3. Relativistic Mechanics
In physics, special relativity (SR, also known as the special theory
of relativity or STR) is the accepted physical theory regarding the
relationship between space and time
General relativity, or the general theory of relativity, is the
geometric theory of gravitation published by Albert Einstein in 1916[1]
and the current description of gravitation in modern physics.
In physics, relativistic mechanics refers to mechanics compatible
with special relativity (SR) and general relativity (GR). It provides a
non-quantum mechanical description of a system of particles, or of a
fluid, in cases where the velocities of moving objects are comparable
to the speed of light.
4. Quantum Mechanics
Quantum mechanics (QM – also known as quantum
physics, or quantum theory) is a branch of physics
which deals with physical phenomena at nanoscopic
scales where the action is on the order of the Planck
constant.
It departs from classical mechanics primarily at the
quantum realm of atomic and subatomic length scales.
Quantum mechanics provides a mathematical
description of much of the dual particle-like and wave-
like behavior and interactions of energy and matter.
Quantum mechanics provides a substantially useful
framework for many features of the modern periodic
table of elements including the behavior of atoms during
chemical bonding and has played a significant role in
the development of many modern technologies.
5. Mechanics of Deformable Bodies:
The mechanics of deformable bodies deals
with how forces are distributed inside bodies,
and with the deformations caused by these
internal force distributions. These internal
force produce "stresses" in the body, which
could ultimately result in the failure of the
material itself.
Principles of rigid body mechanics often
provide the beginning steps in analyzing
these internal stresses, and resulting
deformations. These will be studied in
courses called Strength of Materials or
Mechanics of Materials.
6. Mechanics of Fluids:
The mechanics of fluids is the branch of mechanics that
deals with liquids or gases.
Fluids are commonly used in engineering
applications. They can be classified as incompressible,
or compressible. While all real fluids are compressible
to some degree, most liquids can be analyzed as
incompressible in many engineering applications.
Applications of fluid mechanics abound, from hydraulics
and general flow in pipes to air flow in ducts to
advanced applications in turbines and aerospace.
The study of the mechanics of fluids will be studied in
courses called Fluid Mechanics, Compressible Flow,
Hydraulics, and others
7. Mechanics of Rigid Bodies:
A rigid body is a body which does not
deform under the influence of forces.
In all real applications, there is always
deformation, however, many stuctures
exhibit very small deformations under
normal loading conditions, and rigid
body mechanics can be used with
sufficient accuracy in those cases.
10. Fundamental
Length: Length is the quantity used to describe the position of a point in
space relative to another point. The universally accepted standard unit for
length is the meter.
Time: Time is the interval between two events. The generally accepted
standard unit for time is the second.
Mass: Mass is a property of matter. Mass can be considered to be the
amount of matter contained in a body. The mass of a body determines both
the action of gravity on the body, and the resistance to changes in
motion. This resistance to changes in motion is referred to as inertia, which
is a result of the mass of a body. The internationally accepted unit of mass is
the kilogram.
Mass vs. Weight: As stated above, mass is a fundamental quantity of
matter. It is independent of location and surroundings. The weight of a body
is the force exerted on the body due to gravitational attraction of the Earth.
(W=mg)
11. Comparison of Mass and
Weight
Sr.
no.
Mass Weight
01 Mass is a property of matter.
The mass of an object is the
same everywhere.
Weight depends on the effect of
gravity. Weight varies according to
location.
02 Mass can never be zero. Weight can be zero if no gravity acts
upon an object, as in space.
03 Mass does not change
according to location.
Weight increases or decreases with
higher or lower gravity.
04 Mass is a scalar quantity. It
has magnitude.
Weight is a vector quantity. It has
magnitude and is directed toward the
center of the Earth or other gravity
well.
05 Mass may be measured using
an ordinary balance.
Weight is measured using a spring
balance.
06 Mass usually is measured in
grams and kilograms.
Weight often is measured in newtons,
a unit of force.
07 Unit : Kilogram (Kg) W= mg
Unit : newton (N)
12. Differences between distance
and displacement:
Sr.
no.
Distance Displacement
01 Distance is the length of the path
travelled by a body while moving
from an initial position to a final
position.
Displacement is the shortest
distance between the initial position
and the final position of the body.
02 Distance is a scalar quantity. Displacement is a vector quantity.
03 Distance measured is always
positive.
Displacement can be positive or
negative depending on the
reference point.
04 The total distance covered is
equal to the algebraic sum of all
the distances travelled in
different directions.
The net displacement is the vector
sum of the individual displacements
in different directions.
05 There is always a distance
covered whenever there is a
motion.
Displacement will be zero if the
body comes back to its initial
position.
06 Unit: metre (m) Unit: metre (m)
13. For example:
Q. Suppose you are observing an ant on the table, as
shown in the diagram below. The ant moves from one
corner of the table to the other corner. The blue
irregular line shows the path of the ant.
