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Introduction to Units and Measurements
Unit
How are units decided?
Fundamental and Derived Quantities
Fundamental Quantities
Derived Quantities
Physics explains the law of nature in a special way. This explanation includes a quantitative description, comparison, and measurement of certain physical quantities. To measure or compare a physical quantity we need to fix some standard unit of the quantity. The weight of lion is heavier than a goat. But how many times? Robin is taller than Prashant, but how tall? To answer such questions we need to fix some unit. Suppose mass is the unit, then we can conclude that weight of the lion is 200 times to that of a goat. Similarly, if we use length as a unit, we can easily determine that Robin is 2 times unit taller to that of Prashant. Thus the physical quantities are described in terms of a unit of that quantity.
To measure any quantity or compare two quantities we need an internationally acquired standard called Unit. The measurement of any physical quantity is expressed in terms of a number and a specific unit.
Measurement = Quantity × Unit
Example:
John studies for 3 hours, then “3” is the quantity and “hour” is the unit of time
Ashok weighs 81 kilograms or kg then “81” is the quantity and “kg” is the unit of weight
Ram is 20 cm taller than Akash, here “20” presents quantity and “cm” represents unit of length
How do we choose a standard unit for a physical quantity? There are two points to consider while choosing a unit.
The unit should be internationally accepted; otherwise, everyone will come with their own unit and create a hoax. This would abrupt communication between two countries and end up degrading their economy. The right to decide and mention unit is authorized by a body named “GCPM” also known as “General Conference on Weight and Measures”. The organization held meetings and addresses the changes in measurement through its publications.
The unit should hold good with other international units
There are a large number of physical quantities to measure and every quantity needs a definition of the unit. Remember that all quantities are interdependent. For Example, if a unit of length is defined (meter), we can define the unit of the area too (meter × meter).
Example: 1
If we make a square having its side 1 unit, we can get a standard unit of area and compare other areas with our standard unit.
Example: 2
If a car travels unit length in unit time, then we can define its unit velocity
The quantities which do not depend on other physical quantities of measurement are called Fundamental Quantities. They are also known as Base Quantities. There are only 7 fundamental quantities, rest physical quantities are known as Derived Quantities. The table below shows all the seven fundamental quantities or units. The units determined for fundamental quantities are called Fundamental Units.
Kilogram
It is the unit of mass. The mass of a cylinder made of platinum-iridium alloy placed in International Bureau of Weights and Measures is defined as 1 kg.
Second
It is the unit of time. Cesium-133 atom releases electromagnetic radiation of several wavelengths. A particular radiation is selected corresponding to the transition involved between two hyperfine levels of ground state of Cs-133. Each radiation has a time period. The duration between 9,192,631,770 time periods is defined as 1 second.
Kelvin
We measure temperature in Kelvin. 1 Kelvin is defined as 1/273.16^{th} part of thermodynamic temperature of triple point of water
Ampere
The standard unit of measuring current is Ampere.1 Ampere is defined as the current flowing in same direction placed parallel to each other and attracting each other with a force of 2 × 10^{-7 }Newton/Meter where Newton is the unit of force.
Candela
The standard unit of luminous intensity is 1 cd and is defined as luminous intensity of a black body of surface area 1/600000 m^{2} placed at the temperature of freezing platinum and 101,325 N/m^{2}, in the direction perpendicular to its surface.
Meter
The unit of length is meter. 1 meter is defined as the distance travelled by vacuum in 1/299792458 seconds.
Mole
We measure amount of substance in moles. 1 mole contains as many atoms as in 0.012 kg of C-12 atom.
Example
To measure weight, we use unit kilogram, rather than being dependent on another unit.
Other than seven fundamental quantities, there are two extra fundamental quantities named plane angle and solid angle.
Plane Angle
Angle between two lines in a plane is called Plane Angle. Its unit is radian.
Solid Angle
Solid angle is two-dimensional angle in three dimensional space. The unit of solid angle is Steradian
The physical quantities which depend on other quantities for their measurements are called Derived Quantities. They are many in number and are obtained by mathematical calculations of fundamental quantities. The units which determine derived quantities are called Derived Units.
The table below shows some of the derived units.
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