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The term unit refers to the amount or magnitude of any physical portion that is measurable. Different units are accustomed to indicating other measurements of particular types of quantities. Many physical quantities are measured to experiment, and many material amounts form the basis of mathematical equations. To measure material such amounts, appropriate and unique units are made to measure them accurately.
Understanding the fundamentals and introduction to dimensions of physical quantities is of utmost importance to know the correctness of the equations and conversion of units. Knowing the measurement also helps us search out any missing variable in a given equation.
SI Unit
SI stands for Systeme International. It is the International System of Units. SI system is the standard system of units used by all the countries to measure any physical quantities. The metric system of measurements is the traditional system used by all countries worldwide to measure and quantify material amounts. The SI system was introduced to solve the issue of the usage of different units by different countries.
The SI unit consists of seven fundamental or base units. These are called so because all the other physical quantity units are derived by combining these base units of measurement.
Derived units are any physical quantities derived by the various combinations of the fundamental physical quantities.
Actual Units
Seven physical base amounts form the basis and building blocks for deriving the other physical quantities.
The basic units of measurement
|
Physical Property |
Unit |
Symbol |
|
Length |
Metre |
m |
|
Mass |
Kilogram |
Kg |
|
Time |
second |
s |
|
Temperature |
Kelvin |
K |
|
Electric Current |
Ampere |
A |
|
Amount of Substance |
Mole |
mol |
|
Luminous Intensity |
Candela |
cd |
-
Length- Metre(m)
The metre is the length of the trail travelled by light in a vacuum during a time interval of 1/299,792,458 a second. Length is measured in metres. Distance measures how far an object extends from its source.
-
Time – Second(s)
Time is defined as the irreversible progression of existence and events in the past, present, and future as a whole. A second period is 9,192,631,770 periods of radiation corresponding to transitions between the two ultrafine levels in the ground state of the caesium-133 atom.
-
Mass – Kilogram(kg)
A body’s mass indicates how much matter is contained. There is a kilogram equivalent to the mass of the international kilogram prototype, manufactured from an alloy of platinum and iridium at the International Bureau of Weights and Measures in Sevres, close to Paris.
-
Temperature – Kelvin(K)
The temperature measurement of the intensity of heat present in a substance. It is also the degree of hotness or coldness of a substance. The kelvin is the fraction 1273.16 of the thermodynamic dynamic temperature of the triple point of water.
-
Electric Current – Ampere(A)
Electric current measured in ampere is the movement of electric charges like electrons inside a material. There will be a constant flow of amperes if two straight conductors of endless size are placed parallel in a vacuum, both with negligible circular cross-sections, producing forces between these conductors equal to 2×10-7 newton per metre of length.
-
Amount of substance – Mole(mol)
The number of particles ( atoms or molecules) in a system(element or compound) is called the Amount of substance. Molecular mass is defined as the number of elementary particles in a system that equals the number of atoms in 0.012kg of C- 12 atoms.
-
Luminous Intensity – Candela(cd)
The total amount of visible light emitted in a unit of time per unit of solid angle is luminous intensity. The candela is a unit of intensity in a given direction for monochromatic radiation with the frequency of 540×1012 Hz, which features radiant power density in this direction of 1/683 a watt per steradian.
Supplementary Fundamental Units of measurement
The two additional base units of measurement are radian and steradian. It measures the plane angle and solid angle, respectively.
|
Supplementary Fundamental Quantity |
Supplementary Unit |
Symbol |
|
Plane Angle |
radian |
rad |
|
Solid Angle |
steradian |
Sr |
Derived Units
A physical quantity derived from these seven fundamental physical quantities in addition to these seven quantities is termed as derived quantity. The quantities derived from these relationships are called Derived Quantities.
Some examples of derived quantities are
|
Area |
Metre square |
m2 |
|
Force |
Newton |
N |
|
Frequency |
Hertz |
Hz |
|
Work |
Joule |
J |
Measurement of length and mass
In addition to the fundamental units, there are some other units used for practical ease.
-
Length
The length refers to the distance between the subject and the source. The SI unit of length is metre(m). But for practical use, other units of measurements are also used.
|
Unit |
Symbol |
Relationship with the SI unit |
|
centimetre |
cm |
1 m = 100 cm |
|
millimetre |
mm |
1 m = 1000 mm |
|
kilometre |
km |
1km = 1000m |
|
decimetre |
dm |
1dm = 0.1m |
|
nanometre |
nm |
1 nm = 10-9m |
|
Angstrom |
A° |
1A° = 10-10m |
|
Yard |
yd |
1 yd = 0.914m |
|
Inch |
in |
1 in = 0.0254m |
|
Foot |
ft |
1 ft = 0.3048m |
-
Mass
The mass of a physical body is its amount of matter. The SI unit of mass is a kilogram. Other units used in addition to kg are
|
Unit |
Symbol |
Relation with kilogram(kg) |
|
milligram |
mg |
1 kg = 1000 mg |
|
quintal |
q |
1q = 100kg |
|
tonne |
t |
1t = 1000kg |
|
carat |
c |
1c = 200 mg |
Introduction to Dimensions of Physical Quantities
Dimension – The powers to which the base units are raised to get one unit of a physical quantity has named the dimensions of a physical quantity.
The dimensional formula expresses a physical quantity in terms of the fundamental or base quantities of measurement with correct dimensions.
|
Physical Quantity |
Dimension |
|
Luminous Intensity |
[cd] |
|
Temperature |
[K] |
|
Time |
[T] |
|
Mass |
[m] |
|
Amount of substance |
[mol] |
|
Electric Current |
[A] |
|
Length |
[l] |
The general formula for writing the dimension for a physical quantity is Q= MaLbTc, where a,b,c represent the powers of fundamental units to be raised. The examples of some dimensions of a physical quantity are
Area – [L2]
Density – [ML-3]
Frequency – [T-1]
Force – [M1L1T-2]
Dimensional Analysis
When each physical quantity in a mathematical equation is represented in its dimensional form, dimensional analysis is employed to see whether or not a specific equation is correct dimensionally.
Applications of Dimensional Analysis
- Dimensional Analysis is employed to test the validity and correctness of an equation.
- Dimensional analysis is employed to determine the dimensions of an unknown variable’s dimension in a given equation.
- Dimensional analysis is used to convert units from one system to another.
Conclusion
To measure a physical quantity, we need units. There are seven base units of measurement. They include length, mass, time, electric current, temperature, luminous intensity and amount of substance. Radian and steradian are the two additional base units of measurement.
Using combinations of fundamental units, the derived units are achieved. To introduce dimensions of physical quantities, we need to know what dimensions are. Dimensions are the powers to which a fundamental unit has to be raised to get the physical quantity. The principle of homogeneity states that the dimension on both sides of the equation should be the same in a mathematical equation.
The dimensional analysis is employed to check the correctness of an equation, determine the unknown variable in an equation, and convert units from one system to another.
