Fundamental Quantities

PHYSICAL QUANTITY 

The quantities which can be measured by an instrument and by means of which we describe the laws of physics  are called physical quantities.

Types  of physical quantities

  1. Fundamental 
  2. Derived 
  3.  Supplementary

FUNDAMENTAL QUANTITIES:

“Those physical quantities which are independent of each other and cannot be expressed in terms of one another, are known as fundamental quantities, Absolute or Base Quantities.”

So, certain physical quantities have been chosen arbitrarily and their units are used for expressing all other physical quantities.

An  international body named General Conference on Weights and Measures (CGPM) has chosen seven physical quantities as fundamental.

(1) length                                            

(2) mass                                                          

(3) time

(4) electric current,                             

(5) temperature                                                    

(6) amount of substance

(7) luminous intensity.

               Beside the seven fundamental physical quantities two supplementary quantities are also defined, they are :

  • Plane angle
  • Solid angle

DERIVED QUANTITIES:

Physical quantities which can be expressed as combination of base quantities are called as derived quantities.

For example : Speed, velocity, acceleration, force, momentum, pressure, energy etc.

UNITS

In order to measure a physical quantity, it has to be expressed in terms of a certain reference standard of measurement of that physical quantity which is called a unit. The magnitude of physical quantity is expressed in terms of the number of times of the physical quantity contains that unit.

“The unit of a physical quantity is defined as the reference standard used to measure it.”

 

            The unit for the fundamental or base quantities are called fundamental or base unit. Other physical quantities are expressed as combination of these base unit and hence, called derived units.

Characteristics of base units :

            (A) Well defined                     (b) Accessibility                       

            (c) Invariability                        (d) Convenience in use

            A complete set of units, both fundamental and derive, is called a system of unit.

            There are various system in use over the world : CGS, FPS, MKS etc.

SI System

In the year 1960, the eleventh general conference of Weights and Measures made an attempt to improve the existing unit systems. This conference introduced the International System of Units ( ‘System International d’ Unites’)The SI system is at present widely used throughout the world.

Magnitude of a Physical Quantity:

Magnitude of physical quantity = (numerical value) X (unit)

Magnitude of a physical quantity is always constant. It is independent of the type of unit.

  • numerical value µ 
  • ⇒ (Numerical Value) X (Unit) = Constant

or                                             n1u1 = n2u2 = constant

Derived Units: 

The units which can be derived from the fundamental units are known as derived units. 

 These basic seven quantities with their units and symbols are given as follows:

S. No.

Physical Quantity

S.I. Unit

Symbol

1.

Mass (M)

Kilogram

Kg

2.

Length (L)

Meter

m

3.

Time (T)

Second

s

4.

Temperature (q)

Kelvin

K

5.

Luminous Intensity (L)

Candela

Cd

6.

Electric Current (I)

Ampere

A

7.

Amount of Substance (n)

Mole

mol.

Also, two supplementary units are used as radian (rad) for plane angle and steradian (sr) for solid angle.

DEFINATIONS OF SOME IMPORTANT SI UNITS

Fundamental Units

  1. Meter: It is the length in which 1,650, 763.73 wavelength (in vaccum) of Krypton – 86 corresponding the transition and  .
  2. Kilogram: It is the mass of 1 liter volume of water at 40C temperature.
  3. Second: It is the duration of 9, 192, 631, 770 periods of radiation corresponding to the transition between the tow hyperfine levels of the ground state of Caesium (133) atom.
  4. Ampere: It is the current which when flows through two infnitely long straight conductors of negligible cross-section placed at a distance on meter in air or vaccum produces a force of 2 × 10–7 N/m between them.
  5. Candella: It is luminous intensity in a perpendicular direction, of a surface of 1/6000,000 square meter of a black body at the temperature of freezing platinum under a pressure of 1.013 × 105 N/m2.
  6. Kelvin: It is the 1/273.16 part of the thermodynamic temperature of triple point of water.
  7. Mole: It is the amount of substances of a system which contains as many elelmentary entities as there are in 1 gm of .
  8. Radian: It is the angle between two radii of a circle which cut off on the circumference an are equal in length to the radius.
  9. Steradian: The steradian is the solid angle which having its vertex in the centre of the sphere, cuts off an area of the surface of sphere equal to that of a square with sides of length equal to the radius of the sphere in length to the radius.

