fundamental and derived units (2024)

Introduction

Let’s look at the Fundamental and Derived Units:

Fundamental and Derived Units

Physics is a discipline of science concerned with the study of nature and natural events, as we all know.

Let’s assume I drop a ball from a specific height and it lands on the ground freely. To acquire an exact response to this, you’ll need to measure things like distance, velocity, and time.

What are they, and what do they represent? Let’s learn more:

A System of Units

For all forms of physical quantities, the system of units is the whole collection of units, both basic and derived units. Each system is given a name depending on the fundamental units around which it is built. The following is the standard unit system used in mechanics:

The Foot-Pound System (f.p.s.): A British engineering unit system that employs the foot as the unit of length, pound as the unit of mass, and second as the unit of time.

The Centimeter-Gram-Second System (c.g.s.): A system that employs the centimeter, gram, and second as the three main units for length, mass, and time, respectively.

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

Fundamental Units

Fundamental units are fundamental, in the sense that they may be stated irrespective of any other physical quantity. This means that it can’t be resolved any further in terms of other physical quantities. It is also known as a fundamental physical quantity. Each fundamental quantity has its own set of values and units.

Fundamental Units are self-contained units that are not dependent on one another. Fundamental Units give rise to Derived Units. A basic unit of length is the meter, and a fundamental unit of time is the second. The meter per second (ms-1) is, on the other hand, a derived unit of velocity.

Aside from the seven fundamental units, there are two more fundamental units: Radian and Steradian. Steradian (Sr) is used to measure the solid angle, whereas Radian (Rad) is used to measure the plane angle. Fundamental units are used to create derived units. Velocity (meters per second) and acceleration (meters per second2) are examples of derived units.

The following are the definitions for each fundamental unit:

Kilogram

A kilogram is now defined by a cylindrical piece of platinum-iridium held in the International Committee on Weights and Measures headquarters in Paris. However, since 1879, that lump has shrunk by 50 micrograms, which is why scientists are exploring methods to define a kilogram in terms of natural constants rather than a man-made item.

Meter

Previously, the meter was calibrated by measuring the distance between two “X’s” on a platinum Iridium metal bar held at 0°C in Paris. It was later defined as the length of light’s journey in vacuum at a period of 1/299,792,458 of a second. One meter now holds 1650763.73 wavelengths of orange-red Kr-86 light.

The second was once the length of a typical solar day multiplied by 86,400. Since 1967, a second has been defined as the amount of time that a cesium atom vibrates 9192631770 times in one second.

Kelvin

The 1/273.16 fraction of the thermodynamics temperature of water’s triple point is one Kelvin.

Candela

Candela is the luminous intensity of a source emitting monochromatic radiation with a frequency of 5401012 hertz and a radiant intensity of 1683 watts per steradian in a particular direction.

In a vacuum, an electric current maintained in two straight parallel conductors of infinite length and insignificant cross-section area put one meter apart produces a force of 2 x 10-7 N per meter length between them.

Mole

One mole is the quantity of substance in a system that comprises numerous constituent entities (such as atoms, molecules, ions, electrons, or a collection of particles, as in 0.012 kg of carbon isotope 6C12 and atoms).

Fundamental units are the most basic units, whereas derived units are those that may be represented in terms of fundamental units and are generated by multiplying or dividing fundamental units. The most frequent basic units are length, mass, and time, but fundamental units are also employed to quantify specific physical quantities in the thermal, electrical, and lighting fields. Because these units are only employed when certain specific classes are involved, they might be classified as auxiliary basic units. Every derived unit is derived from a physical rule that defines the unit.

A derived unit is identified by its dimensions, which may be described as the derived unit’s whole algebraic formula. L, M, and T are the dimensional symbols for the fundamental units of length, mass, and time, respectively. As a result, the dimensional symbol for the voltage derived unit is

[V=M. L2I.T3=[M.L2.I-1.T-3]]

Derived units

The derived units are used for commodities in which the units are created by combining basic units. Names are occasionally given to derived units. The SI unit of force, for example, is kg ms-2, sometimes known as Newton (N). A watt is a unit of power equal to kg m2 s-3 (W).

Systems of Units

For all sorts of physical quantities, any system of units encompasses the whole set of both fundamental and derived units. The following is the chosen unit system:

• CGS System (Centimeter Gram Second)

According to the rules of this system, the unit of length is the centimetre, the unit of mass is the gram, and the unit of time is the second.

• FPS System (Foot Pound Second)

According to the rules of this system, the unit of length is the centimetre, the unit of mass is a pound, and the unit of time is second.

• MKS System (Meter Kilogram Second)

According to the rules of this system, the unit of length is meter, the unit of mass is the kilogram, and the unit of time is second.

• SI System

The S.I system, or System International d’Units, has seven basic units and two supplemental fundamental units.

Important Units of Length

The distances might be indefinitely greater in magnitude and cannot be expressed in meters or kilometres. For example, the distances between planets and stars. As a result, bigger units of length, such as ‘astronomical unit, “light-year,’ parsec,’ and so on, must be used when doing such computations, some of which are:

• Astronomical Unit – The average distance between the Earth and the sun is measured in astronomical units.
  1 AU = 1.496 x 1011 m.
• Fermi – The size of a nucleus is measured in fermi.
  1 fermi = 1f = 10-15 m
• Angstrom – Size of a tiny atom
  1 angstrom = 1A = 10-10 m
• Light Year – One year’s distance traveled by light in a vacuum.
  9.46 x 1015 m is the length of a light-year.
• Parsec – The distance at which an arc of the length of one astronomical unit subtends an angle of one second at a point.
  1 parsec = 3.08 x 1016 m

Conclusion

Fundamental units are those that are self-contained and unaffected by other units. All derived units are created by multiplying and/or dividing one or more basic units with or without the addition of any additional numerical element. Fundamental units are those that are independent of other variables, such as length, mass, time, temperature, current, luminous intensity, and substance quantity. Derived units are those that may be stated in terms of basic units and are also dependent on others.