System of Units

There are however many units as there are autonomous amounts. We think about length, mass and time three amounts which are autonomous of one another. Consequently they have three separate units for their estimations. Henceforth it is needed to characterize frameworks of units. 

An arrangement of units is an assortment of units wherein certain units are picked as crucial and all others are gotten from them. This framework is additionally called a flat out arrangement of units. In the majority of the framework, the mass, the length and the time are viewed as essential amounts and their units are called as central units. Coming up next are a few frameworks of units which are in like manner use. 

CGS arrangement of units: The unit of length is centimeter (cm). The unit of mass is gram (g). The unit of time is second (s).

MKS arrangement of units: The unit of length is the meter (m). The unit of mass is the kilogram (kg). The unit of time is second (s). 

FPS arrangement of units: The unit of length is a foot (ft). The unit of mass is a pound (lb). The unit of time is second (s). This framework is not any more being used.

SI System of Units:

In the year 1960, the 11th General Meeting of Loads and Measures presented the Worldwide Arrangement of Units. The Worldwide Standard Association (ISO) and the Global Electrochemical Commission supported the framework in 1962. In October 1971 a substitution of the decimal standard of units was finished with another framework called System International Unites.

Fundamental Units:

SI-Units Table

	Fundamental Quantity	SI unit	Symbol
1.	Length	Metre	m
2.	Mass	Kilogram	kg
3.	Time	Second	s
4.	Temperature	Kelvin	K
5.	Electric current	Ampere	A
6.	Luminous intensity	Candela	Cd
7.	Amount of substance	mole	mol

Besides these seven basic units, there are two supplementary units. S.I. unit for the plane angle is radian (rad) and that of solid angle is steradian (sd).

Supplementary Units:

	Fundamental Quantity	SI Unit	Symbol
1.	Plane angle	radian	rad
2.	Solid angle	Steradian	sd

This system of units is an improvement and extension of the traditional metric system. Now, this system of units has replaced all other systems of units in all branches of science, engineering, industry, and technology.

 

Guidelines for Writing SI Units and Their Symbols:

• All units and their symbol should be written in small case letters e.g. centi-metres (cm), metre (m), kilogram per metre cube   (kg/m³). 
• The units named after scientists are not written with a capital initial letter but its symbol is written in capital letter. Thus the unit of force is written as ‘newton’ or’ N’ and not as ‘Newton’.
• Similarly unit of work and energy is joule (J), S.I. unit of electric current is ampere (A).
• No full stop should be placed after the symbol.
• Index notation should be used to write a derived unit. for example unit of velocity should be written as ms^-1 instead of m/s.
• No plural form of a unit or its symbol should be used. example 5 newtons should be written as 5 N and not as 5 Ns.
• Some space should be maintained between the number and its unit.

Advantages of SI System of Units:

• Units are simple to express.

• This system uses only one unit for one physical quantity. Hence it is a rational system of units.

• Units of many physical quantities are related to each other through simple and elementary relationships For example 1 ampere = 1volt / 1 ohm.

• It is a metric system of units. There is a decimal relationship between the units of the same quantity and hence it is possible
•  to express any small or large quantity as a power of 10. i.e. interconversion is very easy. For e.g. 1kg = 1000 gm = 10³ gm.

• The physical quantities can be expressed in terms of suitable prefixes.

• A joule is a unit of all forms of energy and it is a unit of work. Hence it forms a link between mechanical and electrical units. Hence S.I. the system is a rational system because it uses only one unit for one physical quantity.

• This system forms a logical and interconnected framework for all measurements in science, technology, and commerce.

• All derived units can be obtained by dividing and multiplying the basic and supplementary units and no numerical factors are introduced as in another system of units. Hence S.I. system of units is a coherent system. Hence S.I. system of units is used worldwide.

General Steps to find Derived Unit:

• Step -1 Write the formula for the quantity whose unit is to be derived.

• Step -2 Substitute units of all the quantities in one system of units in their fundamental or standard form.

• Step -3 Simplify and obtain derive unit of the quantity.

Example: To find the unit of acceleration.

Acceleration is a derived quantity. Hence its unit is derived unit.

