DYNAMICS

DYNAMICS - Lecture Notes

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Dokuz Eylül University – Department of Mechanical Engineering, İzmir, Türkiye

With Tips

Professor Mehmet Zor

23, Agust 2024

DYNAMICS - Lecture Notes

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PREFACE

Dear Student and Engineer Friends,

In our daily lives, in our business lives, in industry and in almost every field, we actually live together with many moving solid objects or systems. In order to obtain the desired functionality from many moving products, from transportation vehicles such as automobiles, airplanes, trains, ships to radars, mechanisms, machines, kitchen robots, rockets, it is extremely necessary to be able to analyze speed, acceleration, and position correctly, as well as to calculate the external loads that are the causes of movement correctly, which is a competence expected only from researchers with sufficient knowledge of dynamics and especially from engineers working in fields such as machinery, aircraft, and automotive, which are primarily related to moving solid systems. These lecture notes of mine will create a very good infrastructure in the field of dynamics and will provide you with the competence required in this field. Since I have been teaching the dynamics course in different departments of engineering faculties for many years, I have identified the points that you, the students, have difficulty understanding. I tried to make these points easy and understandable and named them tricks. In addition to emphasizing these tricks, which are the original aspect of our notes, in a way, each subject has been enriched with different examples. In some places in our notes, you can see that the same pictures are placed on consecutive pages. This eliminates the difficulty of going back to previous pages to examine the figures, allowing the subjects or examples to be understood more quickly; it also helps faculty members to explain the course more fluently with our presentations. I hope it will be beneficial for all students, academicians, researchers, engineers…

December 2022- İzmir

Mehmet Zor

23, Agust 2024

DYNAMICS - Lecture Notes / Mehmet Zor

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1- KINEMATICS OF PARTICLE  

1.1 Rectilinear Motion

1.2 Curvilinear   Motion

1.2.1 Main Features

1.2.2 Projectile Motion (oblique and horizontal throwing motion)

1.2.3 Rectangular Components

1.2.4 Normal and Tangential Components

1.2.5 Polar and Cylindrical Components

2- KINETICS OF PARTICLE

2.1 Force and Acceleration

2.2 Work and Energy

2.3 Impulse and Momentum

3- KINEMATICS OF RIGID BODY

3.1 Planar Motion

3.1.1 Equations of motion between points of the same body

3.1.2 Relative Motion: Equations of motion between points located on different objects

3.2 3D Motion

4- PLANE KINETICS OF RIGID BODIES

4.1 Force and Accelaration

4.2 Work and Energy

CONTENTS

Introduction and Motivation

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Contact and Feedback

e-mails: mehmet.zor@deu.edu.tr , mehmetzor66@gmail.com

My Personel WEBSITE: en.mehmetzor.com

a - Course Educational Turkish Videos (tvids)

b- Lecture Notes.pdf (these notes and notes from other courses)

c- Exam questions and solutions

For all your questions, comments and suggestions:

My Youtube Channel for all course turkish videos: https://www.youtube.com/@mehmetzor

Faculty members who want to follow these lecture notes in their own department's course are sufficient to send me an information e-mail. Solutions to the questions marked (*) in the notes are sent to these faculty members, if they wish.

Statement for Faculty Members

Introduction and Motivation

Introduction and Motivation

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DYNAMICS is a sub-branch of Mechanics that studies moving solid objects.

Introduction and Motivation

An engineer with a good foundation in DYNAMICS,

can calculate the speed, acceleration, position values ​​of the center of gravity of any object or any point on the object at any time t, and external loads such as forces and moments that cause movement.

This is the most basic competence that an engineer must have.

DYNAMICS allows us to find clear answers to the questions of how and why movement occurs.

A. DYNAMICS and Its Scope

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How will the DYNAMICS Course be useful for me in real Life?

Introduction and Motivation

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B. How will the DYNAMICS Course be Useful for me in real life?

