PHYSICAL QUANTITY
A quantity which can be measured and by which various physical happenings can be explained and expressed in form of laws is called a physical quantity.
A quantity which can be measured and by which various physical happenings can be explained and expressed in form of laws is called a physical quantity.
Example: Length, Mass, Time, Force etc. On the other hand various happenings in life e.g., happiness, sorrow etc. are not physical quantities because these can not be measured.
Measurement is necessary to determine magnitude of a physical quantity, to compare two similar physical quantities and to prove physical laws or equations.
A physical quantity is represented completely by its magnitude and unit. For example, 10 metre means a length which is ten times the unit of length 1 metre. Here 10 represents the numerical value of the given quantity and metre represents the unit of quantity underconsideration. Thus in expressing a physical quantity we choose a unit and then find that how many times that unit is contained in the given physical quantity, i.e.,
Physical quantity (Q) = Magnitude × Unit = n × u
Where, n represents the numerical value and u represents the unit. Thus while expressing definite amount of physical quantity, it is clear that as the unit (u) changes, the magnitude (n) will also change but product 'nu' will remain same.
i.e., nu = constant
or, n1u1=n2u2= constant
or, n∝1u
i.e., magnitude of a physical quantity and units are inversely proportional to each other. Larger the unit, smaller will be the magnitude.
Types of Physical Quantity:
(1) Ratio (Numerical Value Only):
When a physical quantity is a ratio of two similar quantities, it has no unit.
Example: Relative density =Density−of−the−objectDensity−of−the−water−at−4∘C
Refractive Index =Velocity−of−light−in−airVelocity−of−light−in−medium
Strain =Change−in−dimensionInitial−dimension
Special Notes:
Angle is exceptional physical quantity, which though is a ratio of two similar physical quantities (angle=arcradius) but still requires a unit (degrees or radians) to specify it along with its numerical value.
(2) Scalar (Magnitude Only):
These quantities do not have any direction e.g., Length, time, work, energy etc.
Magnitude of a physical quantity can be negative. In that case negative sign indicates that the numerical value of the quantity under consideration is negative. It does not specify the direction.
Scalar quantities can be added or subtracted with the help of following ordinary laws of addition or subtraction.
(3) Vector (Magnitude and direction):
Vector physical quantities can be added or subtracted according to vector laws of addition. These laws are different from laws of ordinary addition.
Special Notes:
There are certain physical quantities which behave neither as scalar nor as vector. For example, moment of inertia is not a vector as by changing the sense of rotation its value is not changed. It is also not a scalar as it has different values in different directions. (i.e., about different axes). Such physical quantities are called Tensors.
(1) FUNDAMENTAL AND DERIVED QUANTITY:
Out of large number of physical quantities which exist in nature, there are only few quantities which are independent of all other quantities and do not require the help of any other physical quantity for their definition, therefore these are called absolute quantities. These quantities are also called fundamental or base quantities, as all other quantities are based upon and can be expressed in terms of these quantities.
(2) DERIVED QUANTITIES:
All other physical quantities can be derived by suitable multiplication or division of different power of fundamental quantities. These are therefore called derived quantities.
If length is defined as a fundamental quantity then area and volume are derived from length and are expressed in term of length with power 2 and 3 over the term of length.
Special Notes
In mechanics Length, Mass and Time are arbitarily chosen as fundamental quantities. However this set of fundamental quantities is not a unique choice. In fact any three quantities in mechanics can be termed as fundamental as all other quantities in mechanics can be expressed in terms of these. e.g., if speed and time are taken as fundamental quantities, length will become a derived quantity because then length will be expressed as Speed × Time, and if force and acceleration are taken as fundamental quantities, then mass will be defined as ForceAcceleration and will be termed as a derived quantity.
FUNDAMENTAL AND DERIVED UNITS:
Normally each physical quantity requires a unit or standard for its specification so it appears that there must be as many units as there are physical quantities. However, it is not so. It has been found that if in mechanics we choose arbitarily units of any three physical quantities mass, length and time are chosen for this purpose. So any unit of mass, length and time in mechanics is called a fundamental, absolute or base unit. Other units which can be expressed in terms of fundamental units, are called derived units. For example light year or Km is a fundamental units as it is a unit of length while s−1 , m2 or Kg/m are derived units as these are derived from units of time, mass and length respectively.
SYSTEM OF UNITS: A complete set of units, both fundamental and derived for all kinds of physical quantities is called system of units. The common systems are given below -
(1) CGS SYSTEM: The system is also called Gaussian system of units. In it length, mass and time have been chosen as the fundamental quantities and corresponding fundamental units are centimetre (cm), gram (gm) and second (s) respectively.
(2) MKS SYSTEM: The system is also called Giorgi system. In this system also length, mass and time have been taken as fundamental quantities, and the corresponding fundamental units are metre (m), kilogram (kg) and second (s).
