# Physical Quantities

All the quantities which are used to describe the laws of physics are known as physical quantities or in other words “the quantities which can be measured are called physical quantities.”

##### Classification of physical quantities :-

Physical quantities can be classified on the following bases :-

I. Based on their directional properties
1. Scalars :- The quantities which have only magnitude but no direction are called scalar quantities.
Ex. mass, density, volume, time, etc.
2. Vectors :- The quantities which have both magnitude and direction and obey laws of vector algebra are called vector quantities.
Ex. displacement, force, velocity, etc.

II. Based on their dependency
1. Fundamental or base quantities :- The quantities which do not depend upon other physics quantities for their complete definition are known as fundamental or base quantities. An International Organization named CGPM( General Conference on weight and Measures), chose seven physical quantities as basic or fundamental.

2. Derived quantities :- The quantities which can be expressed in terms of the fundamental quantities are known as derived physical quantities.
Ex. Speed (=distance/time), volume, acceleration, force, pressure, etc.
Physical quantities can also be classified as dimensional and dimensionless quantities or constants and variables.

Example :-
Classify the quantities displacement, mass, force, time, speed, velocity, acceleration, moment of intertie, pressure and work under the following categories :
(a) base and scalar (b) base and vector (c) derived and scalar (d) derived and vector
Solution :
(a) mass, time (b) displacement (c) speed, pressure, work (d) force, velocity, acceleration

#### UNITS OF PHYSICAL QUANTITIES

Unit :- The chosen reference standard of measurement in multiples of which, a physical quantity is expressed is called the unit of that quantity.

The unit of a physical quantity is inversely proportional to its numerical value i.e.,

$\displaystyle u\propto \frac{1}{n}$,

where u and n are the unit and numerical value respectively of a physical quantity. Relation between unit and numerical value

n1u1 = n2u2

While choosing the unit of a physical quantity, the following points should be considered :-

1. The chosen unit should be acceptable to all and of proper size and magnitude.
2. The unit should not be affected by the change in temperature, pressure and time.
3. The chosen unit should be easily defined and they should be easy to replicate at all the places.

Classification of Units :- The units of physical quantities can be classified as follows :-

1. Fundamental or base units

The units of fundamental quantities are called base units. In SI system there are seven base units.

• Length – meter (m)
• Time – second (s)
• Amount of substance – mole (mol)
• Electric current – ampere (A)
• Temperature – kelvin (K)
• Luminous intensity – candela (cd)
• Mass – kilogram (kg)

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. meter 1 meter is the distance that contains 1650763.73 wavelength of orange-red light of Kr-86.
3. 1 second 1 second is the time in which cesium atom vibrates 9192631770 times in an atomic clock.
4. 1 kelvin 1 kelvin is the (1/273.16) part of the thermodynamics temperature of the triple point of water.
5. 1 candela 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 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 meter apart in vacuum will produce between them a force 2 x 10-7 N per meter length.
7. 1 mole 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 6C12.

2. Derived units

The units of derived quantities or the units that can be expressed in terms of the base units are called derived units.

• Area – m2
• Volume – m3
• Speed – m/s2
• Density – Kg/m3
• Unit of force – newton (N)
• Unit of frequency – hertz (Hz) etc.

Example :
Find the SI unit of speed and acceleration.

Solution :

speed = distance/time = meter(m)/second(s) = m/s (called as meter per second)

acceleration = change in velocity/time = [m/s]/second = m/sec² ( called as meter per second square)

Next Topic :- System of Units