Fundamental Units
Measuring physical quantities is one of the most essential tasks in science and engineering. Every measurement is expressed using standard and internationally accepted units known as fundamental units. In this chapter, all quantities are expressed using these three basic units:
- Length (L or l)
- Mass (M or m)
- Time (t)
Derived Units
Certain units are formed by combining fundamental units. These are called derived units. Examples include units of area, velocity, pressure, acceleration, and many more.
Systems of Units
Four systems of units are commonly used and globally recognized:
- C.G.S. System
- F.P.S. System
- M.K.S. System
- S.I. System
C.G.S. Units
In this system, the fundamental units are: centimetre for length, gram for mass, and second for time. This system is often referred to as the physicist’s unit system or absolute system.
F.P.S. Units
In the F.P.S. system, the basic units are: foot (length), pound (mass), and second (time).
M.K.S. Units
This system uses metre, kilogram, and second for measuring length, mass, and time respectively. These units are also known as engineering or gravitational units.
International System of Units (S.I. Units)
The 11th General Conference on Weights and Measures introduced a unified system of units known as the International System of Units (S.I.). This system is widely used today across many nations.
In India, the Weights and Measures Act (1956) was later revised to adopt S.I. units officially for industry and commerce.
Commonly Used Derived Units in S.I. System
| Quantity | Unit |
|---|---|
| Density | kg/m³ |
| Force | Newton (N) |
| Pressure | Pascal (Pa) |
| Work/Energy | Joule (J) |
| Power | Watt (W) |
| Viscosity (absolute) | kg/m·s |
| Viscosity (kinematic) | m²/s |
| Velocity | m/s |
| Acceleration | m/s² |
| Angular acceleration | rad/s² |
| Frequency | Hertz (Hz) |
Metre
The international metre may be defined as the shortest distance (at 0°C) between the two parallel lines, engraved upon the polished surface of a platinum-iridium bar, kept at the International Bureau of Weights and Measures at Sevres near Paris.
Kilogram
The international kilogram may be defined as the mass of the platinum-iridium cylinder, which is also kept at the International Bureau of Weights and Measures at Sevres near Paris.
Second
The fundamental unit of time for all the three systems, is second, which is 1/24 × 60 × 60= 1/86 400th of the mean solar day. A solar day may be defined as the interval of time, between the instants, at which the sun crosses a meridian on two consecutive days. This value varies slightly throughout the year. The average of all the solar days, during one year, is called the mean solar day.
1.13 Presentation of Units and Their Values
To simplify communication and keep measurements standardized around the world, ISO (International Organization for Standardization) provides guidelines on how to express units and their multiples. In practice, it is not always convenient to use metre, kilogram, and second for every measurement. Therefore, prefixes are added to basic units to create practical and easy-to-use multiples.
Table: Prefixes Used in Basic Units
| Multiplier | Power of 10 | Prefix | Symbol |
|---|---|---|---|
| 1 000 000 000 000 | 10¹² | tera | T |
| 1 000 000 000 | 10⁹ | giga | G |
| 1 000 000 | 10⁶ | mega | M |
| 1 000 | 10³ | kilo | k |
| 100 | 10² | hecto | h |
| 10 | 10¹ | deca | da |
| 0.1 | 10⁻¹ | deci | d |
| 0.01 | 10⁻² | centi | c |
| 0.001 | 10⁻³ | milli | m |
| 0.000001 | 10⁻⁶ | micro | µ |
| 0.000000001 | 10⁻⁹ | nano | n |
| 0.000000000001 | 10⁻¹² | pico | p |
1.14 Rules for S.I. Units
The following guidelines help maintain clarity when writing S.I. units:
- Numbers with more than four digits should be separated by spaces (not commas), grouping every three digits from both sides of the decimal point.
- No space is needed for four-digit numbers.
- Use a dash to connect units that multiply each other (e.g., N-m).
- Unit symbols never take plural form (e.g., 5 m, not 5 ms).
- Symbols are written in lowercase, except those derived from proper names (e.g., N for newton, W for watt).
- When writing the full name of units derived from a scientist's name, the name begins with a lowercase letter (e.g., 90 newton, not 90 Newton).
Standard Abbreviations Used in Text
| m | metre |
| km | kilometre |
| kg | kilogram |
| s | second |
| min | minute |
| N-m | newton×metre |
| kN-m | kilonewton×metre |
| rev | revolution |
| rad | radian |