Measurement:
The method of comparing any amount of a physical quantity with standard amount of same kind is called measurement. Measurement of a physical quantity consists of a numerical value (n) and a unit(u)
Therefore,
Measurement=Numerical Value(n)*Unit(u)
Unit:
There are 3 kinds of unit.
a) Fundamental unit :
The units of fundamental quantities that cann't be derived from other units.
Example:kg,meter,second etc.
It is 7 in number.
b)Supplementary units:
Example: Units of plane angle and solid angle.
c) Derived units:
The units derived from fundamental and supplementary units.
Example: Joule, Pascal, Newton etc.
Systems of Units:
There are four system of units.
a) CGS System: In this system units for length , mass and time are centimeter(m),gram(m) and seconds(s) respectively.
b) FPS System: Units for length ,mass and time are Foot(ft), pound(lb) and second(s) respectively.
c) MKS System: Units for length for length, mass and time are meter(m), Kilogram(kg) and second(s) respectively.
d) SI System: In this system, there are seven fundamental quantities and fundamental units.
Supplementary Units:
1litre = 10-3 m3
Fundamental Units (In
SI System):
Physical Quantity
|
Units
|
Symbol
|
Length
mass time temperature luminosity electric current amount of substance |
Meter
kilogram second kelvin candela ampere mole |
M
kg s k cd a mol |
Supplementary Units:
Physical Quantity
|
Units
|
Symbol
|
Plane angle
Solid angle |
Radian
steradian |
r
sr |
Conversion Factor:
1litre = 10-3 m3
1 g/cm3 = 103 kg/ m3
1 N = 105 dyne
1 atm = 1.01*105 N/M2
1hp = 746w
1cal = 4.2J
1Kwh = 3.6*106 J
1 N = 105 dyne
1 atm = 1.01*105 N/M2
1hp = 746w
1cal = 4.2J
1Kwh = 3.6*106 J
Dimensions and Dimensional
Formulae:
·
The dimensions of a derived unit may be defined
as the powers to which the fundamental units of mass, length and time must be
raised to represent it.
For example:
Velocity=displacement/time
·
Thus the dimensions of the unit of
velocity are one in length and -1 in time. Its dimension in mass is zero.
·
Work, energy ,quantity of heat , quantity
of light, internal energy, torque each has dimensional formula ML2T-2
(kgm2/s2)
·
Velocity, Speed, distance covered in nth
second have same dimensional formula m0LT-1 (M/S).
·
Pure numbers are dimensions.
Dimensions
of Some Physical Quantities:
S.N
|
Physical Quantity
|
Dimensions
|
SI units
|
1
|
Density (D=M/V)
|
[ML-3]
|
Kg m-3
|
2
|
Force (F=Ma)
|
[MLT-2]
|
Kgms-2
|
3
|
Linear momentum (P=MV)
|
[MLT-1]
|
Kgms-1
|
4
|
Work or Energy(W=F*D)
|
[ML2T-2]
|
Kgm2s-2
|
5
|
Power (P=w/t)
|
[ML2T-3]
|
Kgm2s-3
|
6
|
Pressure (P=F/A)
|
[ML-1T-2]
|
Kgm-1s-2(N/M2)
|
7
|
Impulse(=F*t)
|
[MLT-1]
|
Kgms-1
|
8
|
Strain
|
[M0L0T0]
|
No Unit
|
9
|
Frequency (f)
|
[T1]
|
Hz
|
10
|
Stress (F/A)
|
[ML-1T2]
|
Kgm-1s-2
|