Phenomenon
An observable event or an activity that happens in our universe. It is an occurrence of a thing or an incident that is of significance to mankind and may or may not affect us directly or indirectly. The movement of a particle from one point to another point in space is a phenomenon. The glitters of stars, the bursting of crackers, falling objects, the freezing of water to ice, lighting in the sky, the ageing of living beings, the germination of seeds, the crying of babies, rainfall, thunderstorm, etc. are some examples of the phenomenon.
Physical Quantities
These are phenomena whose magnitude or value can be measured physically. For example – time, distance, velocity, light, force, sound, etc can all be measured in some form or other and hence are physical quantities.
Fundamental Quantities
Quantities that do not depend on any other physical quantity and/or historically which could not be defined in terms of other physical quantities during the course of their scientific evolution are called Base or Fundamental Quantities. Fundamental units are consistent at all times and at all places and do not vary with changes in temperature, pressure, altitude, time, etc. They are easily reproducible at all places and at all times.
The International System of Quantities (ISQ) defines seven fundamental quantities. These are Mass, Length, Time, Electric Current, Temperature, Luminous Intensity, and Quantity of Matter. The SI system also defines two more fundamental quantities (sometimes referred to as Supplementary quantities). These are Radian(Plane Angle) and Steradian(Solid Angle). Each of these quantities has a standard unit, dimension, and symbolic notation. Radians and Steradians don’t have any dimensions.
Derived Quantities
Derived Quantities are those which can be conveniently expressed in terms of Base Quantities or another derived quantity. For example, the area of a rectangle depends on the measurement of the sides – length(fundamental quantity: LENGTH) and width(fundamental quantity: LENGTH). Velocity depends on the distance(fundamental quantity: LENGTH) travelled per unit of time(fundamental quantity: TIME).
Unit
A unit is the smallest undivided whole entity that is internationally chosen as a standard to express magnitudes of physical quantities. Any physical quantity such as length, mass, time, etc. is expressed as a number(N) followed by the unit, which means the value of the physical quantity is N times the unit value.
SI standards for units
The SI system, which stands for – International System of Units ( Système international (d’unités) in French ), is an internationally accepted standard of units. The first version SI standard was adopted by the International Bureau of Weights and Measures (BIPM) in 1960. It has been primarily derived from the metric system. There are seven fundamental units and two supplementary units (as mentioned above). All other units are derived from these base units. These are elaborated on below.
| Fundamental Quantity | Symbol | Fundamental Unit | Unit Symbol | Dimensional Symbol |
|---|---|---|---|---|
| TIME | t | second | s | T |
| LENGTH | l, x, r, etc. | metre | m | L |
| MASS | m | kilogram | kg | M |
| ELECTRIC CURRENT | I,i | ampere | A | I |
| THERMODYNAMIC TEMPERATURE | T,θ | kelvin | K | Θ |
| AMOUNT OF SUBSTANCE | n | mole | mol | N |
| LUMINOUS INTENSITY | Iv | candela | cd | J |
| PLANE ANGLE | α, β, γ, θ, φ, χ, etc. | radian | rad | None |
| SOLID ANGLE | ω, Ω | steradian | sr | None |
(Ref: SI Brochure 9th edition, 2019)
Expressing Physical Units in Dimensions
All physical units can be expressed in dimensions of the fundamental units. We use the dimensional symbol (refer to the above table) to express the dimension of any physical quantity. The dimensions are expressed as the base dimensions raised to appropriate powers i.e. MaLbTcIdΘeNfJg.
Definitions of SI units
SECOND
The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency, ΔνCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s−1.
→ In other words, a second is equal to the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the unperturbed ground state of the 133Cs atom.
METRE
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−1, where the second is defined in terms of the caesium frequency ΔνCs.
→ To simplify, one metre is the length of the path travelled by light in a vacuum during a time interval with the duration of 1/299 792 458 of a second.
KILOGRAM
The kilogram, symbol kg, is the SI unit of mass. It is defined by 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.
AMPERE
The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge, e, to be 1.602 176 634 × 10−19 when expressed in unit C, which is equal to A s, where the second is defined in terms of ΔνCs.
→ One ampere is the electric current corresponding to the flow of 1/(1.602 176 634 × 10−19) elementary charges per second.
KELVIN
The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant, k, to be 1.380 649 × 10−23 when expressed in the unit J K−1, which is equal to kg m2 s−2 K−1, where the kilogram, metre and second are defined in terms of h, c and ΔνCs.
→ One kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy kT by 1.380 649 × 10−23 J.
MOLE
The mole, symbol mol, is the SI unit of the amount of substance. One mole contains exactly 6.022 140 76 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number.
The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.
→ The mole is the amount of substance of a system that contains 6.022 140 76 × 1023 specified elementary entities.
CANDELA
The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It 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 lmW−1, which is equal to cd srW−1, or cd sr kg−1 m−2 s3, where the kilogram, metre and second are defined in terms of h, c and ΔνCs.
→ one candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 Hz and has a radiant intensity in that direction of (1/683) W sr−1.
Plane and Solid Angles
The plane angle, expressed in radian, between two lines originating from a common point is the length of circular arc s, swept out between the lines by a radius vector of length r from the common point divided by the length of the radius vector, θ = s/r rad. The phase angle (often just referred to as the “phaseâ€) is the argument of any complex number. It is the angle between the positive real axis and the radius of the polar representation of the complex number in the complex plane.
One radian corresponds to the angle for which s = r, thus 1 rad = 1. The measure of the right angle is exactly equal to the number π/2.
A historical convention is the degree. The conversion between radians and degrees follows from the relation 360° = 2π rad. Note that the degree, with the symbol °, is not a unit of the SI.
The solid angle, expressed in steradian, corresponds to the ratio between an area A of the surface of a sphere of radius r and the squared radius, Ω = A/r2 sr. One steradian corresponds to the solid angle for which A = r2, thus 1 sr = 1. The units rad and sr correspond to ratios of two lengths and two squared lengths,
respectively. However, it shall be emphasized that rad and sr must only be used to express angles and solid angles, but not to express ratios of lengths and squared lengths in general.
When the SI was adopted by the 11th CGPM in 1960, a category of supplementary units was created to accommodate the radian and steradian. Decades later, The CGPM decided:
(1) to interpret the supplementary units in the SI, namely the radian and the steradian, as dimensionless derived units, the names and symbols of which may, but need not, be used in expressions for other SI derived units, as is convenient, and
(2) to eliminate the separate class of supplementary units (Resolution 8 of the 20th CGPM (1995)).
The above definition has been adapted from the SI Brochure 9th edition, 2019. One is not expected to learn these definitions. It is just for reference to understand the source of these units and their standard adoption.