Physical quantity, units and dimensions
Physical quantity: A quantity
that can be measured by instrument, clearly defined and has proper units
is called physical quantity. Physical quantities are classified as fundamental and derived quantities.
Fundamental units: The physical quantity which
does not depend on any other physical quantity is called a fundamental
physical quantity such as length; mass and time are called fundamental
units.
Derived units: The units that can be obtained from fundamental units are called derived units.
Example:
Find the unit of acceleration?
Find the unit of acceleration?
Solution:
Acceleration = velocity/Time = V/S = (m/s)/s = m/s2 = ms-2
Acceleration = velocity/Time = V/S = (m/s)/s = m/s2 = ms-2
System of units: There are three systems of units.
|
Name of system
|
Fundamental unit of
|
||
|
Length
|
Mass
|
Time
|
|
|
F.P.S.
|
Foot
|
Pound
|
Second
|
|
C.G.S.
|
Centimetre
|
Gram
|
Second
|
|
M.K.S. (S.I.)
|
Meter
|
Kilogram
|
Second
|
In physics SI system is based on seven fundamental and two supplementary units.
(i) Fundamental units:
|
S.No.
|
Basic Physics
|
Fundamental Unit
|
Symbol
|
|
1.
|
Mass
|
kilogram
|
kg
|
|
2.
|
Length
|
meter
|
m
|
|
3.
|
Time
|
second
|
s
|
|
4.
|
Electric current or Charge
|
ampere or coulomb
|
A or Q
|
|
5.
|
Temperature
|
Kelvin or Celsius
|
K or °C
|
|
6.
|
Luminous intensity
|
candela
|
Cd
|
|
7.
|
Quantity of matter
|
mole
|
Mol
|
(ii) Supplementary units:
|
S.No.
|
Supplementary Physical Quantities
|
Supplementary unit
|
Symbol
|
|
1.
|
Plane angle
|
Radian
|
rad
|
|
2.
|
Solid Angle
|
Steradian
|
sr
|
DEFINITION OF FUNDAMENTAL UNITS
(i) Meter: The currently accepted definition of meter is the length of path travelled by light in vacuum in 1/299,792,458th second.
(ii) Kilogram: Kilogram is the fundamental unit of
mass. It is defined as the mass of a specific cylinder of platinum -
iridium kept at the International Bureau of Weights and Measures in
Paris.
(iii) Second: Second is the fundamental unit of
time. It is defined as 86,400th part of a mean solar day. Second is
accurately measured by an atomic clock.
(iv) Coulomb: Coulomb is the fundamental unit of charge. It is defined as the charge required to obtain 9´109newton of force between two equal charges separated at a distance of one meter in vacuum.
(v) Candle: Candle is the fundamental unit of
luminous intensity. It is defined as luminous intensity observed from a
source of monochromatic light of frequency 540´1012 Hz, that has an intensity of 1/683 watt per steradian.
(vi) Kelvin: Kelvin is the fundamental unit of temperature. It has value of zero where the molecular activity of gases cease.
(vii) Mole: Mole is the fundamental unit of
quantity of matter. It is defined as amount of substance of a system
that contains as many elementary particle as there are in 0.012 kg of
carbon-12 (C-12).
BASIC PHYSICAL QUANTITIES
|
Physical quantity
|
Symbol
|
Dimension
|
Measurement unit
|
Unit
|
|
length
|
s
|
L
|
Meter
|
m
|
|
mass
|
M
|
M
|
Kilogram
|
Kg
|
|
time
|
t
|
T
|
Second
|
Sec
|
|
electric charge
|
q
|
Q
|
Coulomb
|
C
|
|
luminous intensity
|
I
|
C
|
Candle
|
Cd
|
|
temperature
|
T
|
K
|
Kelvin
|
oK
|
|
angle
|
q
|
none
|
Radian
|
None
|
Mechanical Physical Quantities (derived)
|
Physical quantity equation
|
Symbol
|
Dimension
|
Measurement (in S.I.)
