Units and Dimensions in a nutshell

Everyday life must measure or compare physical quantities, which necessitates the use of measuring techniques. Physical quantities are measured in terms of the unit of measurement, which is referred to as a standard of that particular physical quantity. Consequently, to measure each of the standard quantities, we designate specific units for them that are widely recognised around the globe.

Other comparable values may also be stated and measured in terms of these units, as can a variety of other related quantities. As a result, to represent any measurement performed, we need the numerical value (n) and the unit (μ).

Measured physical amount = Numerical value x unit of measurement.

For example, the length of any given rod equals 8 m., where 8 is a numeric number, and m (metre) is a unit of measurement for length.

All this, and more, can be checked in the units and dimensions pdf from Vedantu.

Let us learn the fundamentals!

Fundamental quantities are those fundamental physical quantities that do not need the use of any other physical quantity to represent them in any other physical quantity. As a result, they cannot be resolved further in other physical quantities, including time. As a result, fundamental quantities are referred to as fundamental physical quantities. Basic units are the units of measurement that are used to represent these fundamental physical quantities.

Fundamental units of measurement are the kilogramme, the metre, and the second, which are all stated in kilogrammes, metres, and seconds, respectively. The phrase “derived physical quantities” refers to all physical quantities represented in physical fundamental amounts or derived from the combination of two or more fundamental quantities and can be expressed in terms of basic physical quantities. For example, the units of velocity and force are measured in m/s, and kgm/s2, respectively, and are instances of derived units.

Definition of the fundamental unit

The vast majority of SI units are used in scientific research. SI is a logical unit system. Coherent unit systems are those in which the units of derived quantities are multiples or submultiples of some fundamental units. 

1. One second is the duration of 9192631770 cycles of the radiation corresponding to the transition between the two hyperfine levels of caesium-133 atoms’ ground state.
2. Ampere: The current that causes each of two parallel conductors of infinite length and negligible cross-section to experience a force of 2 10-7 newtons per metre of length when put one metre apart in a vacuum is referred to as one ampere.
3. A metre is equivalent to 1650763.73 times the wavelength of light released in a vacuum due to Krypton-86’s electronic transition from the 2p10 to the 5d5 state. However, in 1983, the 17th General Assembly of Weights and Measures defined the metre’s light velocity. A metre is described in this definition as the distance travelled by light in a vacuum during a period of 1/299, 792, 458 of a second.
4. One kilogram is the mass of a platinum-iridium alloy cylinder stored at the International Bureau of Weights and Measures in Serves, near Paris.
5. Kelvin is the fraction of 1/273.16 of the thermodynamic temperature of water’s triple point.
6. The radian is the angle formed by an arc of a circle equal to its radius at its centre. 1 radian is equal to 57o17l45ll.
7. One candela is the luminous intensity of a surface of a black substance with an area of 1/600000 m2 in the perpendicular direction at the temperature of solidifying platinum at a pressure of 101325 Nm-2.
8. A mole is the quantity of material in a system that includes the same number of elementary entities as atoms in 12 10-3 kg of carbon-12.
9. The steradian is the angle subtended at its centre by a one-square-meter portion of the surface of a one-meter radius sphere.

Units System

Previously, three distinct unit systems were employed in various nations. These systems included the CGS, FPS, and MKS. However, the whole globe has now adopted the international SI system of units. Seven quantities are used as the basis quantities in this unit system.

• Centimetre, Gram, and Second are used in the CGS System to indicate length, mass, and time, respectively. 
• In the FPS, the length, mass, and time units are the foot, pound, and second. 
• In the MKS System, length is measured in metres, mass is measured in kilograms, and time is measured in seconds.

In the standard units system, mass, time, length, electric current, thermodynamic temperature, substance concentration, and luminous intensity are all stated in the following units: kilogramme, second, metre, ampere, kelvin, mole, and candela.

What are the dimensions?

The dimensions of a physical quantity are the powers of the basic quantities multiplied by that amount to describe it. A physical quantity’s dimensional formula is an equation that specifies how and which of the basic quantities are included in that quantity. It is written by surrounding the symbols representing base amounts in square brackets with the corresponding power, i.e. 

For instance, the mass dimension symbol is as follows: (M)

A dimensional equation is an equation derived by equating a physical quantity with its dimensional formula.

Dimensional analysis

Dimensional analysis is the process of determining the dimensions of physical quantities to verify their relationships. These dimensions are unrelated to numerical multiples and constants, and every quantity in the world may be stated as a function of them.

Applications of dimensional analysis:

1. To deduce the connection between distinct physical quantities, it is necessary to use the homogeneity of dimension. If the dependent amounts are known, the new relationship among physical quantities may be determined using the homogeneity of dimension.
2. This function converts a physical amount between two different systems of the unit.
3. To determine if a physical relationship is dimensionally accurate, consider the following: If the terms of both sides of a given physical relationship have the same dimensions, the relationship is dimensionally correct. The principle of uniformity of dimensions is the most well-known name for this topic.

Conclusion

We hope that we could clear up any confusion you had about the fundamentals of units and measurements. You must understand the basics when it comes to these units and dimensions in Physics.