Derived Units:

  1. Newton: It is force that produces an accelerations of 1 m/s2 in mass of 1 kg.
  2. Joule: It is work done by 1 N force in displacing a body by 1 meter in a direction of force.
  3. Watt: It is power which produces energy at a the rate of one joule per second.
  4. Coulomb: It is the quantity of electricity transported by a current of one ampere in one second.
  5. Volt: It is the potential difference between two points of a conducting wire carrying a constant current of one ampere when the power dissipated between these points is equal to one watt.
  6. Ohm: It is the electrical resistance between two points of a conductor which have a potential difference of 1 volt between them when a current of 1 ampere flows through it.
  7. Farad: It is the capacitance of the capacitor having a potential difference of 1 volt between its plates when a charge of one coulomb is given to it.
  8. Henry: It is the inductance of a closed circuit in which an e.m.f of 1 volt is induced when the rate of change of current in the circuit is 1 amp/sec.
  9. Lumen: It is huminous flux emitted by a source of one candela in unit solid angle.

The above mentioned international system of units (S.I) are now extensively used for the scientific measurement.

The following practical units are conveniently used and are expressed in terms of S.I system of units also.

  1. Mircons is a small unit for measurement of length 1 micron = 1 mm = 10 – 6 m
  2. Angstron is a unit in which the size of atom is measured and is used in Atomic Physics.
  3. Light Year is a unit of distance traveled by light in free space and is used in Astrophysics.1 light year = 3 × 108 m/s × 365 × 24 × 60 × 60 = 9.5 × 1015 meters
  4. Fermi is a unit of distance in which the size of a nucleus is measured. 1 Fermi = 10 – 15 m
  5. Atomic Mass Unit : It is a unit of mass equal to 1/12th mass of carbon (12) nucleus and is used in measuring the masses of nuclei.

                       1 atomic mass unit = 1.67 × 10 – 27 kg.

 

SI Prefixes

The magnitudes of physical quantities vary over a wide range. The CGPM recommended standard prefixes for magnitude too large or too small to be expressed more compactly for certain powers of 10.

                                               

Table 3 : Prefixes used for different powers of 10.

Power of 10

Prefix

Symbol

Power of 10

 Prefix

Symbol

1018

exa

E

10-1

deci

d

1015

peta

P

10-2

centi

c

1012

tera

T

10-3

milli

m

109

giga

G

10-6

micro

m

106

mega

M

10-9

nano

n

103

 kilo

K

10-12

pico

p

102

hecto

h

10-15

femto

f

101

deca

da

10-18

atto

a

Example :

              1 meter = 1 m                      2 millimeter = 2 X 10-3m = 2mm

 3 kilo meter = 3 X 103 m = 3 km 4 nanometer = 4 X 10-9 m = 4 nm

5 giga meter = 5 X 109 m = 5 Gm

Some special types of units :

  1. 1 Micron (1m) = 10-4 cm         = 10-6 m                       (length)
  2. 1 Angstron (1 Å)          = 10-8 cm          = 10-10 m          (length)
  3. 1 fermi (If)      = 10-13 cm        = 10-15 m          (length)
  4. 1 light year=Distance traveled by light in vacuum in one year = 9.46 X 1015m ≈1016 m (length)
  5. 1 Parses (parallactic second) = 3.08 X 1016 m              (length)
  6. 1 Yard = 0.9144 m = 3 feet                                         (length)
  7. 1 inch = 2.54 cm                                                          (length)
  8. 1 m = 39.37 inch = 3.281 feet                         (length)
  9. 1 mile = 5280 feet = 1.609 km                                                (length)
  10. 1 nautical mile = 6076 feet = 1.151 mile = 1.852 km  (length)
  11. 1 torr  = 1 mm of Hg pressure                          (pressure)
  12. 1 pascal = 1 N/m2                                                        (pressure)
  13. 1 atmosphere = 105 N/m2 = 76 torr = 76 mm of Hg pressure   (pressure)
  14. 1 Mach number = 332 m/s = 1234.8 km/h                               (speed)
  15. 1 Knot = 1nautical mile/hr = 1.852 km/hr = 0.5144 m/s                     (speed)
  16. 1 Liter = 10-3 m3 = 1000cm3                                         (Volume)
  17. 1 gallon (US) = 3.786 liter                                                       (Volume)
  18. 1 gallon (UK) = 4.546 liter                                                       (Volume)
  19. 1 barrel (petroleum) = 158.987 litre                             (Volume)
  20. 1 carat = 0.0002 kg                                                      (weight)
  21. 1 ounce (oz) = 0.02835 kg                                                       (weight)
  22. 1 pound (lb) = 0.4536 kg                                                         (weight)

 

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