Physics 2 (PHY 125)
Classical Mechanics
Dr Manjunatha S
PHYSICAL QUANTITY:
A quantity which can be measured directly or
indirectly is called physical quantity
Measurement means comparison of physical
quantity with another standard.
UNIT
In order to measure a physical quantity, a
standard reference is needed. This standard is
called unit.
Physical Quantity = number x unit
Dr Manjunatha S
2
Measurement
• Being quantitative in Physics requires
measurements
• How tall is Ming Yao? How about
his weight?
– Height: 2.29 m (7 ft 6 in)
– Weight: 141 kg (310 lb)
Number
+
Unit
– “thickness is 10.” has no
physical meaning
– Both numbers and units necessary for
any meaningful physical quantities
Units
Two types of Units
1. Fundamental Units:
In mechanics, the mass, length, and time
are fundamental physical quantities. The
units of these physical quantities are called
fundamental units.
2. Derived Units:
Any physical quantity which can be derived
from the fundamental physical quantities is
called derived units.
Dr Manjunatha S
4
System of units:
A complete set of fundamental and
derived units is known as system of
units. There are four system of
units.
1. CGS system: The unit of length is
centimetre (cm), mass is gram
(g)and time is second (s).
2. FPS system: foot, pound and
second
Dr Manjunatha S
5
System of units:
3. MKS System: meter , Kilogram and
second.
4. SI units (System of International
Units): Modified MKS system,
consists of 7 fundamental units, 2
supplementary units and many
derived units.
Dr Manjunatha S
6
Fundamental Quantities and SI Units
1. Length
meter
m
2. Mass
kilogram
kg
3. Time
second
s
4. Electric Current
ampere
A
Kelvin
K
candela
cd
mole
mol
5. Thermodynamic
Temperature
6. Luminous Intensity
7. Amount of
Substance
Dr Manjunatha S
7
Supplementary Units
S. No
Physical Quantity Name of unit symbol
1
Plane Angle
radian
rad
2
Solid Angle
steradian
Sr
Dr Manjunatha S
8
Derived Units
S.
No.
Physical Quantity
Name of Unit
Symbol
1
2
3
Work, Energy
Power
Force
Joule
Watt
Newton
J
W
N
4
5
6
7
Charge
Magnetic field
Magnetic Flux
Electric Field
Coulomb
tesla
weber
Newton /
Coulomb
C
T
Wb
N/C
Dr Manjunatha S
9
SI Length Unit: Meter
• French Revolution Definition,
1792
• 1 Meter = XY/10,000,000
• 1 Meter = about 3.28 ft
• 1 km = 1000 m, 1 cm = 1/100
m, 1 mm = 1/1000 m
Meter: 1 Meter is defined as the
distance traveled by light in
vacuum during a time of
1/299,792,458 second.
SI Time Unit: Second
Second is defined in terms of an “atomic
clock”– time taken for 9,192,631,770
oscillations of the light emitted by a 133Cs atom.
• Defining units precisely is a science (important, for
example, for GPS):
– This clock will neither gain nor lose a
second in 20 million years.
Dr Manjunatha S
11
SI Mass Unit: Kilogram
• 1 Kilogram – the mass of a
specific platinum-iridium alloy
kept at International Bureau of
Weights and Measures near
Paris. (Seeking more accurate
measure:
• Copies are kept in many other
countries.
• Yao Ming is 141 kg, equivalent
to weight of 141 pieces of the
alloy cylinder.
Dr Manjunatha S
12
Dr Manjunatha S
13
Dimensional Analysis:
• The word dimension has a special meaning
in physics.
• The dimension denotes the physical nature
of a quantity.
• The expression which shows the
fundamental quantity and power of unit is
dimensional equation.
• The mass, length and time as M, L, and T
are expressed in bracket [Ma Lb Tc].
Dr Manjunatha S
14
Dimensional formulae of physical
quantities
S. No.
Physical Quantity
Physical Formula
1
Area
Length x Length
2
Volume
Lxbxt
3
Density
Mass/ volume
4
Velocity
5
Force
6
Pressure
7
Energy/Work
8
Power
9
Surface Tenstion
10
Temperature
11
Gravitational
Constant
12
Volume/second
13
Angular speed
SI Unit
m2
Dimensional
formula
L X L= [M0 L2 T0]
N/m
N m2/kg2
Angle/s
[M0 L0 T-1]
Dimensional formulae of physical quantities
S. No. Physical Quantity
Physical Formula
SI Unit
1
Electric Charge, Q
Current x time
Coulomb
2
Electric Potential, V
Work/charge
Volt
3
Resistance, R
V/I
Ohm
4
Sp. Resistance, ρ
Rx area/l
5
Electric field, E
F/Q
6
Capacity, C
Q/V
7
Magnetic Induction, B F/Qv Sinθ
Dimensional
formula
[M0 L0 T1A1]
Farad
tesla
8
9
10
11
12
13
16
Principle of homogeneity:
The dimension of fundamental quantities of
two sides of a physical relation must be
same.
[Ma Lb Tc ] = [Mx Ly Tz ]
a=x, b=y, and c=z
Dr Manjunatha S
17
Types of variables and constants
• 1. Dimensional variables: Physical quantities
which possess dimensions and have
variables are called dimensional variables
• Ex: area, volume, speed, acceleration, force..
• 2. Dimensionless variables: Quantities which
have no dimension but have variables
called dimensionless variables.
• Ex: angle, gravity, sinθ, cosθ...
Dr Manjunatha S
18
Types of variables and constants
3. Dimensional constants: Physical quantities
which possess dimensions and have constant
value are called dimensional constants.
• Ex: Planck’s constant, gravitational constant,
speed of light
4. Dimensionless constants: Physical quantities
which do not have dimension and have
constant are called dimensionless constant.
– Ex: π, e, pure no. Like 1,2,3,4,5,..
Dr Manjunatha S
19
Conversion of Units
The dimension equation can be used to one
system into another system of unit.
Dr Manjunatha S
20
PROBLEMS:
Example: 1
Joule is the unit of Work in SI system.
Convert Joule into CGS system as erg.
Work = [M1 L2 T-2]; a=1, b=2, c=-2
Dr Manjunatha S
21
PROBLEMS...
Example:2
Convert 10 Newton into dyne using
dimensional analysis.
Dr Manjunatha S
22