Units of Measurement, System of Units, SI Units, Fundamental and Derived Units

Welcome to the foundational chapter of Physics! To understand and describe the physical world, we need a way to quantify physical quantities. This is where the concept of measurement and units comes in. Without a standardized system, comparing observations and communicating scientific findings would be chaotic. This chapter will introduce you to the fundamental concepts of measurement, the systems of units used, and specifically, the internationally recognized SI system.

What is Measurement?

Measurement is the process of assigning a numerical value to a physical quantity by comparing it with a standard unit. For example, when we say a table is 2 meters long, we are comparing its length to a standard unit called a meter. The result of a measurement consists of two parts: a number and a unit.

Physical Quantities

A physical quantity is a property of a phenomenon, body, or substance that can be quantified by measurement. Examples include length, mass, time, temperature, velocity, force, energy, etc.

Units of Measurement

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. For a unit to be a standard, it must be:

• Universally accepted.
• Easily reproducible.
• Invariable (unchanging with time, temperature, pressure, etc.).
• Of convenient size.

System of Units

A system of units is a collection of fundamental and derived units, along with their associated rules and conventions, used to express physical quantities. Historically, several systems of units have been developed and used. Some of the prominent ones include:

1. CGS System (Centimeter-Gram-Second)

This system was developed in France. In this system:

• Length is measured in centimeters (cm).
• Mass is measured in grams (g).
• Time is measured in seconds (s).

While widely used in the past, especially in scientific research, its limitations in handling larger quantities and its incompatibility with electrical measurements led to its gradual replacement.

2. FPS System (Foot-Pound-Second)

This system is primarily used in the United Kingdom and the United States. In this system:

• Length is measured in feet (ft).
• Mass is measured in pounds (lb).
• Time is measured in seconds (s).

The FPS system is less commonly used in international scientific contexts due to its non-decimal nature and difficulties in conversion.

3. MKS System (Meter-Kilogram-Second)

This system evolved from the CGS system, aiming to resolve some of its issues, particularly in electromagnetism. In this system:

• Length is measured in meters (m).
• Mass is measured in kilograms (kg).
• Time is measured in seconds (s).

The MKS system formed the basis for the modern international system of units.

The International System of Units (SI)

The most important and universally accepted system of units is the International System of Units, abbreviated as SI (from the French "Système International d'Unités"). It was established in 1960 by the General Conference on Weights and Measures (CGPM). The SI system is a modernized metric system that is coherent, rational, and practical for all fields of science, technology, and commerce. It is based on a set of fundamental units and provides a framework for defining derived units.

Fundamental Units (Base Units)

Fundamental units are those units that are chosen by convention and cannot be derived from other units. They are independent of each other. The SI system currently recognizes seven fundamental units. These are used to measure seven fundamental physical quantities.

The Seven Fundamental SI Units:

Physical Quantity	SI Unit Name	SI Unit Symbol
Length	meter	m
Mass	kilogram	kg
Time	second	s
Electric Current	ampere	A
Thermodynamic Temperature	kelvin	K
Amount of Substance	mole	mol
Luminous Intensity	candela	cd

It's crucial to remember these seven base quantities and their SI units. They form the building blocks for all other physical measurements.

Definitions of SI Base Units (Brief Overview)

The definitions of these units are precise and are based on fundamental physical constants. While you don't need to memorize the exact definitions for most exams, understanding their basis is important.

• Meter (m): Defined based on the speed of light in a vacuum. It is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.
• Kilogram (kg): Defined based on fundamental constants. It is defined by assigning an exact numerical value of 6.62607015 × 10^-34 J⋅s (the Planck constant) to the Planck constant, h.
• Second (s): Defined based on atomic transitions. It is defined by taking the fixed numerical value of the caesium frequency Δν_Cs to be 9,192,631,770 when expressed in the unit Hz, which is equal to s^-1.
• Ampere (A): Defined based on the elementary charge. It is defined by assigning an exact numerical value of 1.602176634 × 10^-19 C to the elementary charge, e.
• Kelvin (K): Defined based on the Boltzmann constant. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380649 × 10^-23 J⋅K^-1.
• Mole (mol): Defined based on the Avogadro constant. It is defined by taking the fixed numerical value of the Avogadro constant N_A to be 6.02214076 × 10²³ mol^-1.
• Candela (cd): Defined based on luminous efficacy. It is defined by assigning an exact numerical value of 683 lm⋅W^-1 to the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² Hz.

