Basics of classical mechanics and molecular physics : Teaching visual aid

The Ministry of Science and Higher Education of the Russian Federation 
Kazan National Research Technological University 
V. Arkhipov
BASICS OF CLASSICAL MECHANICS 
AND MOLECULAR PHYSICS   
Teaching visual aid 
Kazan 
KNRTU Press 
2023 

UDC 531(075) 
Published by the decision of the Editorial Review Board  
of the Kazan National Research Technological University 
Reviewers: 
Doctor of Engineering Sciences, Professor A. Turanov 
Ph.D. in Physics and Mathematics, Associate Professor I. Lunev 
Arkhipov V. 
Basics of classical mechanics and molecular physics : Teaching visual 
aid / V. Arkhipov; The Ministry of Education and Science of the Russian 
Federation, Kazan National Research Technological University. – 
Kazan : KNRTU Press, 2023. – 124 p. 
ISBN 978-5-7882-3429-8 
The teaching visual aid outlines the main issues of the General Physics course 
(sections Classical Mechanics and Molecular Physics). The presentation of material 
in the form of various information blocks ‒ text, formulas, graphs ‒ allows you 
to improve the quality of teaching, the level of understanding and mastering 
of the material by students. 
The teaching visual aid is intended for students studying in the bachelor's degree program 18.03.01 “Chemical Technology” in all areas of preparation of mechanical and technological profiles in order to consolidate the theoretical foundations of 
the course “General Physics“.  
It is prepared by the Department of Physics. 
UDC 531(075) 
ISBN 978-5-7882-3429-8 
© V. Arkhipov, 2023 
© Kazan National Research Technological 
University, 2023 
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Introduction 
    If I have seen further than others, 
it is by standing upon the shoulders 
of giants / Isaac Newton 
The basic concepts and laws of classical mechanics have been 
formulated in the works of Galileo, Descartes, Leibniz during the scientific revolution of the 16‒17th centuries. Descartes establishes 
the law of conservation of linear momentum (amount of movement): 
“If one body collides with another, it cannot inform it of any other 
movement, except for the one that it will lose during this collision, as it 
cannot and take away from it more than it simultaneously acquires itself”. Galileo formulated the principle of relativity: “Laws of motion 
are the same in all inertial frames of reference”. Leibniz laid the foundations of the doctrine of movement – dynamics, using the concepts 
of “dead” and “living” forces. 
Newton formulated the basic concepts of mechanics and establishes its laws.  Newton's first law: “An object at rest remains at rest, 
or if in motion, remains in motion at a constant velocity unless acted 
on by a net external force”. Newton's second law of motion states that 
F = ma, or the product of the mass of a body and its acceleration equals 
the force acting on the body. A larger net force acting on an object 
causes a larger acceleration, and objects with larger mass require more 
force to accelerate. Newton's third law: “If two bodies exert forces on 
each other, these forces have the same magnitude, but in opposite directions”. 
Academician S. I. Vavilov wrote: “We thought about Newton's 
language, spoke for a long time, and only now attempts are being made 
to invent a new language. That is why it can be argued that on all physics lay the imprint of his thought, without Newton, science would develop differently”. 
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This teaching visual aid “Basics of Classical Mechanics and Molecular Physics”, made in the form of a presentation in PowerPoint format, reflects the main fundamental topics and issues of these sections of 
physics in a concise form. The main topics of classical mechanics are 
considered ‒ kinematics and dynamics of translational and rotational motions of a material point and a rigid body, the laws of conservation of momentum, angular momentum, mechanical energy. 
The topics of oscillatory and wave motions, separated in a distinct block, include questions of the addition of harmonic oscillations, 
patterns of damped and forced oscillations, patterns of wave processes 
and the phenomenon of wave interference. It is recommended to carefully study this block of questions, which will be further connected 
with the theory of an electric oscillatory circuit and the laws of wave 
optics. 
When studying the issues of molecular physics, pay attention 
to how a combination of two independent methods: molecular-kinetic 
(statistical) and thermodynamic, based on the laws of conservation and 
transformation of energy, allows you to describe the properties, phenomena and processes of ideal and real gases. 
A block method of presenting the material is used, which allows focusing on fundamental physical laws, principles and models, 
supported, if necessary, by mathematical calculations in order to develop logical thinking skills.  
The course of general physics is traditionally divided into three 
main sections, determined by the nature of the phenomena being studied, the methods of their description, and the models used. 
In the section “Mechanics and Molecular Physics” the regularities of the mechanical motion of bodies, atoms and molecules in bodies are considered. Models of a material point, an absolutely rigid 
body, an ideal gas are used, the basic laws are Newton's laws and conservation laws.  
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KINEMATICS
I do not know what I may appear to the world, but to myself 
I seem to have been only like a boy playing on the sea-shore, 
and diverting myself in now and then finding a smoother 
pebble or a prettier shell than ordinary, whilst the great ocean 
of truth lay all undiscovered before me / Isaac Newton
 
