Si Derived Units.pdf

Si derived units

1. SI DERIVED UNITS
A 6.1 Some SI
Derived
Units expressed in SI Base Unita
SI Unit
Physical quantity
Symbol1
Name
square metre
cubic metre
m2
Area
Volumee
m
Speed, velocity
Angular velocity i
Acceleration
metre per second
radian per second
metre per second
m/s o m s-l
rad/s or rad s-1
m/s2 or ms-2
square
radian per second rad/s2 or rad s-2
Angular acceleration
Square
per metre
kilogram per cubic
m-1
Wave number
Density, mass density
kg/m3 or kg m-3
metre
A/m2 or A m2
Current density
ampere per square
metre
Magnetic
field strength, magnetic ampere per metre
intensity,magnetic moment
density
Concentration (of amount of
substance)
Specific volume
A/m or A m-1
mole per cubic metre mol/m3 or mol mn3
m3/kg or m3 kg cubic metre per
kilogram
candela per square Luminance, intensityof
illumination
cd/m2 or cd m2
metre
Kinematic viscosity square metre per m2/s or m2 s-
second
Momentum kilogram metre per kg m s
secondd
Moment of inertia
Radius of gyration
Linear/superficial/volume
expansivitles
Flow rate
kilogram square metre kg m
metre m
per kelvin K-1
cubic metre per m3 s-l
second

2. ENDICES
A 6.2 SI Derived Units with special names
Physical quantity SI Unit
Expression in
terms of other
Expression in
terms of SI
base Units
Name Symbol
units
s1
Frequency hertz Hz
kg m s2 or
kg m/s2
Force newtona N
kg m-l s2 or
kg /s2 mn
kg m2 s-2or
kg m2/s2
kg m2 s-3or
kg m2/s3
Pressure, stressS pascal N/m2
or N m-2
Pa
N m
Energy, work, quantity of
heat
joule
J
Power, radiant flux W J/s
or J s-l
watt
As
Quantity of electricity,
electric charge
Electric potential,
potential difference,
electromotive force
coulomb C
kg m2s 3 A-l or
kg m2/s3 A
volt V
W/A or WA-1
Capacitance
Electric resistance
A2 s4 kg1 m2
C/V
/A
4/
Vs or J/A
Wb/m2
farad
kg m2
s-3 A-2
m-2 kg-1 s3 A2
kg m2 s2 A-1
kg s-2 A-1
ohm
Conductance
siemens S
Magnetic flux
Magnetic field, magnetiC
flux density, magnetic
induction
weber Wb
tesla T
Inductance
henry kg m2 s-2 A2
cd /sr
H Wb/A
Luminous flux, luminouss
lumen Im
power
Tiluminance
Activity (of a radioo
nuclide/radioactive
source)
lux
lm/m2 m2 cd sr-1
becquerel Bq S-1
Absorbed dose, absorbed
dose index
gray Gy J/kg
m2/s2 or m2 s-2
A6.3 Some SI Derived Units
expressedby means of SI Units with special na
SI Unit
Physical quantity
Name
Symbol Expression in
terms of SI
base units
m A
Magnetic moment
Dipole moment
Dynamic viscosity
Joule per tesla
coulomb metre
JT
C m sAm
poiseiulles or pascal
second or newton
Pl or Pa s or m kg s
N s m
second per square
metre
Torque, couple, moment
of force
Surface tension
Power density,
iradiance, heat flux
density
newton metre
N m
m kg s
newton per metre
watt per square metre
N/m
W/m
kg s
kg s

3. Joule per kelvin
joule per kilogram
kelvin
J/K
J/kg K
m
kg s K
m s K
Heat capacity, entropy
Specific heat capacity,
specific entropy
Specific energy, latent
heat
J/kg ms
joule per kilogramn
Radiant intensity
Thermal conductivity
Energy density
Electric field strength
Electric charge density
watt per steradian
watt per
metre kelvin
joule per
cubic nmetre
volt per metre
coulomb per cubic
metre
W sr
Wm' K
J/m
V/m
C/m
kg m s sr
m kgs' K
kg m* s*
m
kg s' A
m As
coulomb per square C/m m As
Electric flux density
metre
Permittivity
Permeability
Molar energy
Angular momentum,
Planck's constant
farad per metre
henry per metre
joule per mole
joule second
F/m
H/m
J/mol
m kg' s'A
m kgs* A
m kgs'mol
kg m' s Js
J/mol K m kgs*K
mol
joule per
mole kelvin
Molar entropy, molar
heat capacity
coulomb per kilogram C/kg kg' s A Exposure (x-rays and
rays
Absorbed dose rate gray per second Gy/s m's
Pa
newton per square N/m or Nm kgm' s
Compressibility per pascal m kg' s
Elastic moduli
metre
Pressure gradienat pascal per metre Pa/m or Nm* kg
m* s
Surface potential
joule per kilogramn
m s* J/kg orr
Nm/kg
Pressure energy
Impulse
Angular impulse
Specific resistance
Surface energy
kg m s
kg ms
kg m's
kg m s A
kg s
pascal cubic metre Pa m or N m
newton second Ns
newton metre second
Nms
ohm metre
Qm
joule per square metre J/m or N/m

