Converting from One Unit to Another

Fundamental quantities

These are those quantities which are represented independently and are not defined in terms of other physical quantities; these are known as fundamental quantities . Examples of fundamental quantities are – length ,time , temperature , electric current and so on .

Derived quantities

These are defined as those physical quantities that can be represented in the form of other fundamental quantities.So all the quantities other than the seven fundamental quantities are derived.Some examples of physical quantities are velocity , Acceleration ,force power etc 

In order to measure various units their is a system known as system of units.There are four system of units these are –

• Cgs system- this system is setup at France and centimetre ,gram and second are the units of length , weight and time.
• Fps system – It is a British system with foot , pound and second as the fundamental units of length ,mass and time.
• Mks system – it is a French system and the fundamental units are metre , kilogram and second.
• SI : It stands for International system of units .SI is the abbreviation for “Systeme Internationale d’ United “.It is the modernised form of MKS system .It was adopted by eleventh General Conference of weights and measures .It is based on seven basic units and two supplementary units .

The seven basic units are -:

There are two other quantities these are plane angle having a unit radian and solid angle with the unit steradian.

SI unit system characteristics 

• It is an internationally accepted sytem.
• SI is a metric system.
• SI is a rational system of units.
• SI is a coherent system
• SI is an absolute system of units.

SI unit of some derived quantities

SI Unit of density 

Density is defined as mass per unit volume .So it can be written as follows -:

Density = Mass ÷ volume

Here mass has a SI unit of kg and volume as the unit of m3.so the SI unit of density is Kg / m3.

SI unit of acceleration

Acceleration is defined as the change in velocity divided by the time taken .The SI unit of velocity is m/s and the SI unit of time is Second .

So acceleration = change in Velocity /time 

a= m/s×s = m/s2.

Conversion of one unit to the other

For converting one unit to the other there are some conversion factors that are used. For example -:

Measuring small distance 

• Fermi – it is a unit used to measure small nuclear size distance.The other name is femtometre.Here 1 Fermi = 10-15m.Proton has the radius of 1.2 Fermi.
• Angstrom- This unit is used to express the wavelength of light .

1 angstrom= 10-10m or we can say 

1angstrom= 10-8cm.

• Nanometre- it is a measure used to express the wavelength of light .

1 nanometre-1nm= 10-9m.

• Micron – it is unit used to measure distance . 

1 micron  = 10 -6m.

Practical units used to measure large distance 

• Light year – It is defined as the distance traveled by light in vacuum in one year.
• 1 light year = Speed of light in vacuum ×1year = 3×108m/s×365.25×24×60×60
• 1 light year = 1 ly = 9.467 ×1015m

• • Light year is also used to measure the distance of stars.

• Astronomical unit -It is used as the distance from Sun to earth.It is a mean distance.

• 1 AU = 1.496 ×10 11
• Parsec – also known parallactic second . It is defined as the largest pratical unit of Distance.
• It is defined as the distance at which an arc of length 1 AU subtends an angle of 1 second of arc 
• 1 parsec = 3.08×1016m= 3.26ly.

Practical units for measuring area

• Barn – used to measure small areas . 1 barn = 10 -28m2
• Acre – measuring large area .1 acre = 4047 m2.
• Hectare – 1 hectare = 104m2.

Practical units for large masses

• 1 tonne = 1000kg
• 1 quintal = 100kg
• 1 pound = 1lb 

Practical units for small masses

• Atomic mass unit – It is defined as the 1/12 th of the mass of c-12.

Units for measuring Time 

• Solar day
• Sedrial day 
• Tropical year 
• Leap year 
• Lunar month

Practical units used for measuring pressure

• Bar

1 bar = 105 Pascal

• Torr

1 torr = 1mm of Hg 

• 1 atmospheric pressure= 1 bar = 760 mm of Hg column = 760 torr.

Conclusion

The measurement of quantities is essential.In physics there are physical quantities which are of – Fundamental and derived quantities . Further a physical unit is one in which there are fundamental and derived units.The system that is used to measure all kinds of quantities.The various systems are the – Cgs system ,mks system ,fps system abd the SI system.