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Units and Measurements-Derived Units-Characteristics
There are a total of 7 base units which are length, mass, time, electric current, temperature, amount of substance, and luminous intensity. Using these base units, we establish a system of equations to arrive at the derived units.
There are several derived units of measurements.
Derived quantity Name Symbol
plane angle | radian (a) | rad | ||
solid angle | steradian (a) | sr (c) | ||
frequency | hertz | Hz | ||
force | newton | N | ||
pressure, stress | pascal | Pa | ||
energy, work, quantity of heat | joule | J | ||
power, radiant flux | watt | W | ||
electric charge, quantity of electricity | coulomb | C | ||
electric potential difference, electromotive force | volt | V | ||
capacitance | farad | F | ||
electric resistance | ohm | Ω | ||
electric conductance | siemens | S | ||
magnetic flux | weber | Wb | ||
magnetic flux density | tesla | T | ||
inductance | henry | H | ||
Celsius temperature | degree Celsius | °C | ||
luminous flux | lumen | lm | ||
illuminance | lux | lx | ||
activity (of a radionuclide) | becquerel | Bq | ||
absorbed dose, specific energy (imparted), kerma | grey | Gy | ||
dose equivalent (d) | sievert | Sv | ||
catalytic activity | katal | kat |
The mathematical combination of the base units results in the forming of derived units. A few examples of the derived units are speed, energy, and force. The rest of the derived units are mentioned in the table above.
Characteristics of the units:
The derived unit characteristics are given as
- They should be well defined
- They should be a constant
- They must be easily available
- They should be universally agreed
Usually, when written in full, the names of the derived units are in lowercase, but the units named after people have the initial letter in uppercase, like the symbol for Hertz is “Hz”, whereas the symbol for metre is “m.”
In the given table, 20 units have dimensions, and the rest two units are dimensionless derived units. Those two are radian(rad) and steradian(sr).
The derived unit characteristics are similar to that of fundamental unit characteristics since they are made from the base units themselves.
Similarities between the Fundamental and the Derived Units:
- The fundamental units and the derived units are standardised, and they are internationally accepted and part of the SI system of units.
- They are used worldwide for expressing physical quantities for common purposes.
Differences between the Fundamental and the Derived units:
Fundamental units | Derived units |
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The derived units are widely used in the field of physics,
- For momentum, the SI unit used is kilogram metre per second(kgm/s)
- For magnetic field, the SI unit used in Tesla
There are other derived units, but they don’t have any special names. Below is the list of a few examples,
Quantity | Symbol | Unit | Abbreviation | Derivation |
area | A | square metre | m2 | length x width |
volume | V | cubic metre | m3 | length x width x height |
density | ρ | kilograms per cubic metre | kg/m3 | mass / volume |
concentration (molarity) | c or M | moles per litre | mol/L | amount / volume |
speed | v | metres per second | m/s | length / time |
acceleration | a | metres per second per second | m/s2 | speed / time |
angular velocity | rad/s | radians per second | rad/s | angle / time |
current density | A/m2 | ampere per square metre | A/m2 | current / time |
wave number | m-1 | reciprocal metre | m-1 | 1 / length |
Since derived units can be made using the base units, that doesn’t mean anyone can come up with derived units. The unit is considered legitimate only if published in The International System of Units.
The International System of Units is managed by the General Conference of Weights and Measures (CGPM), and it makes recommendations to the International Committee of Weights and Measures(CIPM).
The updated units and reports are periodically assessed by the International Bureau of weights and measures (BIPM).
Conclusion
Derived units are the units that are obtained by either multiplication or division of the base units without affecting the numerical factors. They are generally expressed by algebraic combinations of base quantities. The fundamental units consist of 7 base units, and these base units make a number of derived units. In the total derived units, some have dimensions, and some are dimensionless derived units. The fundamental units and the derived units are standardised, and they are internationally accepted and part of the SI system of units. Length-weight are examples of fundamental units. Energy and power are examples of derived units.
