System of Units

Introduction to Units and Dimensions

All measurements are composed of two parts. One is a quantitative magnitude or number (n), and another part is given by the way this quantity is measured, or the so-called unit (u). This principle applies to any kind of quantity, for example, the length of an object = 40 cm. To be able to carry out operations between different quantities, it is necessary to maintain the same unit as a base. In this way, the operations performed between them follow the same rules as simple mathematical operations. For example, if we have n1 and n2 as numerical values of a physical quantity with their corresponding equivalent units u1 and u2, then n1u1 = n2u2.

Types of Quantities

There are two main types of quantities. The first are known as fundamental quantities, which are independent of other quantities. The second type of units is the so-called derived units. The latter refer to quantities that are derived from the fundamental quantities and are called derived quantities.

Systems of Units

There are three globally recognised systems of units. These systems and their main units are explained below: – C.G.S. system (also known as the French system): as its acronym indicates, this system has as its unit of length the centimetre (cm), as its unit of mass the gram (g) and, finally as its unit of time the second (s). – F.P.S. system (known as the imperial or British system): on the other hand, in this system length is expressed in feet (ft), mass in pounds (lb) and time in seconds (s). – M.K.S. system (also called metric system): the units of length, mass and time vary again. Thus, the units are the metre (m), kilogram (kg) and second (s), respectively.

International SI System

To have a consolidated basis throughout the scientific world, the international or SI system has been developed. This system defines the universal measurements used in the world of technical and scientific research

SI Fundamental Units

The fundamental units within the international system are listed below, considering their magnitudes.

1. Length: the unit defined is the metre.

This measurement is defined by the distance that light travels in a vacuum for 1 / 299792458 seconds.

2. Mass: the unit for this quantity is kg.
3. Time: this quantity is represented in seconds. One second represents the time it takes 9192631770 radiation periods of a Cesium 133 atom.
4. Current: its corresponding unit is the ampere. This unit represents the constant current that would be passed between two parallel straight conductors placed in a vacuum 1 metre apart, producing a force of 210 newtons per metre of length.
5. Temperature: Although not as well-known as other measurements in everyday life, the temperature has a standard unit of reference called Kelvin. This unit is defined as a fraction of 1/273.16 of the temperature at which the triple state of water is found.
6. Quantity of substance: different from mass, this unit is related to the number of particles and is known as a mole. A mole represents a quantitative measure of the substance contained in a system, where there is an equal number of elementary entities and atoms. To relate mass to the mole, the molecular mass of the different chemical elements is used.
7. Luminous intensity: it is a unit in the international system of the candela, which is defined as the luminous intensity in a defined direction. This intensity is emitted from a source of monochromatic radiation at a specific voltage.

SI Derived Units

Derived units are the result of operations using the base units. Therefore, these units are unlimited. In these cases, the units are expressed using the dimensions of the base units. Another way of expressing these units is to express them in terms of the base and derived units. Some examples of these units are shown in the following list:

1. Force with its unit being a Newton. N=kg⋅m⋅s^-2
2. Frequency and its unit, Hertz. Hz=s^-1
3. Electric charge expressed in Coulombs. C=s⋅A
4. Electric potential (or voltage) with Volt as SI unit. V=kgm²s^-3A^-1
5. Inductance discovered by the American scientist Henry, after whom the unit is named. H=kgm²s^-2A^-2
6. Capacitance in Farads.  F=kg^-1m^-2s⁴A²
7. Resistance, Impedance, Ohm Reactance. =kgm²s^-3
8. Electrical conductance expressed in Siemens. S=kg^-1m^-2s³A²
9. Magnetic flux in its Weber unit. Wb=kgm²s^-2A^-1
10. Magnetic flux density or magnetic field, both represented in Tesla. T=kgs^-2A^-1
11. Energy, work, heat are different quantities that are expressed in the same unit, in this case, the Joule. J=kgm²s^-2
12. Power is expressed as the amount of energy in one second or Watts. W=kgm²s^-3
13. Angle is not expressed in degrees as we most commonly know them but in Radians. This unit is dimensionless as it represents the ratios of two distances. Rad=mm^-1
14. Momentum (P) is expressed in kilogram metre per second (kg⋅ m/s).
15. Velocity represented as distance over time, i.e. in m/s.