Fundamental vs Derived Quantities
Experimentation is a core aspect of physics and other physical sciences. Theories and other hypothesis are verified and established as scientific truth by means of experiments conducted. Measurements are an integral part of experiments, where the magnitudes of and the relations amongst different physical quantities are used to verify the truth of the theory or hypothesis tested.
There are very common set of physical quantities that are often measured in physics. These quantities are considered as fundamental quantities by convention. Using the measurements for these quantities and the relations amongst them, other physical quantities can be derived. These quantities are known as derived physical quantities.
Fundamental Quantities
A set of fundamental units are defined in every units system, and the corresponding physical quantities are called the fundamental quantities. Fundamental units are independently defined, and often the quantities are directly measurable in a physical system.
In general, a system of units requires three mechanical units (mass, length, and time). One electrical unit is also required. Even though above set of units may suffice, for convenience few other physical units are considered fundamental. c.g.s (centimeter-gram-second), m.k.s (meter-kilogram second), and f.p.s (feet-pound-second) are formerly used systems with fundamental units.
SI unit system has replaced much of the older units systems. In the SI system of units, by definition, following seven physical quantities are considered as fundamental physical quantities and their units as fundamental physical units.
|
Quantity |
Unit |
Symbol |
Dimensions |
|
Length |
Meter |
m |
L |
|
Mass |
Kilogram |
kg |
M |
|
Time |
Seconds |
s |
T |
|
Electric Current |
Ampère |
A |
|
|
Thermodynamic Temp. |
Kelvin |
K |
|
|
Amount of Substance |
Mole |
mol |
|
|
Luminous intensity |
Candela |
cd |
|
Derived Quantities
Derived quantities are formed by product of powers of fundamental units. In other words, these quantities can be derived using fundamental units. These units are not defined independently; they depend on the definition of other units. Quantities attached to derived units are called derived quantities.
For example, consider the vector quantity of speed. By measuring the distance traveled by an object and the time taken, the average speed of the object can be determined. Therefore, speed is a derived quantity. Electric charge is also a derived quantity where it is given by the product of current flow and time taken. Each derived quantity has derived units. Derived quantities can be formed.
|
Physical Quantity |
Unit |
Symbol |
||
|
plane angle |
Radian (a) |
rad |
– |
m·m-1 = 1 (b) |
|
solid angle |
Steradian (a) |
sr (c) |
– |
m2·m-2 = 1 (b) |
|
frequency |
Hertz |
Hz |
– |
s-1 |
|
force |
Newton |
N |
– |
m·kg·s-2 |
|
pressure, stress |
Pascal |
Pa |
N/m2 |
m-1·kg·s-2 |
|
energy, work, quantity of heat |
Joule |
J |
N·m |
m2·kg·s-2 |
|
power, radiant flux |
Watt |
W |
J/s |
m2·kg·s-3 |
|
electric charge, quantity of electricity |
Coulomb |
C |
– |
A·s |
|
electric potential difference, |
Volt |
V |
W/A |
m2·kg·s-3·A-1 |
|
capacitance |
Farad |
F |
C/V |
m-2·kg-1·s4·A2 |
|
electric resistance |
Ohm |
V/A |
m2·kg·s-3·A-2 |
|
|
electric conductance |
Siemens |
S |
A/V |
m-2·kg-1·s3·A2 |
|
magnetic flux |
Weber |
Wb |
V·s |
m2·kg·s-2·A-1 |
|
magnetic flux density |
Tesla |
T |
Wb/m2 |
kg·s-2·A-1 |
|
inductance |
Henry |
H |
Wb/A |
m2·kg·s-2·A-2 |
|
Celsius temperature |
Degree Celsius |
°C |
– |
K |
|
luminous flux |
Lumen |
lm |
cd·sr (c) |
m2·m-2·cd = cd |
|
illuminance |
Lux |
lx |
lm/m2 |
m2·m-4·cd = m-2·cd |
|
activity (of a radionuclide) |
Becquerel |
Bq |
– |
s-1 |
|
absorbed dose, specific energy (imparted), kerma |
Gray |
Gy |
J/kg |
m2·s-2 |
|
dose equivalent (d) |
Sievert |
Sv |
J/kg |
m2·s-2 |
|
catalytic activity |
Katal |
kat |
s-1·mol |
|
What is the difference between Fundamental and Derived Quantities?
• Fundamental quantities are the base quantities of a unit system, and they are defined independent of the other quantities.
• Derived quantities are based on fundamental quantities, and they can be given in terms of fundamental quantities.
• In SI units, derived units are often given names of people such as Newton and Joule.