Understanding derived quantities and their corresponding SI units (System International d’Unités) is essential for studying science, engineering, and applied physics. This article simplifies these concepts with examples, explanations, and a helpful table of derived SI units.
What Are Derived Quantities?
Definition:
Derived quantities are the physical quantities obtained by combining two or more fundamental quantities according to the laws of physics.
For example:
- Velocity = Distance / Time → derived from length and time.
- Force = Mass × Acceleration → derived from mass, length, and time.
- Energy = Force × Distance → derived from mass, length, and time.
These quantities cannot be measured directly; instead, they are calculated using formulas involving fundamental quantities.
What Are Derived Units?
Every derived quantity has a corresponding derived unit, which is obtained by combining the units of fundamental quantities.
For example:
- The SI unit of velocity = metre per second (m/s).
- The SI unit of force = newton (N).
- The SI unit of energy = joule (J).
So, derived units are those units that are expressed in terms of base (fundamental) units.
Fundamental vs Derived Quantities
| Aspect | Fundamental Quantities | Derived Quantities |
|---|---|---|
| Definition | Cannot be expressed in terms of other quantities | Obtained from two or more fundamental quantities |
| Examples | Length, Mass, Time, Electric current, Temperature, Luminous intensity, Amount of substance | Velocity, Force, Pressure, Energy, Momentum |
| SI Units | metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd) | metre/second (m/s), newton (N), joule (J), pascal (Pa), watt (W) |
| Measurement | Measured directly | Calculated using formulas |
| Number of Quantities | 7 (base units) | Infinite (can be derived from combinations) |
This table highlights that all derived quantities depend on the seven base quantities defined by the International System of Units.
The Seven Fundamental Quantities in SI System
| Quantity | Symbol | Unit (SI) | Symbol (Unit) |
|---|---|---|---|
| Length | l | metre | m |
| Mass | m | kilogram | kg |
| Time | t | second | s |
| Electric current | I | ampere | A |
| Temperature | T | kelvin | K |
| Luminous intensity | Iv | candela | cd |
| Amount of substance | n | mole | mol |
These seven fundamental quantities form the building blocks for all other physical quantities.
How Derived Units Are Formed
Derived units are formed by mathematical combinations (multiplication or division) of the fundamental units.
Examples:
1. Velocity = Distance / TimeUnit = metre/second → m/s
Unit = (metre/second) / second → m/s²
Unit = kilogram × metre/second² → kg·m/s² → newton (N)
Unit = newton × metre → N·m = joule (J)
Unit = newton/metre² → N/m² = pascal (Pa)
Thus, every derived unit can be expressed in terms of base units like kg, m, s, A, K, mol, and cd.
Some Important Derived Quantities and Their SI Units
Here’s a table of important derived quantities commonly used in physics and engineering:
| Physical Quantity | SI Unit | Symbol |
|---|---|---|
| Force | newton | N |
| Energy / Work | joule | J |
| Speed / Velocity | metre per second | m/s |
| Angular velocity | radian per second | rad/s |
| Frequency | hertz | Hz |
| Moment of inertia | kilogram metre square | kg·m² |
| Momentum | kilogram metre per second | kg·m/s |
| Angular momentum | kilogram metre square per second | kg·m²/s |
| Pressure | pascal | Pa |
| Power | watt | W |
| Surface tension | newton per metre | N/m |
| Viscosity | newton second per metre square | N·s/m² |
| Thermal conductivity | watt per metre kelvin | W/m·K |
| Electric charge | coulomb | C |
| Electric potential (voltage) | volt | V |
| Capacitance | farad | F |
| Electrical resistance | ohm | Ω |
| Inductance | henry | H |
| Magnetic flux | weber | Wb |
| Luminous flux | lumen | lm |
| Impulse | newton second | N·s |
Each of these derived quantities plays a crucial role in different branches of science, from mechanics to electromagnetism and thermodynamics.
Explanation of Key Derived Quantities
a) Force (Newton, N)
Defined by Newton’s Second Law:
Force = Mass × Acceleration
SI Unit = kg·m/s²
1 newton = The force required to accelerate a 1 kg mass by 1 m/s².
b) Energy / Work (Joule, J)
Energy is the capacity to do work.
