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In engineering and science, dimensional analysis is the analysis of the relationships between physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure.
The international system of units, or SI, includes seven base units and several derived units with special names. These are used to measure a variety of dimensions.
Mass
Mass is the quantitative measure of inertia, a fundamental property of matter. Its value is always constant for a body.
It is the sum of mass and weight and is measured in the International System of Units (SI) as a kilogram. It also reflects the amount of force that is exerted on an object when it is accelerated due to gravity at the earth’s surface, or on the moon or in interstellar space.
The SI defines seven units, called base units, which are a preferred set of physical quantities for measurement and analysis. These are the second, the metre, the kilogram, the ampere, the kelvin, the mole and candela.
Length
Length is one of the fundamental dimensions in a System of Units. It is defined as the distance between two endpoints of a line segment or curve.
Depending on the object being measured, length is expressed in meters or feet. In the metric system, it is also expressed in kilometers (km), millimeters (mm), centimeters (cm) and decimeters (dm).
Units used to express different physical quantities are related by convention and standardized. They are usually chosen from a basis set. In addition, a conversion factor is derived from this basis set and related to each physical quantity.
Time
Time is one of the most important dimensions in physics, but it’s also a difficult concept to define. Various philosophers and scientists have different views of what time means.
The most common is the realist view, which holds that time is part of a fundamental structure in which events occur in sequence. This view has influenced the way that non-relativistic classical mechanics is understood.
In the International System of Units, the base units for length, mass and time are the kilogram (kg), the meter (m) and the second (s). Derived dimensions can be obtained from these.
Electric Charge
One of the most important physical properties of matter is electric charge. This property causes matter to repel other objects with the same charge and attract those with the opposite charge.
Many particles of matter, including protons and electrons, have charge. It can be positive or negative (commonly carried by protons and electrons respectively).
Electric charge is quantized; it comes in integer multiples of a fundamental unit called the elementary charge, e, about 1.602×10-19 C. This is the smallest charge that can exist freely.
Temperature
Temperature is the quantity that relates to the average kinetic energy of atom-scale particles. It determines how fast the particles move within a material and is measured with a thermometer or calorimeter.
Temperature has two known reference points: the Celsius scale and the Kelvin scale. The Celsius temperature scale is used for everyday temperature measurements in most countries, while the Kelvin temperature scale is used in scientific environments.
There are also a few absolute temperature scales. The internationally agreed Kelvin scale uses a numerical zero at the absolute zero of temperature, which is the point at which all molecular motion ceases.