Study Notes
What is a Unit?
A unit is a standard reference used to express a physical quantity.
For example:
- Length is expressed in meter (m)
- Speed is expressed in meter per second (m/s)
Here, meter and meter per second are the units of length and speed respectively.
System of Units
Different systems of units are used depending on how fundamental quantities like mass, length, and time are measured. Based on this, there are four main systems of units:
- CGS system
- FPS system
- MKS system
- SI system
Comparison of Systems
| Quantity | CGS System | FPS System | MKS System |
|---|---|---|---|
| Length | Centimeter | Foot | Meter |
| Mass | Gram | Pound | Kilogram |
| Time | Second | Second | Second |
SI System of Units
The SI system (International System of Units) is an extension of the MKS system. It includes units for all fundamental physical quantities.
Fundamental Quantities and SI Units
| Quantity | SI Unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric Current | ampere | A |
| Temperature | kelvin | K |
| Luminous Intensity | candela | Cd |
| Amount of Substance | mole | mol |
Types of Units
There are three main types of units:
- Fundamental units
- Derived units
- Supplementary units
1. Fundamental Units
Fundamental units are the units of fundamental quantities.
They are independent and cannot be expressed in terms of other units.
There are seven fundamental units in SI:
- meter (m)
- kilogram (kg)
- second (s)
- kelvin (K)
- candela (Cd)
- mole (mol)
- ampere (A)
2. Supplementary Units
Supplementary units are used for geometric angles.
| Quantity | Unit | Symbol |
|---|---|---|
| Plane angle | radian | rad |
| Solid angle | steradian | sr |
3. Derived Units
Derived units are formed from fundamental and supplementary units.
They depend on fundamental units.
Examples:
- Velocity = m/s
- Acceleration = m/s$^{2}$
- Force = kg m s$^{-2}$
SI Prefixes (Powers of Ten)
To express very large or very small measurements conveniently, SI prefixes are used for powers of ten.
| Powers of Ten | Prefix | Symbol | Powers of Ten | Prefix | Symbol |
|---|---|---|---|---|---|
| $10^{24}$ | Yotta | Y | $10^{-24}$ | Yocto | y |
| $10^{21}$ | Zetta | Z | $10^{-21}$ | Zepto | z |
| $10^{18}$ | Exa | E | $10^{-18}$ | Atto | a |
| $10^{15}$ | Peta | P | $10^{-15}$ | Femto | f |
| $10^{12}$ | Tera | T | $10^{-12}$ | Pico | p |
| $10^{9}$ | Giga | G | $10^{-9}$ | Nano | n |
| $10^{6}$ | Mega | M | $10^{-6}$ | Micro | $\mu$ |
| $10^{3}$ | Kilo | k | $10^{-3}$ | Milli | m |
| $10^{2}$ | Hecto | h | $10^{-2}$ | Centi | c |
| $10^{1}$ | Deca | da | $10^{-1}$ | Deci | d |
Important Size Orders (for Exam)
- Size of nucleus ≈ $10^{-14}$ m
- Size of atom ≈ $10^{-10}$ m
These values are important for entrance exam questions.