Measurements
The comparison of any physical quantity with its standard unit is called measurement.
Physical Quantities:
All the quantities in terms of which laws of physics are described, and whose measurement is necessary are called physical quantities.
OR
A physical quantity (or simply quantity)[1][a] is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=n kg, where n is the numerical value and kg is the unit symbol (for kilogram).
Units:
- A definite amount of a physical quantity is taken as its standard unit.
- The standard unit should be easily reproducible, internationally accepted.
Fundamental / Base Unit :
Those physical quantities which are independent to each other are called fundamental quantities and their units are called fundamental units.
In SI, seven physical quantities chosen as base / fundamental quantities and their corresponding units are called fundamental / base quantities.
S.No. Fundamental Quantities Fundamental Units Symbol;
1. Length meter m
2. Mass Kilogram Kg
3. Time Second s
4. Electric current Ampere A
5. Temperature Kelvin k
6. Amount of substance mole n
7. Luminous intensity Candela Cd
Definitions of Fundamental Units:
The seven fundamental units of SI have been defined as under.
1. 1 kilogram A cylindrical prototype mass made of platinum and iridium alloys of height 39 mm and diameter 39 mm. It is mass of 5.0188 x 1025 atoms of carbon-12.
2. 1 metre is the distance that contains 1650763.73 wavelength of orange-red light of Kr-86.
3. 1 second is the time in which cesium atom vibrates 9192631770 times in an atomic clock.
4. 1 kelvin is the (1/273.16) part of the thermodynamics temperature of the triple point of water.
5. 1 candela is (1/60) luminous intensity of an ideal source by an area of cm’ when source is at melting point of platinum (1760°C).
6. 1 ampere is the electric current which it maintained in two straight parallel conductor of infinite length and of negligible cross-section area placed one metre apart in vacuum will produce between them a force 2 x 10-7 N per metre length.
7. 1 mole is the amount of substance of a system which contains a many elementary entities (may be atoms, molecules, ions, electrons or group of particles, as this and atoms in 0.012 kg of carbon isotope 6C -12.
Derived Units:
Those physical quantities which are derived from fundamental quantities are called derived quantities and their units are called derived units. e.g., velocity, acceleration, force, work etc.
Some of the derived quantities are given by;
1. Area A m²
2. Volume v m³
3. Spead, Velocity V ms-¹ or (m/s)
4. Acceleration a ms-² or (m/s²)
Supplementary Fundamental Units:
Radian and steradian are two supplementary fundamental units. It measures plane angle and solid angle respectively.
S.No. Supplementary Fundamental Quantities Supplementary Unit Symbol
1. Plane angle (2d) radian rad
2. Solid angle (3d). Steradian sr
Systems of Units:
A system of units is the complete set of units, both fundamental and derived, for all kinds of physical quantities. The common system of units which is used in mechanics are given below:
1. CGS System In this system, the unit of length is centimetre, the unit of mass is gram and the unit of time is second.
2. FPS System In this system, the unit of length is foot, the unit of mass is pound and the unit of time is second.
3. MKS System In this system, the unit of length is metre, the unit of mass is kilogram and the unit of time is second.
4. SI System This system contain seven fundamental units and two supplementary fundamental units.
Relationship between Some Mechanical SI Unit and Commonly Used Units
S.No. physical quantities. Unit
1. Length (a) 1 micrometre = 10-⁶ m
(b) 1 angstrom =10-¹⁰ m
2. Mass (a) 1 metric ton = 10³ kg
(b) 1 pound = 0.4537 kg
(c) 1 amu = 1.66 x10-²³ kg
3. Volume 1 litre = 10-³²m³
4. Force (a) 1 dyne = 10-⁵N
(b) 1 kgf = 9.81 N
5. Pressure (a) 1 kgfm²= 9.81Nm-²
(b) 1 mm of Hg = 133 Nm-²
(c) 1 pascal = 1 Nm-²
(d) 1 atmosphere pressure = 76 cm of Hg = 1.01 x 10⁵ pascal
6. Work and energy (a) 1 erg =10-⁷J
(b) 1 kgf-m = 9.81 J
(c) 1 kWh = 3.6 x 10⁶J
(d) 1 eV = 1.6 x 10-¹⁹ J
7. Power (a) 1 kgf- ms-¹= 9.81W
1 horse power = 746 W
Some Practical Units:
1. 1 fermi =10-15 m
2. 1 X-ray unit = 10-13 m
3. 1 astronomical unit = 1.49 x 1011 m (average distance between sun and earth)
4. 1 light year = 9.46 x 1015 m
5. 1 parsec = 3.08 x 1016 m = 3.26 light year
Some Approximate Masses:
Object Kilogram
Our galaxy 2 x 1041
Sun 2 x 1030
Moon 7 x 1022
Asteroid Eros 5 x 1015
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