What is the difference between fundamental and derived?

Fundamental refers to something that is basic, essential, or foundational. It is the underlying principle or concept that something is based on. Derived, on the other hand, refers to something that is obtained or developed from something else. It is not original or primary, but rather comes from or is based on something else. In other words, fundamental is the core or basis, while derived is the result or outcome.

Fundamental Quantities:

- Basic units of measurement that cannot be expressed in terms of other quantities.
- Examples: length (meter), mass (kilogram), time (second), electric current (ampere), temperature (kelvin), amount of substance (mole), luminous intensity (candela).

Derived Quantities:

- Quantities that can be expressed in terms of fundamental quantities using mathematical operations.
- Examples:
- Speed (derived from length and time)
- Volume (derived from length)
- Density (derived from mass and volume)
- Energy (derived from mass, length, and time)
- Pressure (derived from force and area)

Key Differences:

| Feature | Fundamental Quantities | Derived Quantities |
|---|---|---|
| Nature | Basic, not expressible in other terms | Expressible in terms of fundamental quantities |
| Units | SI base units (e.g., meter, kilogram) | SI derived units (e.g., meter per second, cubic meter) |
| Measurement | Direct measurement | Derived from measurements of fundamental quantities |
| Dependence | Independent | Dependent on fundamental quantities |

Implications:

- Fundamental quantities form the basis for all other measurements.
- Derived quantities are useful for describing and quantifying various physical phenomena.
- The relationship between fundamental and derived quantities is essential for understanding and applying physical laws.