Derived Units

Derived units are units that can be obtained by combining fundamental units through multiplication, division, or powers. They are used to express physical quantities that are derived from the base quantities. The SI system has a coherent set of derived units.

Examples of Derived Units:

• Area: The unit of area is the square of the unit of length. In SI, it is square meter (m²).
• Volume: The unit of volume is the cube of the unit of length. In SI, it is cubic meter (m³).
• Velocity: Velocity is distance divided by time. So, its unit is meter per second (m/s).
• Acceleration: Acceleration is change in velocity divided by time. Its unit is (m/s) / s = m/s².
• Force: According to Newton's second law (F = ma), force is mass times acceleration. Its unit is kg × m/s². This derived unit is given a special name: Newton (N). So, 1 N = 1 kg⋅m/s².
• Energy (Work): Work is force times distance. Its unit is N × m. This is also given a special name: Joule (J). So, 1 J = 1 N⋅m = 1 kg⋅m²/s².
• Pressure: Pressure is force per unit area. Its unit is N/m². This is also given a special name: Pascal (Pa). So, 1 Pa = 1 N/m² = 1 kg/(m⋅s²).
• Electric Charge: Charge is current times time. Its unit is Ampere × second (A⋅s). This is given a special name: Coulomb (C). So, 1 C = 1 A⋅s.

There are many derived units in SI, each defined in terms of the base units. Some of these derived units have special names and symbols (like Newton, Joule, Pascal, Coulomb, Watt, Volt, Ohm, etc.) to simplify expressions.

SI Prefixes

The SI system also includes a set of prefixes that are used to form decimal multiples and submultiples of SI units. These prefixes are essential for expressing very large or very small quantities conveniently. They are standardized internationally.

Common SI Prefixes:

Prefix	Symbol	Factor	Example
yotta	Y	1024	1 Ym = 1024 m
zetta	Z	1021	1 Zs = 1021 s
exa	E	1018	1 EG = 1018 g
peta	P	1015	1 PB = 1015 bytes
tera	T	1012	1 THz = 1012 Hz
giga	G	109	1 GeV = 109 eV
mega	M	106	1 MW = 106 W
kilo	k	103	1 km = 103 m
hecto	h	102	1 hg = 102 g
deca	da	101	1 dam = 101 m
(none)	(none)	100 = 1	1 m, 1 kg
deci	d	10-1	1 dm = 10-1 m
centi	c	10-2	1 cm = 10-2 m
milli	m	10-3	1 mm = 10-3 m
micro	μ	10-6	1 μm = 10-6 m
nano	n	10-9	1 ns = 10-9 s
pico	p	10-12	1 pF = 10-12 F
femto	f	10-15	1 fm = 10-15 m
atto	a	10-18	1 as = 10-18 s
zepto	z	10-21	1 zs = 10-21 s
yocto	y	10-24	1 ym = 10-24 m

Why SI Units are Important

The adoption of the SI system has brought about numerous benefits:

• Universality: It provides a common language for scientists, engineers, and technicians worldwide, facilitating international collaboration and trade.
• Consistency: It reduces errors and ambiguities that arise from using different units and conversion factors.
• Simplicity: The decimal nature and coherence of SI units make calculations simpler and more intuitive.
• Foundation: It provides a stable and precise foundation for scientific research and technological development.

Dimensional Analysis

Dimensional analysis is a powerful tool in physics that uses the fundamental units to analyze the relationships between physical quantities. Every physical quantity can be expressed in terms of the fundamental dimensions: Mass (M), Length (L), and Time (T). For example:

• Velocity: [LT^-1]
• Acceleration: [LT^-2]
• Force: [MLT^-2]
• Energy: [ML²T^-2]

Understanding dimensions helps in checking the correctness of equations and deriving relationships between physical quantities.

Conclusion

Mastering the concepts of units, systems of units, and especially the SI system is the first step towards a successful journey in Physics. These fundamental units and the prefixes associated with them are used extensively throughout the NEET syllabus. Ensure you are comfortable with them, as they form the basis for understanding all physical laws and equations.