|
Unit
|
|
area
|
A
|
L2
|
square meter
|
m2
|
|
volume
|
V
|
L3
|
cubic meter
|
m3
|
|
velocity
|
v
|
L/T
|
meter per second
|
m/sec
|
|
angular velocity
|
W
|
1/T
|
radians per second
|
1/sec
|
|
acceleration
|
a
|
L/T2
|
meter per square second
|
m/sec2
|
|
angular acceleration
|
a
|
1/T2
|
radians per square
second
|
1/sec2
|
|
force
|
F
|
ML/T2
|
Newton
|
Kg m/sec2
|
|
energy
|
E
|
ML2/T2
|
Joule
|
Kg m2/sec2
|
|
work
|
W
|
ML2/T2
|
Joule
|
Kg m2/sec2
|
|
heat
|
Q
|
ML2/T2
|
Joule
|
Kg m2/sec2
|
|
torque
|
t
|
ML2/T2
|
newton meter
|
Kg m2/sec2
|
|
power
|
P
|
ML2/T3
|
watt or joule/sec
|
Kg m2/sec3
|
|
density
|
D or r
|
M/L3
|
kilogram per
cubic meter
|
Kg/m3
|
|
pressure
|
P
|
ML-1/T2
|
newton per square meter
|
Kg m-1/sec2
|
|
impulse
|
p
|
ML/T
|
newton second
|
Kg m/sec
|
|
inertia
|
I
|
ML2
|
Kilogram square meter
|
Kg m2
|
|
luminous
flux
|
f
|
C
|
lumen (4Pi candle for point source)
|
cd sr
|
|
Illumination
|
E
|
C/L2
|
lumen per
square meter
|
cd sr/m2
|
|
entropy
|
S
|
ML2/T2K
|
joule per degree
|
Kg m2/sec2K
|
|
volume
rate of flow
|
Q
|
L3/T
|
cubic meter
per second
|
m3/sec
|
|
kinematics
viscosity
|
n
|
L2/T
|
square meter
per second
|
m2/sec
|
|
dynamic
viscosity
|
m
|
M/LT
|
newton second
per square meter
|
Kg/m sec
|
|
specific
weight
|
g
|
M/L2 T2
|
newton
per cubic meter
|
Kg m-2/sec2
|
Electrical Physical Quantities (derived)
|
Physical quantity equation
|
Symbol
|
Dimension
|
Measurement (in S.I.)
|
Unit
|
|
electric
current
|
I
|
Q/T
|
Ampere
|
C/sec
|
|
emf, voltage,
potential
|
E
|
ML2 /T2 Q
|
Volt
|
Kg m2/sec2C
|
|
resistance or
impedance
|
R
|
ML2 /TQ2
|
ohm
|
Kg m2 /secC2
|
|
electric
conductivity
|
s
|
TQ2 /M2L2
|
mho per meter
|
sec C2/Kg m3
|
|
capacitance
|
C
|
T2 Q2 /ML2
|
Farad
|
sec2 C2/Kgm2
|
|
inductance
|
L
|
ML2 /Q2
|
Henry
|
Kg m2 /C2
|
|
current density
|
J
|
Q/TL2
|
ampere per
square meter
|
C/sec m2
|
|
charge density
|
r
|
Q/L3
|
coulomb per cubic meter
|
C/m3
|
|
magnetic flux,
Magnetic induction
|
B
|
M/TQ
|
weber per
square meter
|
Kg/sec C
|
|
magnetic
intensity
|
H
|
Q/LT
|
ampere per meter
|
C/m sec
|
|
magnetic vector
potential
|
A
|
ML/TQ
|
weber/meter
|
Kg m/sec C
|
|
electric
field intensity
|
E
|
ML/T2 Q
|
volt/meter or
newton/coulomb
|
Kg m/sec2 C
|
|
electric displacement
|
D
|
Q/L2
|
coulomb per square meter
|
C/m2
|
|
permeability
|
m
|
ML/Q2
|
henry per meter
|
Kg m/C2
|
|
permittivity,
|
e
|
T2Q2/ML3
|
farad per meter
|
sec2 C2/Kg m3
|
|
dielectric constant
|
K
|
M0L0T0
|
None
|
None
|
|
frequency
|
f or n
|
1/T
|
Hertz
|
sec-1
|
|
angular frequency
|
W
|
1/T
|
radians per second
|
sec-1
|
|
wave length
|
l
|
L
|
Meters
|
M
|
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