Work = Force × Distance
SI Unit = N·m = kg·m²/s²
c) Pressure (Pascal, Pa)
Pressure = Force / Area
SI Unit = N/m²
1 pascal = 1 newton acting on 1 square metre.
d) Power (Watt, W)
Power = Work / Time
SI Unit = J/s = kg·m²/s³
e) Frequency (Hertz, Hz)
Frequency = Number of cycles per second
SI Unit = s⁻¹
f) Electric Charge (Coulomb, C)
Charge = Current × Time
SI Unit = A·s
1 coulomb = Charge flowing through a conductor in 1 second with current 1 ampere.
g) Electric Potential (Volt, V)
Potential = Work / Charge
SI Unit = J/C = kg·m²/(s³·A)
h) Resistance (Ohm, Ω)
Resistance = Potential Difference / Current
SI Unit = V/A = kg·m²/(s³·A²)
i) Magnetic Flux (Weber, Wb)
Magnetic flux measures the quantity of magnetism.
SI Unit = V·s = kg·m²/(s²·A)
j) Luminous Flux (Lumen, lm)
It represents the total visible light emitted from a source.
SI Unit = cd·sr (candela steradian).
Derived Units Expressed in Terms of Fundamental Units
| Derived Unit | In Fundamental SI Units |
|---|---|
| 1 newton (N) | 1 kg·m/s² |
| 1 joule (J) | 1 kg·m²/s² |
| 1 watt (W) | 1 kg·m²/s³ |
| 1 pascal (Pa) | 1 kg/(m·s²) |
| 1 coulomb (C) | 1 A·s |
| 1 volt (V) | 1 kg·m²/(s³·A) |
| 1 ohm (Ω) | 1 kg·m²/(s³·A²) |
| 1 farad (F) | 1 s⁴·A²/(kg·m²) |
| 1 weber (Wb) | 1 kg·m²/(s²·A) |
| 1 lumen (lm) | 1 cd·sr |
This breakdown helps students link abstract symbols to physical reality and understand how fundamental quantities combine mathematically.
Importance of Derived Quantities in Physics
Derived quantities are essential for:
- Simplifying complex phenomena: e.g., expressing motion, heat, or electricity using measurable relationships.
- Standardizing measurements: ensures that scientists worldwide can compare results accurately.
- Connecting concepts: derived quantities like power, pressure, or energy bridge different branches of physics.
- Engineering applications: from designing machines to predicting weather and constructing buildings.
Without derived quantities, it would be impossible to express physical relationships clearly or maintain uniformity across experiments.
Fun Fact – Named SI Units
Many derived SI units are named after famous scientists:
| Unit | Named After |
|---|---|
| newton (N) | Sir Isaac Newton |
| joule (J) | James Prescott Joule |
| watt (W) | James Watt |
| pascal (Pa) | Blaise Pascal |
| volt (V) | Alessandro Volta |
| ohm (Ω) | Georg Simon Ohm |
| farad (F) | Michael Faraday |
| henry (H) | Joseph Henry |
| weber (Wb) | Wilhelm Weber |
| hertz (Hz) | Heinrich Hertz |
| lumen (lm) | From Latin lumen (light) |
This helps students connect historical discoveries with the modern scientific measurement system.
Real-Life Applications of Derived Quantities
- Force and Momentum: Used in sports science, vehicle safety, and motion control.
- Energy and Power: Key concepts in electricity generation and mechanical engineering.
- Pressure: Applied in hydraulics, meteorology, and medical equipment like blood pressure monitors.
- Resistance and Capacitance: Essential for designing circuits and electronic devices.
- Thermal Conductivity: Important in material science and architecture for insulation.
Every device or technology you use daily — from smartphones to airplanes — relies on derived quantities for its design and operation.
| Concept | Definition | Example | SI Unit |
|---|---|---|---|
| Derived Quantity | Obtained from two or more fundamental quantities | Force, Pressure, Energy | kg·m/s², N/m², J |
| Derived Unit | Unit formed by combining base units | Newton, Joule, Pascal | N, J, Pa |
| Relation | Expressed in terms of base units | 1 N = kg·m/s² |
FAQ
Q1. What is the difference between fundamental and derived quantities?
Fundamental quantities are independent physical quantities (like mass, length, and time), while derived quantities depend on them (like velocity, force, and energy).
Q2. What are derived units?
Derived units are the SI units of derived quantities, obtained by combining base units mathematically.
Q3. Give five examples of derived quantities.
Velocity (m/s), Force (N), Pressure (Pa), Power (W), Energy (J).
Q4. What is the SI unit of force?
The SI unit of force is newton (N), which equals kg·m/s².
Q5. Why are derived units important?
They allow consistent measurement, simplify formulas, and make communication of scientific results universal.
Q6. Which derived unit represents energy?
The joule (J) represents energy in the SI system.
Q7. What is the relationship between joule and newton?
1 joule = 1 newton × 1 metre (1 J = 1 N·m).
Q8. How many fundamental SI units are there?
There are seven fundamental SI units.