4. DIMENSIONAL FORMULA
Relationship with other
physical quantities
UANTITTES
Dimensions
imensional
Physical quantity
formula
S. No
Length x breadth
M 1T
Area
Length
x
breadth x height L' M°L T
Volume
Mass/volume [MV[L'] or [ML') ML'T
Mass density
1/time period VIT [M° LT'
Frequency
Displacement/time [LIT M°LT'
Velocity, speed
Velocity /time
Lr V[T] MLT
Acceleration
Mass x acceleration [M]LT' [M LT'
Force
Forcex time [M LT IT] [M LT'
Impulse
Forcex distance MLT'1 L MLTT
Work, Energy
Work/time [MLTV [T [MLT]
10.
Power
Mass x velocity
[M [LT' MLT
11
Momentum
Force/area [M LT VL [ML T
12.
Pressure, stress
Change in dimension L]/[L] or [L'j/[Lj M°LT
13
Strain
Oringinal dimension
MLT
[MLT
IM°L°T°]
14
Modulus of elasticity
Stress/strain
Surface tension Force/length
[MLT VLI [MLT
15
Surface enerEy Energy/area [MLTVL
MLT
16.
Velocity Velocity/distance [LT VL)
MLT
17.
gradient
18 Pressure gradient Pressure/distance [ML T*V [ML T
19. Pressure energy Pressure x volume [MLT][L [ML T
20 Coefficient of
MLT
Force/area x velocityY
gradient
[MLT
LLT/LI
viscosity
21 Angle, Angular
displacement
[M'L TI
Arc/radius [L[LI
22 M'LT
Trigonometric ratio
(sine, cos0, tan6, etc.)
Length/length
[LVILI
23 Angular velocity Angle/time L"VT]
[M'L'TT

5. PPENDICES
Angular acceleration Angular velocity/time TVT (M°LT'I
Radius of gyration L)
[M'LT
Distance
Moment of inertia Mass x (radius of gyration [M][L']
[MI T
26
IMI T' Moment of inertia x angular [ML'JIT'I
velocity
27 Angular momentum
Moment of force, Force x distance (MLT'J[LJ
ML T' 28,
moment of couple
Torque Angular momentum/time, [ML'T']/[T] IML T'
Or or
Force x distance
[MLT' JL
30 Angular frequency 21t Frequency [T'] MLT
Wavelength Distance
[L MLT
31.
Hubble constant Recession speed/distance
LT'VLI MLT
Intensity of wave
Energy/timeyarea MIL' TTVLL'1 ML'T
Radiation pressure
Intensityof wave
Speedof light
[MT VLT' MLT1
34.
35 Energy density Energy/volume [MILTy L1 MLT
36. Critical velocity Reynold's umber x coefficient of viscocity
M°1T°MLT
[MLILI
[MLT'
Mass density x radius
37 Escape velocity (2 acceleration due to
gravity xearth's radius) 2
[LTx[L
MLT']
Heat energy, internal Work (Force x distance)
[MLT ]L] ML T
38.
energy
Kinetic energy (1/2) mass x (velocity) [M] [LT'} [ML T
40 Potential energy Mass x acceleration
due to gravity x height
[M LTIL [ML T
41 Rotational kinetic 4* moment of inertia x
(angular velocityy
[ML'T] [M }x[T"f ML'T
energy
42.
Efficiency [MLT* Output work or energ8y
Input work or energy
ML'T
[ML'T* 1
49 Angular impulse Torque x time [ML'T'1(T MLTI
44
Gravitational IMLT 1LC
M IM
Force x (distance M'LT)
constant mass mass
Planck constant
Energy/trequency [ML' T)/T [ML'T'1

