IntroductionIntroduction toto DynamicsDynamics

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 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. 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 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 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 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 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 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 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 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. with mass also take part in relationships.

NEWTON’S LAWS

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.speed) if there is no unbalanced force acting on it.

0F =∑r

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.

amFrr

=∑

)Newton (Ns

mkgmaF

2=⋅==

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 magnitude, opposite in direction, and

collinear.

GRAVITATION Newton’s law of gravitation, which governs

the mutual attraction between bodies, is stated as

G = a universial constant called the constant of gravitation

2

21

r

mmGF =

21mmGF =

2

21

r

mmGF =

2

2121

r

mmGFF ==

2

3

2

22

21

2

skg

m

kgkgs

mmkg

kgkg

mN

mm

rFG

⋅=

⋅⋅

⋅⋅=

⋅

⋅=

⋅=

2

21

rGF =

2

31110673.6

skg

mG

⋅×=

−

amFrr

=∑

UNITS

The International System of metric units

(SI) is defined and used in this lecture.

amFrr

=∑UnitsQuantity Symbol UnitamF

r=∑ amF

r=∑Quantity Symbol Unit

Mass m kg (kilogram)

Time t s (second)

Length L m (meter)

Force F N (Newton)