The acceleration is given by, Acceleration = Velocity/time

S.I. unit of Acceleration = S.I. unit of Velocity/ S.I. unit of time = m/s²

Where S.I. unit of velocity is m/s & S.I. unit of time is s.

Thus S.I. unit of acceleration is m/s²

^{SI defined units}

Quantity	Unit	Defining Equation
Capacitance	farad, F	1 F = 1 A s/V
Electrical resistance	ohm, Ω	1 Ω = 1 V/A
Force	newton, N	1 N 1 kg m/s2
Potential difference	volt, V	1 V = 1 W/A
Power	watt, W	1 W = 1 J/s
Pressure	pascal, Pa	1 Pa = 1 N/m2
Temperature	kelvin, K	K = °C + 273.15
Work, heat, energy	joule, J	1 J = 1 N m

 ^{Prefixes Used in SI System:}

Number	Prefix	Symbol	Number	Prefix	Symbol
101	Deka	da	10-1	deci	d
102	Hecto	h	10-2	centi	c
103	Kilo	K	10-3	milli	m
106	Mega	M	10-6	micro	μ
109	Giga	G	10-9	nano	n
1012	Tera	T	10-12	pico	p
1015	Peta	P	10-15	femto	f
1018	Exa	E	10-18	atto	a
1021	Zeta	Z	10-21	zepto	z
1024	Yotta	Y	10-24	yocto	y

 

Physical constants in SI units:

Quantity	Symbol	Value
-	e	2.718281828
-	π	3.141592653
-	gc	1.00000 kg m N-1 s-2
Avogadro constant	N	6.022169 x 1026 kmol-1
Boltzmann constant	k	1.380622 x 1023 J K-1
First radiation constant	C1=2πhc2	3.741844 x 10-16 W m2
Planck constant	h	6.626196 x 10-34 J s
Second radiation constant	C2=hc/k	1.438833 x 10-2 m K
Stefan-Boltzmann constant	σ	5.66961 x10-8 W m-2 K-4
Speed of light in a vacuum	c	2.997925 x 108 m s-1

Conversion factors: 

Physical Quantity	Symbol	Conversion Factor
Area	A	1ft2=0.0920 m2 1in.2= 6.452 x 10-4 m2
Density	ρ	1 lbm /ft3 = 16.018 kg/m3 1 slug/ft3 = 515.379 kg/m3
Energy, heat	Q	1 Btu = 1055.1 J 1 cal = 4.186 J 1 (ft)(lbm) = 1.3558 J 1 (hp)(h) = 2.685 x 106 J
Force	F	1 lbm = 4.448 N
Length	L	1 ft = 0.3048 m 1 in. = 2.54 cm = 0.0254 m 1 mile = 1.6093 km = 1609.3 m
Mass	m	1 lbm = 0.4536 kg 1 slug = 14.594 kg
mass flow rate	ṁ	1 lbm/h = 0.000126 kg/s 1 lbm/s = 0.4536 kg/s
Power	P	1 hp = 745.7 W 1 (ft)(lbf)/s = 1.3558 W 1 Btu/s = 1055.1 W 1 Btu/h = 0.293 W
Pressure	P	1 lbf/in. = 6894.8 N/m2 (Pa) 1 lbf/ft = 47.88 N/m2 (Pa) 1 atm = 101,325 N/m2 (Pa)
Volume	V	1 ft3 = 0.02832 m3 1 in.3 = 1.6387 x 10-5 m3 1 gal (U.S. liq.) = 0.003785 m3
Kinematic Viscosity	ν	1 ft2/s = 0.0929 m2/s 1 ft2/h = 2.581 x 10-5 m2/s
Dynamic Viscosity	μ	1 lbm/(ft)(s) = 1.488 N s/m2 1 centipoise = 0.00100 N s/m2
Velocity	UꝎ	1 ft/s = 0.3048 m/s 1 mph = 0.44703 m/s
Temperature	T	T(°R) = (9/5)T(K) T(°F) = [T(°C)](9/5) + 32 T(°F) = [T(K) - 273.15](9/5) + 32