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### The physical phenomena which can be measured are called Physical Quantities.

1. $\to$ Length, Time, Speed, and Magnetic Field are Physical Quantities as they can be measured.

$\to$ Smell, Taste are not Physical Quantities as they can not be measured in a general sense.

$\to$ There are two types of physical quantities: Fundamental Quantities and Derived Quantities.

2. Fundamental Quantities:

$\to$ The quantities that are independent of other quantities are called fundamental quantities.

$\to$ There are seven fundamental quantities. They are Length, Mass, Time, Temperature, Electric Current, Luminous Intensity, and Amount of Substance.

3. Derived Quantities:

$\to$ The quantities that are dependent on other quantities are called derived quantities.

$\to$ Area = Length $\times$ Length and Speed = $\dfrac{\text{Distance}}{\text{time}}$. Here, area depends on length and speed depends on length and time hence they are derived quantities.

$\to$ Other derived quantities are Volume, Force, Power, Intensity of sound, Magnetic Flux, etc.

### Units

1. Unit is the standard reference in which physical quantity is expressed.

$\to$ Length is expressed in meters and speed is expressed in meters/second. The meter and meter/second are the units.

2. System of Units

$\to$ The standard references can vary based on which unit Mass, Length, Time, and other fundamental quantities are measured. On the basis of that, there are four systems of units. They are CGS, FPS, MKS, and SI systems.

QuantityCGS SystemFPS SystemMKS System
1. LengthCentimeterFootMeter
2. MassGramPoundKilogram
3. TimeSecondSecondSecond

$\to$ SI system is an extension of the MKS system in which units of all fundamental quantities are included.

QuantitySI UnitSymbol
1. Lengthmeterm
2. MassKilogramkg
3. TimeSeconds
4. Electric CurrentAmpereA
5. TemperatureKelvinK
6. Luminous IntensityCandelaCd
7. Amount of SubstanceMolemol
3. Types of Units

$\to$ There are three types of units. Namely, Fundamental units, Derived Units, and Supplementary Units.

$\to$ Fundamental Units: The units of fundamental quantities which are independent of other units are called fundamental units. There are seven fundamental units. eg. m,kg, s, K, Cd, Mol, A.

$\to$ Supplementary Units: The units of plane angle and solid angle which are two purely geometric angles are called supplementary units.

QuantityUnitSymbol

$\to$ Derived Units: The units of derived quantities which are dependent on fundamental units and supplementary units are called derived units. For eg. m/s, kgms$^{-2}$, m/s$^{2}$ etc.

4. To cover all the scientific measurements in terms of SI unit, the prefixes are used for the powers of ten.

Powers of TenPrefixesSymbolPowers of TenPrefixessymbol
$10^{24}$YottaY$10^{-24}$Yoctoy
$10^{21}$ZettaZ$10^{-21}$zeptoz
$10^{18}$ExaE$10^{-18}$Attoa
$10^{15}$PetaP$10^{-15}$femtof
$10^{12}$TeraT$10^{-12}$Picop
$10^{9}$GigaG$10^{-9}$nanon
$10^{6}$MegaM$10^{-6}$micro$\mu$
$10^{3}$KiloK$10^{-3}$Millim
$10^{2}$Hectoh$10^{-2}$centic
$10^{1}$decada$10^{-1}$decid

The size of the nucleus is in order of $10^{-14}$ m and the size of an atom is in order of $10^{-10}$

### Common Non-SI Units

1. SI units are commonly used worldwide and cover all scientific measurements. Due to historical, political, and situational significance, there are common Non-SI units in use.

2. Length

Common Non-SI unitSymbolValue in SI unitSignificance
1 Astronomical Unit1 AU1.496 $\times$ 10$^{11}$ mThe distance from Earth to the Sun
1 Light Year1 Light Year9.46 $\times$ 10$^{15}$ mThe distance covered by light in one year
1 Parallactic Second1 Parsec3.084 $\times$ 10$^{16}$ m/(3.26 Light Year)the distance at which the length of one astronomical unit subtends an angle of one second of an arc.
1 Angstrom1 $\AA$1 $\times$ 10$^{-10}$mnamed after 19th-century Swedish physicist Anders Jonas Ångström
1 Fermi1 Fermi1 $\times$ 10$^{-15}$mThe smallest unit of distance used in nuclear physics/ named after Enrico Fermi
1 X-ray Unitxu1 $\times$ 10$^{-13}$mused to quote the wavelength of X-rays and gamma rays.
1 Inch1 "0.0254 mImperial System
1 Foot1 ft/ 1'0.3048 mImperial System
1 Yard1 yd0.9144 mImperial System
1 mile1 mile1609.344 mImperial System
1 Nautical mile1 Nm1852 mUsed in air, marine, and space navigation
3. Mass

Common Non-SI unitSymbolValue in SI unitSignificance
1 Pound1 lb0.4536 kgImperial System
1 Slug1 slug14.59 kgBritish system based on standard gravity
1 Quintal1 Q100 kghistorical unit of mass
1 Metric tonne1 t1000 kghistorical unit of mass
1 amu1 amu1.66 $\times$ 10$^{-27}$ kgprecisely 1/12 the mass of an atom of carbon-12
4. Time

Common Non-SI unitSymbolValue in SI unitSignificance
1 Minute1 min60 sConvenience
1 Hour1 hr= 60 min = 3600 sConvenience
1 Day1 day= 24 hr = 86,400 sConvenience
1 year1 yr1= 365.25 day = 3.156 $\times 10^7$sConvenience
1 shake1 Shake1 $\times$ 10$^{-8}$ sUsed in nuclear physics
5. Other Conversion

QuantitiesNon SI valuesValue in SI unit
Pressure1 Pascal1 Nm$^{-2}$
Pressure1 atm = 760 mmHg1.01 $\times 10^{5}$ Nm$^{-2}$
Pressure1 bar= 1 atm1.01 $\times 10^{5}$ Nm$^{-2}$
Pressure1 torr= 1 mmHg133.322 Nm$^{-2}$
Volume1 liter = 1 cm$^3$$1 \times 10^{-3} m^3$
Energy1 eV1.6 $\times 10^{-19}$ J
Energy1 erg1 $\times 10^{-7}$ J
Energy1 KwHr3.6 $\times 10^{6}$ J
Power1 Hp746 W
Power of lens1 D1 m$^{-1}$
Plane Angle1 Degree$\dfrac{\pi}{180} rad$

### Measurement

1. The comparison of the amount of physical quantity in terms of standard reference of the same quantity is called measurement.
2. $\to$ The standard reference amount is a unit (u).

$\to$ The scale of the amount with reference to the unit is the numerical value (n).

Hence,

Measured Quantity(Q) = Numerical value (n) $\times$ unit (u)

$\to$ Eg. 10 Kg where, numerical value = 10 and unit = 1 Kg.

1. For a given measurement, the measured quantity is constant. i.e. Q = nu = constant.

n_1 u_1 = n_2 u_2