• Imagine that you work for a car manufacturer. The company has determined the following performance criteria for the car it plans to produce as its latest model:The car must be able to enter a 100m radius curve at a speed of at least 100km/h, continue on its way at the same speed, and exit the curve at the same speed without skidding.You have all the material and design information for the car that has not yet been produced, and you have been asked to calculate the maximum speed at which the car can travel on this winding road without skidding.
• If the speed you calculate is 100km/h or greater, the desired criterion will theoretically be met and the first prototype will be produced. Otherwise, various revisions will be made to the design or materials until this criterion matches your calculations.

• After production, the first prototype car produced will be tested on the driving track prepared for this criterion and indirectly, the verification of your calculations will also be realized before your eyes. As a result, thanks to your calculations, you will have a value that can be applied to real life.
• You can only make these calculations that are expected of you if you have sufficient knowledge of the basic subjects and calculations of Dynamics.

Example 1

We will try to answer this question with two different examples:

Introduction and Motivation

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• Imagine that you are working as a mechanical engineer in a company that

manufactures fighter jets.

• The R&D unit wants to develop an electronic indicator that will warn you when to

drop a bomb so that a bomb dropped in free fall can accurately hit any target with

specified coordinates on the ground.

• You are asked to develop the equations of motion that will determine when to drop the bomb.
• The equations that give the moment the bomb is dropped will definitely be related to variables such as the aircraft's speed, acceleration, trajectory, height above the ground, the target's coordinates and the effect of the wind.

Example 2

• These equations received from you will later be used in the software infrastructure of the indicator by the electronics and software engineers in your unit.Developing these equations is only possible with a good Dynamics infrastructure.
• As can be seen, a good Dynamics knowledge and calculation competence are extremely necessary for you to take an active role in such R&D studies and to obtain products that are useful for real life.

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It is possible to divide the science of DYNAMICS into two as Kinematics and Kinetics.

1- Kinematics: It does not investigate the cause of the movement, but seeks an answer to the question of how it happens. For any moment of time, the fact that the speed, acceleration and position values ​​of the particle or any point on the rigid body can be found shows that this movement has been solved kinematically.

2- Kinetics: It seeks an answer to the question of why the movement happens. It is a sub-branch of science in which the relationships between the external loads that are the cause of the movement and the acceleration, speed and position of the body are established.

C. DEFINITIONS AND IMPORTANT CONCEPTS

Introduction and Motivation

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Introduction and Motivation

There are two types of particle motion:

Rectilinear motion and Curvilinear motion.

These will be explained in the topics.

Examples: a train moving in a straight line or a rolling ball.Another definition:

Objects that only take into account the motion of a single point (usually the center of gravity) can be examined as particles.

3- Particle

All objects whether large or small, each points of which have the same speed and acceleration, or objects, whose movement of the center of gravity only takes into account, due to their small size, are defined as particles in terms of dynamics.

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4- Rijid Body :

• The speed and acceleration of each point of the objects that make rotational motion and whose dimensions cannot be neglected are different and these types of objects are defined as rigid objects in terms of dynamics.
• Rigid objects that only translate, even if they are large in size, have the same speed and acceleration of each point, the orbits of the points are parallel to each other and these types of rigid objects can also be examined as particles. If the orbits are linear, it is called linear translation, if the orbits are curved, it is called curvilinear translation.

Introduction and Motivation

• The speed and acceleration of the points of the objects that rotate around an axis or point are different from each other.
• Rigid objects can perform both translation and rotation at the same time. This is called general motion.

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5- Velocity) (v): The distance an object travels in unit time. In calculations, the unit should be taken as meter/second (m/s).

6- Acceleration (a): It is the change in speed per unit time. It is also defined as the speed of speed. Its unit should be taken as meter/second squared (m/s²) in calculations.

7- Konum (S) : It is the coordinate of the object at a time t with respect to the reference point. In calculations, meter (m) should be the unit.

8- Force (F): It is a physical external effect that forces an object into motion. Its unit should be taken as Newton (N) in calculations. 1 Newton force is the force that gives a 1kg mass an acceleration of 1m/s² in its own direction.

9- Other concepts related to dynamics: Impulse, Momentum, Kinetic Energy, Potential Energy, Work, Relative Velocity, Relative Acceleration, Coriolis acceleration, angular velocity, angular acceleration etc.These concepts will be explained within the topics.

Introduction and Motivation