is defined as the taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10–34 when expressed in the unit J s, which is equal to kg m2 s–1, where the metre and the second are defined in terms of c and ΔνCs.
1 ampere :- One ampere is defined as time rate of flow charge.
1 Kelvin :-
One kelvin(K) is defined as the product of one kg and one meter squared divided by the product of one second squared and Boltzmann constant(k) which is 1.380649 × 10⁻²³ Kg.m².s⁻².K⁻¹.
Mathematically, 1K = 1kg . 1m² . 1s⁻² . k
Mathematically, 1K = 1kg . 1m² . 1s⁻² . k
1 Candela :-
The candela (cd) is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, to be 683 when expressed in the unit lm W-1, which is equal to cd sr W-1, or cd sr kg-1 m-2 s3, where the kilogram, meter and second are defined in terms of h, c and ∆νCs.
One mole (mol) is defined as exactly 6.02214076 × 10²³ numbers of elementary entities.
Mass
The quantity of matter contained in a body is called mass. It is measured using beam balance or physical balance.
A beam balance which has two pans one at each end. At the middle there is a pivot on which a needle is hinged. The inclination of the needle toward any pan indicates the heavier side than the other. When it is not inclined to any side this means both the sides has equal masses. One of its side contains standard mass whose mass is known while on the other side the object which mass is to be known is kept. Using hit and trial with various standard masses when the inclination is zero the unkown mass is calculated.
A beam balance which has two pans one at each end. At the middle there is a pivot on which a needle is hinged. The inclination of the needle toward any pan indicates the heavier side than the other. When it is not inclined to any side this means both the sides has equal masses. One of its side contains standard mass whose mass is known while on the other side the object which mass is to be known is kept. Using hit and trial with various standard masses when the inclination is zero the unkown mass is calculated.
Weight
Weight is defined as the force by which the earth attracts an object toward it center. It is measured using spring balance or top-pan balance.
Mathematically,
Weight(W) = mass(M) * acceleration due to gravity(g)
As weight of body depends upon acceleration due to gravity(g) it varies as value of "g" varies.
Mathematically,
Weight(W) = mass(M) * acceleration due to gravity(g)
As weight of body depends upon acceleration due to gravity(g) it varies as value of "g" varies.
Mass vs weight
| Mass | Weight |
|---|---|
| The amount of matter contained in a body is called its mass. | The force with which a body is attracted toward the centre of a celestial body is called weight of the body at that place. |
| Mass of a body remains constant. | Weight of a body varies with place. |
| Mass is a fundamental quantity. | Weight is a derived quantity. |
| Mass is a scalar quantity. | Weight is a vector quantity. |
| Mass of a body can’t be zero. | Weight of a body can be zero. |
| Mass is measured using beam balance. | Weight is measured using spring balance or top balance. |
| S.I. unit of mass is Kg. | S.I. Unit of weight is Newton (N). |
| CGS unit of mass is gram. | CGS unit of weight is dyne. |
Distance
Distance is defined as measure of apartness between two points either along a straight path or combination of straight paths or curved path.
Rular and measuring tape are used to measure distance. Rular are convenient only for measuring short distance along straight path while measuring tapes can be used even to measure distance in kilometer range and along crved path too. Beside these in physics laboratory vernier calipers and micrometer screw gauge are used to measure distance in range smaller than millimeter.
Time
Time is defined as duration between two events.
Clock and watches are used to measure time. Atomic watches are used by scientist and physicist. They uses atomic watches because atomic watches use resonance frequency for to track time. These resonance frequency are in range of gigahertz. So such atomic watches can be used to measure hundreds of thousand fraction of a second and also there time fluctuation may not vary a single second in a 100 million years.
The time taken by the earth to complete one rotation about its axis is called one solar day.
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