System of Units and Measurement

Measurement 

Measurement is defined as the action of associating numerical with their possible physical quantities and phenomena. Measurement is a technique in which the properties of an object are determined by comparing them to a standard quantity. Also, measurement is the essential metric to express any quantity of objects, things and events. 

Unit 

Unit is defined as the physical quantity which is measured in terms of the chosen standards of measurement. The unit of a specified physical quantity can be considered as an arbitrarily chosen standard that can be used to estimate the quantities belonging to similar measurements. The units are well accepted and recognized by the people and well within all guidelines. 

System of Units 

The system of units is the complete set of units, both fundamental units and derived units, for all kinds of physical quantities. Each system is named with reference to fundamental units on which it is based. The common system of units utilized in mechanics is as follows. 

1) F.P.S or Foot-Pound System 

The F.P.S. system is a variant of the non-metric system, widely used in the states of the U.S. before the global audience universally accepted the S.I system. It uses the foot as the unit of measurement of length, and pound as the unit of mass and second as the unit of time. 

2) C.G.S or Centimeter-Gram-Second System 

The C.G.S. system is a metric system of measurement. This system uses centimeter, gram and second as the three basic units for length, mass and time respectively. 

3) M.K.S or Meter-Kilogram-Second System 

The fundamental units of length, mass and time are meter, kilogram and second respectively.

Fundamental Units

Every quantity is measured in terms of some internationally accepted units, called fundamental units. All the physical quantities in mechanics are expressed in terms of three fundamental quantities, i.e. Length, Mass and Time. 

1) Mass 

The fundamental property of all material things to resist any change in momentum is referred to as mass. It is independent of the object’s temperature, pressure or position in space. The downward force produced when a mass is in a gravitational field is referred to as weight. The metric units of mass are grams and kilograms, and both are mass units. The mass of an object can also include the total number of electrons, protons and neutrons, which an object contains.

2) Length 

Length is defined as the measurement or extent of something from end to end. The length of any object can be found in either way such as using a scale (i.e., ruler) or measuring tape. 

3) Time 

It is a concept for ordering the flow of events. Time is the change or the interval over which change occurs. It is impossible to know that time has passed unless something changes. It can be measured in terms of seconds, minutes, hours, days, weeks, months and years.

S.I. System of Units

In the year 1960, the Eleventh General Conference of Weights and Measures introduced the International System of Units. The International Standard Organization (ISO) and the International Electrochemical Commission endorsed the system in 1962. In October 1971 a replacement of the metric system of units was done with a new system called Systeme Internationale d’ Unites, International System of Units (S.I. Units).

Fundamental SI Units

Fundamental Quantity	SI Unit	Symbol
Length	Meter	M
Mass	Kilogram	kg
Time	Second	s
Electric Current	Ampere	A
Temperature	Kelvin	K
Luminous Intensity	Candela	cd
Amount of Substance	Mole	mol

Two supplementary units on the SI system are Radian and Steradian.

Quantity	SI Unit	Symbol
Plane Angle	Radian	rad
Solid Angle	Steradian	sr

1) Radian 

It is the unit of a plane angle. One radian is equivalent to an angle subtended at the center of a circle by an arc of length equal to the radius of the circle. 

Fig. 1 Radian

2) Steradian 

It is the unit of solid angle. One steradian is the solid angle subtended at the centre of a sphere, by the surface of a sphere which is equal in area to the square of its radius.

Fig. 2 Steradian

Properties of Fundamental Units 

Any standard unit should have the following properties. 

• Consistency or invariability 
• Availability or reproducibility 
• Imperishability or permanency 
• Convenience and acceptability

Derived Units

The units which are derived from the basic fundamental units are said to be derived units. These units are used to measure the physical quantities but the fact that these can be further resolved into simpler units or the fundamental units.

Quantity	Derived Unit	Symbol
Force	Newton	N
Moment	Newton-meter	Nm
Work	Joule	J
Power	Watt	W
Velocity	Meter per second	m/s
Pressure	Pascal or Newton per square meter	Pa or N/m2

Definition of Fundamental Units

1) Meter (m)

It is the unit of length. One meter is the distance traveled by light through a vacuum in 1/299,792,458 (3.33564095 x 10^-9) of a second. The meter was originally defined as one ten-millionth (0.0000001 or 10^-7) of the distance around the earth's surface, as measured in a great circle passing through Paris, France, from the geographic North Pole to the equator.

Fig. 3 A bar of platinum - iridium metre kept at a temperature of 0º C

2) Kilogram (kg)

It is the unit of mass. The value of the kilogram is now based on the Planck constant, which is 6.62607015 × 10^-34 Js. Prior to 2018, the kilogram was defined as the mass of a specific international prototype made of platinum-iridium and kept at BIPM (The International Bureau of Weights and Measures (Bureau International des Poids et Mesures)) headquarters. Before that, the kilogram was defined as the mass of one liter (10^-3 cubic meters) of pure water.

Fig. 4 The standard platinum - iridium is kept at the International Bureau of Weights and Measures in France

3) Second (s)

It is the unit of time. One second is the time that elapses during 9.192631770 periods of the radiation produced by the transition between two hyperfine levels of the Cesium-133 atom in an unperturbed ground state. It is also the time required for light to travel 299,792,458 (2.99792458 x 10^8) meters through a vacuum.

4) Kelvin (K)

It is the unit of thermodynamic temperature. The value of the Kelvin is now based on the Boltzmann constant, which is 1.380649 × 10^-23 J/K-1. Prior to 2018, a Kelvin was considered equal to 1/273.16 (3.6609 x 10^-3) of the thermodynamic temperature of the triple point of pure water (H2O).

5) Ampere (A)

It is the unit of electric current. The value of the ampere is now based on the elementary charge, which is 1/1.602176634 × 10^-19 times the elementary charge per second. Prior to 2018, the ampere was based on the force between two current carrying conductors that fixed the value of vacuum magnetic permeability at 4π × 10^−7 H m−1.

6) Candela (cd)

It is the unit of luminous intensity. The value of the candela is now based on the luminous efficacy of monochromatic radiation of frequency 540 × 1014 Hz, which is 683 lm/W. Prior to 2018, the candela was the measure of electromagnetic radiation, in a specified direction, that had an intensity of 1/683 (1.46 x 10^-3) watt per steradian at a frequency of 540 terahertz (5.40 x 10^14 hertz).

7) Mole (mol)

It is the unit of an amount of substance. The value of the mole is based on the Avogadro constant, which is 6.02214076 x 10^23 mol−1. One mole has exactly 6.022169 x 10^23 elementary entities.