Download Time

Introduction to Dynamics
Dynamics is that branch of mechanics
which deals with the motion of bodies
under the action of forces. Dynamics
has two distinct parts: kinematics and
kinetics. Kinematics is the study of
motion without reference to the forces
which cause motion. Kinetics relates the
action of forces on bodies to their
resulting motions.
When machines and structures started to
operate with high speeds it became necessary
to make calculations based on the principles
of dynamics rather than on the principles of
statics.
The rapid technological developments of the
present day require increasing application of the
principles of mechanics. These principles are
basic to the analysis and design of moving
structures, fixed structures subjected to shock
loads, robotic devices, automatic control
systems, rockets and machinery of all types.
BASIC CONCEPTS
The basic concepts in mechanics are
space, time, mass and force. Among
these, space, time, mass are absolute
quantities, which mean that they are
independent of each other and cannot be
expressed in terms of other quantities or in
simpler terms. Force, on the other hand, is
a derived quantity.
Space (uzay) is the geometric region occupied
by bodies. Position in space is specified by linear
or angular measurements with respect to a
geometric reference system. In Newtonian
Mechanics the basic reference system is named
as the “primary inertal system” (birincil mutlak
sistem) and it is a virtual system assumed as
neither rotating or translating in space.
For the examination of motion occurring on or
near Earth, it is suitable to use a reference
system attached to Earth as the primary inertial
system.
Time (zaman) is a measure of the
succession of events and is considered an
absolute quantity in Newtonian mechanics.
Mass (kütle) is the quantitative measure
of the inertia or resistance to change in
motion of a body. Mass can also be
considered as the amount of matter within
a body. Although the mass of a body is an
absolute quantity, its weight can change
depending on the gravitational force
(W=mg).
Force (kuvvet) is the action of one body
on another. A force possesses both
magnitude and direction, therefore it is a
vector quantity.
A particle (parçacık veya maddesel nokta) is a
body of negligible dimensions. Generally a particle
is thought to be an infinitesimally small element
which possesses all properties of a body. But
when the dimensions of a body are irrelevant to
the description of its motion or the action of forces
on it, a large body may also be treated as a
particle.
A particle has mass but no shape and dimensions.
The body is considered to be concentrated at a
single point which usually will be its mass center.
All the forces acting on the body will have to pass
from this point, i.e. the forces will be concurrent.
Some examples to particles are shown here; a
ball, a block, even an airplane can be considered
as particles.
A rigid body (rijit veya katı cisim) is a body
whose changes in shape are negligible compared
with the overall dimensions of the body or with the
changes in position of the body as a whole. The
shape and dimensions of a rigid body will remain
the same under all conditions of loading and at all
times.
Some examples of rigid bodies are
shown here.
Displacement (Yer Değiştirme) Time rate of
change of position coordinates. Displacement is
a vector quantity. Examination of displacement
is carried out by means of a suitable coordinate
system. The selected coordinate system can
either be an absolute (fixed) or a moving
system.
Trajectory / Path (Yörünge) It is a line or a
curve obtained when all the points a body
occupies within a specific time period are joined.
Kinematics (Kinematik) Observes motion
without considering the forces that cause the
motion. In other words, it deals with the geometry
of motion. It constitutes relationships between
path, velocity, acceleration and time.
Kinetics (Kinetik) Observes motion by
considering the forces that cause the motion. In
this field, in addition to the quantities in
kinematics, forces and / or moments, together
with mass also take part in relationships.
NEWTON’S LAWS
The laws which constitute the basis of engineering
mechanics are formulated in 1687 by Sir Isaac
Newton. These are:
Law I. (Equation of Equilibrium) A particle
remains at rest or continues to move with uniform
velocity (along a straight line with a constant
speed) if there is no unbalanced force acting on it.

F  0
NEWTON’S LAWS
Law II. (Equation of Motion)The acceleration of
a particle is proportional to the resultant force
acting on it and is in the direction of this force.


 F  ma
m
F  ma  kg  2  Newton (N )
s
NEWTON’S LAWS
Law III. (Principle of Action and
Reaction) The forces of action and reaction
between interacting bodies are equal in
magnitude, opposite in direction, and
collinear.
F G
m1m2
r2
GRAVITATION Newton’s law of gravitation, which governs
the mutual attraction between bodies, is stated as
m1 m 2
FG 2
r
Gm m= a universal constant called the constant of gravitation
F G
1
2
r2
G  6.673  10
11
m3
k g s2
F r2
N  m2
kg  m  m 2
m3
G

 2

m1m 2
kg  kg s  kg  kg
kg  s 2
UNITS
The International System of metric units
(SI) is defined and used in this lecture.
Units
Quantity
Mass
Time
Length
Force


Symbol
 F  ma
m
t
L
F
Unit
kg
s
m
N
(kilogram)
(second)
(meter)
(Newton)