Fundamental and Derived Units of Measurement

Fundamental and derived units are essential components of the measurement system in physics. Fundamental units are the standard units used to measure basic quantities like length (meter), mass (kilogram), and time (second). These units are independent and form the foundation of all measurements. Derived units, on the other hand, are obtained from combinations of fundamental units through mathematical relationships. Examples include speed (meters per second) and force (newton). Together, they enable accurate and consistent scientific measurements.

History of Measurement

Before humans created a standardized system of measurement, many cultures utilized local traditions for measuring objects. These are as follows: 

• The Cubit - This measurement originated in Egypt about 3000 B.C. It was used to build pyramids. 

• The Fathom - It is a unit of length in the imperial and the U.S. customary systems equal to 6 feet (1.8288 m).   

• The Hand-Span - It is the distance between the tip of the smallest finger and the tip of the thumb. We still use this to measure the height of horses.   

Need for Measurement 

We all know that Physics is a branch of Science that deals with the study of nature and natural phenomena. 

Let’s say I drop a ball from a certain height; it falls freely on the ground.

Being a physics enthusiast to understand this natural phenomenon; I will search for answers to the following questions:

• Why did this ball fall on the ground? 

• At what speed does an object fall? 

• Is the velocity of a ball constant? 

• How much will it take for a ball to reach the ground? 

• Is the velocity of a body directly related to its mass?

To get a precise answer to these questions, measuring the quantities like distance, velocity, and time becomes essential. 

A 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 are as follows: 

• The F.P.S or Foot-Pound System: A British engineering system of units that use the foot as the unit of measurement of length, and pound as the unit of mass, and the second as the unit of time. 

• The C.G.S or Centimeter-Gram-Second System: A Gaussian system that uses centimeter, gram, and second as the three basic units for length, mass, and time respectively. 

• The M.K.S or Meter-Kilogram-Second System: The fundamental units of length, mass, and time are meter, kilogram, and second respectively.

Fundamental and Derived Units

The quantities which we can measure directly or indirectly are known as physical quantities. Fundamental units are the basic units of measurement that serve as the foundation for all other derived units in physics.

For example, distance, displacement, momentum, etc.

The Physical Quantities are Divided into Two Categories: 

• Fundamental quantities, and 

• Derived quantities

Fundamental Quantities

The physical quantities that do not depend upon the other quantities are the fundamental quantities.

There are Seven Fundamental Quantities

Row 8, and 9: Two supplementary units on the SI system are: 

• The Radian - It is the unit of a plane angle. One radian is the angle subtended by the centre of a circle by an arc and is equal in length to the radius of a circle. 

• The 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. 

Derived Quantities 

The physical quantities that depend upon the fundamental quantities are known as the derived quantities. 

Let’s take examples of derived units: 

Derived Units Table: The Table Shows the List of Derived Units 

Some Important Practical Units 

1.  In macrocosm measurements, i.e., measurement of very large distances: 

• Astronomical units (A.U.) 

 It is the average distance of the center of the sun from the center of the earth. 

1 A.U. = 1.496 x 10¹¹m ≃ 1.5 x 10¹¹m 

• A light-year (ly)  

 One light-year is the distance traveled by light in a vacuum in one Earth year.  

 As the speed of light in a vacuum is 3 x 10⁸ m/s, and  

1 year = 365 x 24 x 60 x 60 seconds. 

 Therefore, one light-year = 3 x 10⁸ x 365 x 24 x 60 x 60 meter 

   1 ly = 9.46 x 10¹⁵meter  

• Parsec 

 It is the unit of long distances and represents the parallactic seconds. 

Parsec is the distance at which 1 A.U. a long arc subtends an angle of 1”. 

