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**What are Physical Quantities?**

The quantities that can be measured by an instrument and by which we can describe physics laws are called

physical quantities.

- A physical quantity possesses at least two characteristics in common, one is the numerical magnitude and the other is the unit in which it is measured
- For Example, mass can be quantified as n kg, where n is the numerical value and kg is the unit
- In physics, there are seven fundamental physical quantities that are measured in base or physical fundamental units: length, mass, time, electric current temperature, amount of substance, and luminous intensity.

**Classification of Physical Quantities**

**1. Based on their directional properties**

**Scalars:**The physical quantities which have only magnitude but no direction are called scalar quantities.**Example:**Mass, Density, Volume, Time, etc.**Vectors:**The physical quantities which have both magnitude and direction and obey laws of vector algebra are called vector quantities.**Example:**Displacement, Force, Velocity, etc.

**2. Based on their dependency **

**Fundamental**

- Although the number of physical quantities we measure is very large, we need only a limited number of units to express all the physical quantities since they are interrelated.
- So, certain physical quantities have been chosen arbitrarily, and their units are used for expressing all the physical quantities, such quantities are known as
**Fundamental, Absolute,**or**Base Quantities**(such as**length, time and mass in mechanics)** - All other quantities may be expressed in terms of fundamental quantities.
- They are independent of each other and cannot be obtained from one another.
__An international body named General Conference on Weights and Measures chose seven physical quantities as fundamental:__- In mechanics, we treat
**length**,**mass**, and**time**as the three basic or fundamental quantities.

Try yourself:The base quantity among the following is

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**Derived**

- Physical quantities that can be expressed as a combination of base quantities are called
**derived quantities**.**Example:**Speed, velocity, acceleration, force, momentum, pressure, energy, etc.

**Supplementary**

- Besides the seven fundamental physical quantities, two supplementary quantities are also defined.
**(i)****Plane angle**

Plane Angle is defined as the amount of rotation about the point of intersection of two lines that is required to make them overlap on one another. It is measured in radian.**(ii) Solid angle**

A solid angle is a cone subtended by a surface on the centre of the sphere of which the surface is a part. It is defined by the ratio of the area of the surface and the square of the radius. It is measured in steradian.

In the diagram, the area S of the sphere subtends a solid angle, Ω = S/r^{2}

**Magnitude of Physical Quantity**

**Magnitude of physical quantity = (numerical value) x (unit)**

The magnitude of a physical quantity is always constant. It is independent of the type of unit.**Example:**The length of a metal rod bar is unchanged whether it is measured as 2 meters or 200 cm. Observe the change in the Numerical value (from 2 to 200) as a unit is changed from meter to cm.

**International System of Units**

Measurement of any physical quantity is expressed in terms of an internationally accepted certain basic reference standard called unit.

- The units for the fundamental or base quantities are called fundamental or base unit. Other physical quantities are expressed as a combination of these base units and hence, called
**Derived units**. - A complete set of units, both fundamental and derived, is called a
**system of units.**

**Principle Systems of Unit**

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

Units of Some Physical quantities in different systems

**Supplementary Units**

- Plane angle:
**radian (rad)** - Solid angle:
**steradian (sr)** - The SI system is at present, widely used throughout the world.

**Metre:**1 m = 1,650, 763.73 wavelengths, in vaccum, of radiation corresponding to organ-red light of krypton-86.**Second:**1 s = 9,192, 631,770 time periods of a particular from Ceasium-133 atom.**Kilogram:**1 kg = mass of a 1-litre volume of water at 4°C.**Ampere:**It is the current which when flows through two infinitely long straight conductors of negligible cross-section placed at a distance of one meter in a vacuum produces a force of**2 × 10**between them.^{-7}N/m**Kelvin:**1 K = 1/273.16 part of the thermodynamic temperature of the triple point of water.**Mole:**It is the amount of substance of a system that contains as many elementary particles (atoms, molecules, ions, etc.) as there are atoms in 12 g of Carbon-12.**Candela:**It is luminous intensity in a perpendicular direction of a surface of (1/600000)m^{2}of a black body at the temperature of the freezing point under a pressure of 1.013 × 10^{5}N/m^{2}.**Radian:**It is the plane angle between two radii of a circle that cut-off on the circumference, an arc equal in length to the radius.**Steradian:**The steradian is the solid angle which having its vertex at the centre of the sphere, cut-off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere.

**S.I. 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 a certain power of 10.

**General Guidelines for using Symbols for SI Units, Some other Units, and SI prefixes**

- Symbols for units of physical quantities are printed/written in Roman (upright type), and not in italics.
**Example:**1 N is correct, but 1*N*is incorrect. - Unit is never written with capital initial letter even if it is named after a scientist.
**Example:**SI unit of force is**newton**(correct)**Newton**(incorrect) - For a unit named after a scientist, the symbol is a capital letter. But for other units, the symbol is NOT a capital letter.
**Example:**

Note:The single exception is L, for the unit litre.

Try yourself:Which of the following is a unit that of force?

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- Symbols for units do not contain any final full stop at the end of the recommended letter and remain unaltered in the plural, using only the singular form of the unit.
**Example:** - Use of slash (/) is recommended only for indicating a division of one letter unit symbol by another unit symbol. Not more than one slash is used.
**Example:** - Prefix symbols are printed in
**roman**(upright)**type**without spacing between the prefix symbol and the unit symbol. Thus certain approved prefixes written very close to the unit symbol are used to indicate decimal fractions or multiples of a SI unit when it is inconveniently small or large.

Example: - The unit
**'fermi'**, equal to a**femtometre**or**10**has been used as the convenient length unit in nuclear studies.^{-15}m - When a prefix is placed before the symbol of a unit, the combination of prefix and symbol is considered as a new symbol, for the unit, which can be raised to a positive or negative power without using brackets. These can be combined with other unit symbols to form a
**compound****unit**.**Example:** - A prefix is never used alone. It is always attached to a unit symbol and written or fixed before the unit symbol.
**Example:**10^{3}/m^{3}= 1000/m^{3}or 1000 m^{-3}, but not k/m^{3}or k m^{-3}. - Prefix symbol is written very close to the unit symbol without spacing between them, while unit symbols are written separately with spacing with units are multiplied together.
**Example:** - The use of double prefixes is avoided when single prefixes are available.

Example: - The use of a combination of units and the symbols for the unit is avoided when the physical quantity is expressed by combining two or more units.

**Characteristics of Base Units or Standards**

- Well defined
- Accessibility
- Invariability
- Convenience in use

**Some Special Types of Units**

**Micron**(1μ) = 10^{-4}cm = 10^{-6}m (length)**Angstrom**(1 Å) = 10^{-8}cm = 10^{-10}m (length)**Fermi**(1 f) = 10^{-13}cm = 10^{-15}m (length)**Inch**= 2.54 cm (length)**Mile**= 5280 feet = 1.609 km (length)**Atmosphere**= 10^{5}N/m^{2}= 76 torr = 76 mm of Hg pressure (pressure)**Litre**= 10^{-3}m^{3}= 1000 cm^{3 }(volume)**Carat**= 0.0002 kg (weight)**Pound**(Ib) = 0.4536 kg (weight)

Try yourself:One astronomical unit is a distance equal to

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