For figure (B) &
(C), Find
Distance ?
Displacement?
Answer :
•For Length of this blue line is the distance covered
by the ant.
•The straight green line, which is the minimum
distance between the two corners of the table is the
displacement of the ant. Called the displacement.
Figure
(B)
Figure
(A)
Figure
(C)
14. Sr. no Speed velocity
01 Speed is refers to "how fast an object
is moving."
Velocity refers to "the rate at which an
object changes its position."
02 Speed is a scalar quantity. Velocity is a vector quantity.
03 Speed is the rate of motion, or the
rate of change of position.
velocity is the rate of change of
displacement.
04 Speed is thus the magnitude
component of velocity.
Velocity contains both the magnitude
and direction components.
05 Explanation :
How fast my hand is moving to
slapped on your face, this is speed
Explanation :
When you get the slap and changes
your face from right to left.. i.e the rate
at which your face changes its position,
this is Velocity....
06 speed= total distance/time taken velocity= displacement(shortest root
from initial to the final position) /time
taken
including direction.
07 Unit: km/hr like 60km/hr, Unit: 60km/hr in east direction
15. Units of Measure
The force unit is called a newton (N), and is defined as the
force required to accelerate a mass of 1 kg at a rate of 1
meter/sec. So, we can write:
1 N = (1 kg)(1 m/s2) or 1 N = 1kg.m/s2
The weight of an object is the gravitational force which is
exerted on that object which causes it to accelerate
downward at the acceleration due to gravity So, we can
write for the weight of a 1 kg mass:
W = mg
W = (1 kg)(9.807 m/s2)
W = 9.807 N
16. SI prefixes
Multiplier Prefix Symbol
109 giga G
106 mega M
103 kilo k
10-2 centi c
10-3 milli m
10-6 micro µ
10-9 nano n
10-12 pico p
18. Fundamental laws:
1. Newton's first law
"An object at rest stays at rest and an object
in motion stays in motion with the same
speed and in the same direction unless acted
upon by an unbalanced force. This law is
often called the law of inertia.
Objects tend to "keep on doing what they're
doing." In fact, it is the natural tendency of
objects to resist changes in their state of
motion. This tendency to resist changes in
their state of motion is described as inertia.
Example :The motion of a kite when the wind
changes can also be described by the first
law.
20. 2. Newton's second law
“ The rate of change of
momentum is directly
proportional to
impressed force and
takes place in the
direction of force”.
Fundamental laws:
21.
22. 3. Newton's third law
For every action there is an equal
and opposite reaction.
Fundamental laws:
23. Vectors and Scalars
All physical quantities (e.g. speed and force)
are described by a magnitude and a unit.
VECTORS – also need to have their direction
specified
examples: displacement, velocity,
acceleration, force.
SCALARS – do not have a direction
examples: distance, speed, mass, work,
energy.
24. Addition of vectors
With two vectors acting at
an angle to each other:
Draw the first vector.
Draw the second vector with
its tail end on the arrow of the
first vector.
The resultant vector is the line
drawn from the tail of the first
vector to the arrow end of the
second vector.
This method also works with
three or more vectors.
4N
3N
Resultant vector
= 5N
4N
3N
25.
26.
27. Resolution of vectors
It is often convenient to split a
single vector into two
perpendicular components.
Consider force F being split into
vertical and horizontal
components, FV and FH.
In rectangle ABCD opposite:
sin θ = BC / DB = DA / DB = FV / F
Therefore: FV = F sin θ
cos θ = DC / DB = FH / F
Therefore: FH = F cos θ
F
FV
FH
θ
C
BA
D
FV = F sin θ
FH = F cos θ
28. Question
Calculate the vertical and
horizontal components if F
= 4N and θ = 35o.
FV = F sin θ
= 4 x sin 35o
= 4 x 0.5736
FV = 2.29 N
FH = F cos θ
= 4 x cos 35o
= 4 x 0.8192
FH = 3.28 N
F
FV
FH
θ
29. The moment of a force
Also known as the turning effect of a
force.
The moment of a force about any point is
defined as: force x perpendicular
distance from the turning point to the
line of action of the force
moment = F x d
Unit: Newton-metre (Nm)
Moments can be either CLOCKWISE or
ANTICLOCKWISE
Force F exerting an
ANTICLOCKWISE
moment through the
spanner on the nut
30. Question
Calculate the moments of the 25N
and 40N forces on the door in the
diagram opposite.
moment = F x d
For the 25N force:
moment = 25N x 1.2m
= 30 Nm CLOCKWISE
For the 40N force:
moment = 40N x 0.70m
= 28 Nm ANTICLOCKWISE
hinge
door
40N
25N
1.2 m
31. Couples and Torque
A couple is a pair of
equal and opposite
forces acting on a body,
but not along the same
line.
In the diagram above:
total moment of couple = F x + F(d - x) = F d
= One of the forces x the distance between the
forces
Torque is another name for the total moment of a
couple.
