Introduction to Physics - Part II

2. Fundamental, derived and supplementary units 

Fundamental units of measurements are those that are unique and cannot be derived. Their representations or prototypes are maintained in many international centres world wide, like the International Bureau of Weights and Measures at Sevres near Paris, National Institute of Standard Technology or National Physical Laboratory in the USA. Fundamental units are also called base units.

Unit of mass : Mass is the quantity of matter present in a body. The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram (kg). The prototype is an exactly cylindrical piece of platinum-iridium alloy. Accurate copies of the standards are manufactured and maintained by countries.

Although mass and weight are used in the same manner in everyday language, their meanings are very different in scientific term. Weight is the force by which a mass is attracted to earth.  Weight of a body changes with its position from the centre of the earth, or it changes on the moon even though its mass remains unchanged. 

Unit of length : The speed of light is invariant in the universe and it is 2,99,792,458 meters/second. So this gives a convenient measure of length. Meter (m) is the standard measure of length. The meter is defined as the length of the path travelled by light in vacuum during a time interval of 1 / 299 792 458 of a second.  

Unit of Time : Human beings are conscious of the flow of time; past, present and future. But what is time? How can one define it ? It is very difficult to define time, because our measuring standard itself may vary! Time is the epoch that elapses between repeated successive events. Second (s) is the unit of time. Internationally a standard second is measured by a Caesium atomic clock. These clocks are placed in many parts of the earth. ¹³³Cs atom jumps from its one atomic level to another with a frequency of 9,192,631,770 Hertz. Each jump produces a photon which can be detected. Time is inverse of frequency, hence a second is defined as the inverse of the quantity 9,192,631,770.  

Derived units are expressed algebraically in terms of fundamental units or other derived units. The symbols for derived units are obtained by means of the mathematical operations of multiplication and division.

Table below gives some of the S.I. derived units    

There are some derived units which have special names and symbols. This is for simplicity of use.

Derived quantity	Special name	Special symbol	Expression in   terms of other   S.I. units	Expression in  terms of  S.I.  base units
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	-	s.A
electric resistance	ohm		V/A	m2 … kg … s-3 … A-2

              
In the class of supplementary units, there are only two items : radian which is the unit for measuring plane angle (angles in two dimensions) and steradian which is a unit for measuring solid angles (angles in three dimensions). Both radian and steradian are dimensionless quantities. 

In S.I. units, decimal prefixes are also standardized. If a quantity is too low or too large, standard allowed prefixes are used. A prefix attaches directly to the name of a unit, and a prefix symbol attaches directly to the symbol for a unit. For example, one kilometer, symbol 1 km, is equal to one thousand meters, symbol 1000 m or 10³ m. When prefixes are attached to S.I. units, the units so formed are called "multiples and sub-multiples of S.I. units". Alternative definitions of the S.I. prefixes and their symbols are not permitted. Units used in computers such as bytes, kilobytes are not accepted in the system of standard units.

Units of length, mass and time are Meter, Kilogram and Second. This system of Units is while performing a measurement, the system of units is called the MKS system. When Centimeter, Gram, Seconds are used then the system of units is called the CGS system. If instead Foot, Pound, Second is being used, then the system of units is called the FPS system.

Summary

We have seen which branches of science are encompassed by Physics. In this chapter we have also seen what is a unit of measurement. We have seen the basic definition of fundamental, derived and supplementary units. All units of measurement are strictly followed by international standards.  

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