IEMDaily - Video Lecture Notes

Example

Units of Physical quantities arising from certain operation on given physical quantity

Density =

\frac{m a s s}{v o l u m e}

Mass has unit

k g

.
Volume has unit

m^{3}

So the unit of density is

k g / m^{3}

Definition

Units and symbols of some common fundamental quantities

Quantity	Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Temperature	kelvin	K
Luminous Intensity	candela	cd
Electric current	ampere	A
Amount of substance	mole	mol*
Angle	radian	rd

Solid angle steradian st-rd

Definition

Definition of SI units

1. Unit of length: Metre
Definition: The metre is the length of the path travelled by light in vacuum during a time interval of 1 / 299792458 of a second.

2. Unit of Mass: kg,
Definition: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

3. Unit of time: Second
Definition: The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the ceasium 133 atom.

4. Current: Ampere
Definition: The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to

2 10^{7}

newton per metre of length.

5. Unit of Temperature: Kelvin
Definition: The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

6. Unit for amount of substance: mol
Definition: The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12, its symbol is 'mol'.

7. Unit of luminous Intensity: Candela
The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5401012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

Definition

Define derived quantities and their units

The Fundamental Quantity is independent Physical Quantity that is not possible to express in other Physical Quanitity. It is used as pillars for other quantities aka Derived Quantities. In Physics, Length, Mass, Time, Electric Current, Thermodynamic Temperature, etc are examples of Fundamental Quantities.

Area

= m^{2}

Volume

= m^{3}

Force

= k g m / s^{2}

Pressure

= k g / (m s^{2})

Density

= k g / m^{3}

The seven fundamental S.I units are:−
metre → for length
second → for time
kilogram → for mass
kelvin → for temperature
ampere → for electric current
candela → for luminous intensity
mole → for the amount of substance.

Definition

Some commonly used derived units

A derived unit is a SI unit of measurement comprised of a combination of the seven base units. Like SI unit of force is the derived unit, newton or

N

where

N = \frac{1 \times m \times k g}{s^{2}}

There are some commonly used derived units which includes:

1. Pressure =

\frac{F o r c e}{A r e a} = \frac{N}{m^{2}}

2. Mass density=

\frac{k g}{m^{3}}

3. Specific volume =

\frac{m^{3}}{k g}

4. Current density =

\frac{Ampere}{{meter}^{2}} = \frac{A}{m^{2}}

5. Magnetic field strength =

\frac{Ampere}{Meter} = \frac{A}{m}

6. Capacitance =

Farad = F = \frac{C}{V} = m^{- 2} k g^{- 1} s^{4} A^{2}

Definition

Identify and give examples of some derived units

The units of all quantities other than fundamental units is called derived unit. Derived units are obtained in terms of fundamental quantities.

Quantity	Definition	Derived Unit	Abbreviation/Symbol
1. Area	length $\times$ breadth	metre $\times$ metre	$m^{2}$
2. Volume	Length $\times$ breadth $\times$ height	metre $\times$ metre $\times$ metre	$m^{3}$

Definition

Conventions for writing SI units

The conventions followed while writing SI units:

Only units of the SI and those units recognised for use with the SI should be used to express the values of quantities.
All unit names are written in small letters (newton or kilogram) except Celsius.
The unit symbol is in lower case unless the name of the unit is derived from a proper name, in which case the first letter of the symbol is in upper case.
Unit symbols are unaltered in the plural.
Unit symbols and unit names should not be mixed.
Abbreviations such as sec (for either s or second) or mps (for either m/s or meter per second are not allowed.
For unit values more than 1 or less than -1 the plural of the unit is used and a singular unit is used for values between 1 and -1.
A space is left between the numerical value and unit symbol (25 kg, but not 25-kg or 25kg). If the spelled-out name of a unit is used, the normal rules of English are applied.
Unit symbols are in roman type, and quantity symbols are in italic
type with superscripts and subscripts in roman or italic type as
appropriate.