(3) FPS SYSTEM: In this system foot, pound and second are used respectively for measurements of length, mass and time. In this system force is a derived quantity with unit poundal.
(4) SI SYSTEM: It is known as International system of units, and is infact extended system of units applied to whole physics. There are seven fundamental quantities in this system. These quantities and their units are given in the following table.
Quantitity
|
Name of the Unit
|
Symbol
|
---|---|---|
Length
|
metre
|
m
|
Mass
|
kilogram
|
kg
|
Time
|
second
|
s
|
Electric Current
|
ampere
|
A
|
Temperature
|
Kelvin
|
K
|
Amount of Substance
|
mole
|
mol
|
Luminous Intensity
|
candela
|
cd
|
Besides the above seven fundamental units two supplementary units are also defined -
Radian (rad) for plane angle and Steredian (sr) for solid angle.
Special Notes:
(1) Apart from fundamental and derived units we also use very frequently practical units. These may be fundamental or derived units.
Example: light year is a practical unit (fundamental) of distance while horse power is a practical unit (derived) of power.
(2) Practical units may or may not belong to a system but can be expressed in any system of units.
Example: 1 mile = 1.6km = 1.6×103m
SI PREFIXES
In physics we have to deal from very small (micro) to very large (macro) magnitudes as one side we talk about the atom while on the other side of universe, e.g., the mass of an electron is 9.1×10−31kg while that of the sun is 2×1030kg. To express such large or small magnitudes simultaneously we use the following prefixes.
Power of 10
|
Prefix
|
Symbol
|
---|---|---|
1018
|
exa
|
E
|
1015
|
peta
|
P
|
1012
|
tera
|
T
|
109
|
giga
|
G
|
106
|
mega
|
M
|
103
|
kilo
|
k
|
102
|
hecto
|
h
|
101
|
deca
|
da
|
10−1
|
centi
|
c
|
10−3
|
milli
|
m
|
10−6
|
micro
|
μ
|
10−9
|
nano
|
n
|
10−12
|
pico
|
p
|
10−15
|
femto
|
f
|
10−18
|
atto
|
a
|
STANDARD of Length, Mass and Time:
(1) Length: Standard metre is defined in terms of wavelength of light and is called atomic standard of length. The metre is the distance containing 1650763.73 wavelength in vaccum of the radiation corresponding to orange red light emitted by an atom of krypton - 86. Now a days metre is defined as length of the path travelled by light in vaccum in 1299, 7792, 458 part of a second.
(2) Mass: The mass of a cylinder made of platinum-iridium alloy kept at International Bureau of Weights and Measures is defined as 1 kg. On atomic scale, 1 kilogram is equivalent to the mass of 5.0188×1025 atoms of C-12 (an isotope of carbon).
(3) Time: 1 second is defined as the time interval of 9192631770 vibration of radiation in Cs-133 atom. This radiation corresponds to the transition between two hyperfine level of the ground state of Cs-133.
PRACTICAL UNITS:
(1) Length:
(i) 1 fermi = 1 fm = 10−15m
(ii) 1 X-ray unit = 1 XU = 10−13m(iii) 1 angstrom = 10A = 10−10m = 10−8cm = 10−7mm = 0.1μmm
(iv) 1 micron = 1μm = 10−6m
(v) 1 astronomical unit = 1 A.U. = 1.49×1011m≈1.5×1011m≈108km
(vi) 1 Light year = 1 ly = 9.46×1015m
(vii) 1 Parsec = 1 pc = 3.26 light year
(2) Mass:
(i) Chandra Shekhar unit: 1 CSU = 1.4 times the mass of sun = 2.8×1030kg
(ii) Metric tonne: 1 Metric tonne = 1000 kg(iii) Quintal: 1 Quintal = 100 kg
(iv) Atomic mass unit (amu): 1 amu = 1.67×10−27kg mass of proton or neutron is of the order of 1 amu.
(3) Time:
(i) Year: It is the time taken by earth to complete 1 revolution around the sun in its orbit.
(ii) Lunar month: It is the time taken by moon to complete 1 revolution around the earth in its orbit.
1 LM = 27.3 days
(iii) Solar Day: It is the time taken by earth to complete one rotation about its axis with respect to sun. Since this time varies from day to day, average solar day is calculated by taking average of the duration of all the days in a year and this is called Average Solar day.
1 Solar year = 365.25 average solar day
or, average solar day = 1365.25 the part of solar year.
(iv) Sedrial day: It is the time taken by earth to complete one rotation about its axis with respect to a distant star.
1 Solar year = 366.25 Sedrial day = 365.25 average solar day
Thus 1 Solar day is less than 1 Solar day.
(v) Shake: It is an obsolete and practical unit of time.
1 Shake = 10−8 sec
Sir Please give some techniques to solve free body diagram related problem in mechanics.
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