Mechanics

Fundamental units and their definitions

Units

The fixed and definite quantity taken as the standard of reference with which other quantities of the same kind are measured is defined as a “unit”.

Fundamental Units

The units of fundamental quantities are called “fundamental units”. For example, units of length, mass and time or those of fundamental units. Table lists all fundamental and supplementary units and their symbols.

Physical QuantitySI UnitDimensional SymbolUnit Symbol
LengthMeterLm
MassKilogramMkg
TimeSecondTs
TemperatureKelvinKk
Electric CurrentAmpereAA
LuminousCandelaICd

 

Derived Units

Units of derived physical quantities are called “derived units”. For example, units of velocity, density,force, momentum and volume.

Initially three system of units, namely, CGS, FPS and MKS based on three fundamental quantities, length, mass and time, came into existence. In 1970, in a world confidence a consensus evolved and a standard international system of units.

Physical QuantitySI UnitDimensional SymbolUnit Symbol
Intensity
Amount of substancemolemolmol
Supplementary units
AngleRadianrad
Solid anglestredianstr

 

Standards of Length

The most common unit is the meter (m), Foot is also used sometimes. In 1889 the standard meter was defined as the distance between two fixed marks engraved on a platinum-iridium bar preserved at a constant temperature of 73.16 K and the constant pressure of 1 bar in the international bureau of weights and measures at Serves near Paris in France. All other meters are calibrated with it to an accuracy of 0.1 ppm.

In 1960 the standard meter was defined in terms of the wavelength of Kr-86 and is called the atomic standard of length.1m is the distance covered by 1650763.73 wavelengths of orange-red light of Kr-86 in the vacuum. An accuracy 1:109 parts can be obtained with it.

In 1983 meter was defined as the length of the path traveled by light in vacuum in 1/299,792,458th  seconds.

Some other important units of the length are

1A = 10-10

1 x-ray unit (1 XU) 10-13m

1 yard = 3 foot = 0.9144 m,

1” (inch) = 2.54 cm

1 astronomical unit (1 AU) = 1.49 x 1011 m.

1 light year (1 ly) = 9.6 x 1015 cm,

1 parsec ( 1 pc) = 3.08 x 1016 m = 3.26 1y

Standard of Mass

Originally, 1 kg mass was defined as the mass of 1 liter (103 cc) of water at 4°C, nowadays standard kg is the mass of platinum-iridium cylinder stored in the special vault in the International Bureau of the standard at Serves (France). The accuracy of this standard is 1 in 108 parts.

To measure atomic masses, the unit amu (or u) is used.

 

1 u = 1/12th of the mass  atom

Or

1 u = 1/12th x  kg

= 1.67 x 10-27 kg

In FPS system pound (lb) is the unit of mass, sometimes slug is also used.

1ib = 0.453592737 kg,

1 slug = 32.2 lb = 14.59 kg

In astrophysics, we sometimes come across Chandrasekhar limit.1 Chandrasekhar limit = 1.4 times mass of sun = 2.8 x 1030 kg. Chandrasekhar showed that if the mass of an object becomes 1.4 times the mass of the sun, under gravitational collapse it turns out to be the white dwarf.

Standards of Time

Initially, it was defined on the basis of the solar or lunar motion.

1 mean solar day = 1 year/ 365.25 days

And 1s = 1 year / 365.25 x 24 x 60 x 60

But because of tidal friction, the length of a day is increasing at a rate of 7 µs per year. Therefore, in 1965 the atomic standard as defined. According to this standard, 1s is the interval of 91192631770 vibrations of the radiation corresponding to the transition between two specific hyperfine levels in 133 Cs (cesium) clocks which will go wrong by 1s in 3000 years. Hydrogen MASER promises a producing error of 1s in 33, 000, 000 years.

(i) Time can never flow back, i.e., negative time does not exist and (ii) at a given instant of time, a particle cannot be present in more than one position in space.

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