6. PHYSICS
[ML TV[K]
Heat energy/ temperature
MIT K Heat capacity,
46
entropy
Heat Energy [MLTVIM IK]
[MLT K
Specific heat capacity
Mass x temperature
[ML TVM Heat energy/mass
[ML T Latent heat
LI/LIK] Change in dimension
Original dimension x temperature [MLK 1
9
Thermal expansion
coefficient or
Thermal expansivity
[MLTIIL) Heat enegY * thickness
Area
x temperature
x time MLT K'
S0
Thermal conductivity
Volume x (change in pressure)
(change in volume)
Lj[ML 'T*]
[L
[MLT)
Bulk modulus
or (compressibility)
(Velocity) lradius [LT' /[L]
[M' LT
Centripetal
acceleration
(Energy/ area x time))
(Temperature)
[MT
(T] K
M TK Stefan constant
Wavelength x temperature L [K) M LT°K Wien constant
Energy/temperature [MIL T*VK] LML'TK1 Boltzmann constant
[MLTL
mol) [K]
[M TK Pressure x volume
mole x temperature
Universal gas
constant
mol ]
Charge Current x time [A] [T [MLTA]
Current density Current/area [A]/[L' MLTA
Work/charge [ML'T V[AT]
ML TA]
Voltage, electric
potential,
electromotive force
59
ML T A
IMLT A']
[A
60 Resistance Potential difference
Current
61 Capacitance Charge/potential difference
[ML'T A
[AT]
[ML T'A]
ML' T A
[ML' TA*]
LVLI
62 Electrical
resistivity
or (electrical
Resistance x area
length
conductivity'
Electric field
IMLT A
Electrical force/charge [MLT V[AT]
64 Electric flux
EML T A"]
Electric ficld x area MLT A L']

7. [M LTA]
Electric dipole
Torque/electric field [ML T
65
moment (MLT' A"]
[MLT A*
Electric field strength
or electric intensity
[ML'TA)
L
66.
Potential difference
distance
[MLT V[A]L)
ML TA
Magnetic field,
magnetic flux density,
magnetic induction
67.
Force
Current length
[MTA) L
MLTA1
68 Magnetic flux Magnetic field x area
[M T AA
Magnetic fux
Current
[ML'T A"
[A]
69
Inductance
Torque/magnetic field
[MLT]/ [MT A*][M'LTA}
70
Magnetic dipole
moment
or
Or
CuITentx area
AJ L
L'A]
'
MLTAJ
Magnetic moment Magneticfield
strength, magnetic
intensity or magnetic
moment density
Volumee
ML TA
Permittivity constant Charge x charge
[AT][AT]
[MLT JLF
(of free space) 4T xelectric force x (distance)
Permeability constant
(of free space)
[M°L' TIMLTIU MT A
[A][AJL]
27 forcex distance
current currentxlength
LT LT] [M°LT]
Speed of ight in vacuum
Speed of light in medium
Refractiveindex
[ATmol] M'LTA mol
Avogadro constant x
elementary charge
Faraday
constant
27t/wavelength [MLT|/ [ [ML T
Wave number
[MLT V[T] MI'T
Radiant flux, RadiantBnergy emitted/time
power
[ML'T/ [M°LTI IML T
Luminosity of radiant Radiant power or radiant fhus of source
flux or radiant
18
Solid angle
intensity
[ML TVIT [ML T Luminous energy emited
Luminous power or
luminous flux of
time
Source

8. [ML T']
[MLT
2 Luminous flux
ML T
Luminous intensity or
illuminating power of
Soild angie
80.
[ML' TVL
[ML'T
SOurce
Luninous intensity
Intensity of
illumination or 81
(distance)
[ML'T]
[MIL T']
luminance
Luminous fiux of a source of
gven wavelength
Juminous filx of peak sensitivityy
wavelength (555 nm)
source of
same powver
MLT)
82
Relative luminosity
[ML' T/[ MLT] MLT
Total luminous flux
83.
Luminous efficiency
Total radiant flux
Luminous flux incident
[MLT VL
[ML'T)
Iluminance or
illumination
84
area
(sum of masses of nucleons)-
(mass of the nucleus)
[M
[ML'T 85.
Mass defect
Binding energy of
nucleus
Mass defect
x (speed of light [M[LTr
in vacuum
86. [ML' T']
Decay constant 0.693/half life [T]
[MLT
87.
88. Resonant frequency
[M'L' A° T
(Inductance
x capacitance)
2
[ML TA?
[MLTA?J
89 Quality factor or Q
factor of coil
Resonant frequency x inductance
[T]MLTA] [M'LT]
Resistance
[MLPTA
90 Power of lens
(Focal length
[ML'T]
91.
Magnification
Image distance
Object distance
[L]/L] [M'LT]
92 Fluid flow rate
(T/8) (pressure)x (radius
viscosity coefficient)x length
(ML T] M'L'T]
IML'T] li
93
Capacitive reactance
(Angular frequency x
capacitance
ITTM'L'T'AT' [ML T A
94
Inductive reactance
(Angular frequency x
inductance)
IT IML T A) [ML T A