 
Space and time in classical mechanics
All physical processes take place in space and time.
Space reflects the order of coexistence of individual objects, 
time ‒ the order of change of phenomena
In classical mechanics, space and time:
1) are not related to each other;
2) do not depend on objects and ongoing processes
The space is:
1) isotropic ‒ all directions are equal;
2) homogeneous ‒ all points are equal;
3) three-dimensional and Euclidean;
4) bodies do not affect the properties of space
United absolute universal time:
1) flows equally and evenly in all reference frames;
2) does not depend on the state of motion of bodies
 
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Reference frame
The problem of kinematics is to describe the motion of a body, that is, to determine 
the position, velocity, accelaration of a body in space at any time
Mechanical motion ‒ a change 
in the relative position of bodies 
or their parts in space over time
Trajectory
Radius-vector
Reference frame – the clock, coordinate system 
and some set of bodies,
in relation to which the movement is considered
 
 
Law of motion of a material point
A material point or point mass (point-like mass) is a body, the size and shape
of which can be neglected under the conditions of a given motion
At a sufficiently large distance, 
any body of finite size will look 
Is it possible to consider 
the Earth 
as a material point?
and behave like a point mass
Radius-vector connects
coordinate system origin 
Law of motion
with a given material point
r
f (t )

x = x(t)
1
r
2
r
z
o
y = y(t)
z = z (t)
3
r
x
y
 
6 

Radius-vector




r
x i
y j
z k
i, j, k 
unit vectors 
of the Cartesian 
Z
coordinate system
z



i
j
k
1
r
k
y
O
j
Y
i
x
2
2
2



r
x
y
z
x
X
Velocity
Instantaneous velocity
1
Z
Velocity ‒ the rate
2
r
of  change in a body 
position
r(t )
k

r(t
t )
V dr
O
j
Y
Velocity is always 
i
directed tangentially
to the trajectory
X
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Velocity
Z
V

Vz
V
V
V
k
Vy
O
j
Y
Vx
i
x
X


V
V 
(
)
x
y
z
V V ,V ,V
1


x
y
z
dx
dy
dz
V
;  V
;   V
dt
dt
dt




=
x
y
z
V V
i
V
j
V
k





– unit vector,
directed tangentially 
to the trajectory
Acceleration
‒ acceleration 
2
a
is the rate of change
of a body's velocity
2
0






t
V
dV
d r
a
lim
t
dt
dt
Z
(
)
x
y
z
a a ,a ,a
2
aZ


x
x
2
2
a


y
y
2
k
2
aY


z
z
2
Y
о
dV
d x
a
dt
dt
dV
d y
a
dt
dt
dV
d z
a
dt
dt
j
i
aX
X






y
x
z
dV
dV
dV
a
i
j
k
dt
dt
dt
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Tangential and normal acceleration
Let us decompose the acceleration vector 
into two directions - along and perpendicular to the velocity vector:
a


n
a
a
a

V
a

n
a
V ;
a
V

According to 
the Pythagorean theorem:
n
a
a
2
2


n
a
a
a

 
 
Tangential and normal acceleration
Let's use unit vectors directed along and perpendicular
1


n

to the velocity vector




n
a
a
a
n

V
a

dV
a
dt

2

n
V
a
R
n
a
2


dV
V
a
n
dt
R

n
a
 
9 

V

Normal acceleration

a



2

n
V
a
R
n
a

Normal or centripetal acceleration 
Tangential acceleration
directed perpendicular to the trajectory. 
Characterizes the rate of change
in the direction of the velocity vector.
Directed always towards the center 
dV
a
dt

of curvature of the trajectory
It characterizes the rate of change 
R – radius of curvature
of the module of the velocity vector 
of the trajectory, radius of a circle 
(the rate of change of the velocity value).
inscribed in the trajectory 
Directed tangential to the trajectory
in a given area
 
 
Kinematic characteristics of rotational motion

angle of rotation,
[Δφ ] = rad


d
dt




angular velocity,
[ω] = rad/s
2
2


d
d
dt
dt



angular acceleration,    [ε] = rad/s2
‒  axial vectors directed along the axis of rotation
,
,

in accordance with the rule of the right gimlet
 
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