As 1 A.U. = 1.496 x 10¹¹m, and 

Ө = 1/60 min  = 1/60 x 60 degree = 1/60 x 60 x π/180 radian 

Since the radius of an arc, r = length of an arc (l)/angle subtended (Ө) 

Therefore, 1 parsec = 1 A.U./1 sec = (1.496 x 10¹¹) x (60 x 60 x 180)/(π) 

So,  

1 parsec = 3.1 x 10¹⁶m

The Evolution of Measurement 

The concept of measurement is one of the most fundamental concepts in scientific theory. Scientists would have a difficult time conducting experiments and forming theories if they did not have the ability to measure their results. The word "measurement" is derived from the Greek word "metron," which literally translates as "limited ratio." 

An object's properties can be determined by comparing them to a standard, which is achieved through the use of measurement techniques. 

To provide scientists with a quantity, measurement necessitates the use of tools. A quantity is a way of describing how much of something there is and how many of them there are in total. Researchers employ a system of measurement known as the "metric system," which is still widely used today. It was developed in France in the 1790s and was the world's first standardized system of measurement. Except for the United States, this is the standard unit of measurement in every country except the United States today. 

Measurement Units  

The Seven Fundamental Units of Measurement (BMUs) 

Length is measured in meters (m) 

In Physics, it is defined as the length of the path taken by light in an interval of precisely one second. 

A foundation for this theory is the fundamental quantity, the speed of light in a vacuum, which is 299 792 458 m/s. 

Seconds are Measured In Time (S) 

The time taken by 9 192 631 770 periods of oscillations of the light emitted by a cesium -133 atoms to transition between two hyper-fine levels of the ground state, as measured by the time taken by 9 192 631 770 periods of oscillations of the light emitted by a cesium -133 atoms. Atomic clocks, which are extremely precise, are used to determine this. 

Kilogram is the Unit of Mass (kg) 

It is the mass of a prototype platinum-iridium cylinder, which is kept at the International Bureau of Weights and Measures in Paris, France, as a permanent record. Many countries, including the United States, keep copies of this cylinder because they use it to standardize and compare weights. 

Ampere is the Unit of Electric Current (A) 

The constant current that, if maintained in two straight parallel conductors of infinite length and negligible circular cross-section when placed 1 m apart in vacuum, would produce a force equal to the product of the square of the distance between the conductors. 

The force between these conductors is one Newton for every meter of length between them. While it may appear that electric charge should have been used as a base unit, measuring current is far more straightforward, and as a result, current was selected as the standard base unit for all calculations. 

Kelvin is the Unit of Temperature (K) 

The Kelvin temperature unit is used in the International System of Units. That is exactly what it is. 

273.16-the thermodynamic temperature of water's triple point, as measured in degrees Celsius It is the temperature and pressure at which the solid, liquid, and gaseous states of water can all exist at the same time that is known as the triple point of water. 

Molecules are Units of Measurement for the Amount of a Substance (mol) 

It is measured in moles, which is the amount of substance that contains the same number of entities as there are atoms in 0.012 kilograms of carbon-12. A mole is made up of an Avogadro number of different entities. Check out our chemistry articles to learn more about the Avogadro number and other related topics. 

Candela is the Unit of Luminous Intensity (cd) 

It refers to the luminous intensity of a source that emits radiation with a constant frequency of a particular wavelength. 

Units Derived from Other Units 

SI-derived units are the units of measurement that are derived from the seven base units specified by the International System of Units and are used in scientific and engineering applications. Either they are dimensionless or they can be expressed as a product of one or more of the base units, which may then be scaled by an appropriate power of exponentiation, depending on the situation. When written in full, the names of SI-derived units are always written in lowercase letters. The symbols for units that are named after people, on the other hand, are written with an uppercase initial letter. "Hz," for example, represents the frequency unit, whereas "m" represents the unit of measurement meter. In the table below, we've provided a list of derived units for your convenience. 

Conclusion

Fundamental units are independent and not influenced by other units. Derived units, on the other hand, are formed by multiplying and/or dividing one or more fundamental units, sometimes with an additional numerical factor. Fundamental units, such as length, mass, time, temperature, electric current, luminous intensity, and the amount of substance, are self-contained and independent of other quantities. In contrast, derived units are expressed in terms of fundamental units and rely on them for their definition.