Dynamics Dynamics ديناميكا ديناميكا(( : المادة : رقم المادة ((804222804222رقم

: الدكتور :محاضرات الدكتور محاضراتفدعق علي عبداإلله فدعق حسن علي عبداإلله حسن

الدراسي الدراسي الفصل :الثانيالثانيالفصل :لعام لعام هـ هـ 1427/14281427/1428

Introduction

Lecture I

Talking Points

What is dynamics? Historical background Why do we need to study

dynamics Subject outline Some relevant concepts Units

What is Dynamics?

MechanicsBranch of physical sciences that

deals with the state of rest or motion of bodies subjected to the action of

forces

StaticsDeals with the action of forces on

bodies at rest

DynamicsDeals with the motion of bodies

under the action of forces

0

0

M

F

0

0

M

F

What is Dynamics? (Cont.)

Dynamics

KinematicsStudy the motion without reference to

the forces that cause it

KineticsRelates the action of forces on bodies

to their resulting motions

Historical Background

Galileo (1564-1642): Bodies in free fall, motion on inclined

plane, and motion of the pendulum

Historical Background (Cont.)

Newton (1642-1727) Laws of motion, law of universal

gravitation

(F = ma)

Euler, D’Alembert, Lagrange, Laplace, Coriolis, Einstein,etc.

Why do we need to study dynamics

Dynamics principles are basic to the analysis and design of moving structures, such as, engine parts (cams, pistons, gears, etc.), air crafts, missiles, rockets, automatic control systems, turbines, pumps, machine tools, etc.

Why do we need to study dynamics (Cont.)

How do we decide how big to make the pistons? Where should they be placed in the engine block? How do we make the engine run smoothly?

Well, we could answer these questions by trial and error. But the 'errors' would be expensive exercises. Why not study the dynamics of engines and make some predictions instead?

Why do we need to study dynamics (Cont.)

Or suppose we want to build a robot. How do we decide how big to make the motors? How fast can we expect it to move from one place to another? How accurate will it be while it moves and stops? How many joints should it have and where?

Subject Outline

Dynamics

Kinematics Kinetics

Rigid Bodies

Rigid Bodies

ParticlesParticles

- Rectilinear motion- Curvilinear motion

- Rectangular coords- n-t coords- Polar coords

- Relative motion- Constrained motion

- Newton’s second law - Work & Kinetic Energy- Potential Energy- Impulse-Momentum- Constrained motion

- Rigid body assump- tion- Same motions as in particles + rota- tional motion

Kinematics of Particles

Rectilinear Motion

Curvilinear Motion

s s

O P P

t t+t

P

Path of P

Reference Frame

O

r

Kinematics of Particles

RelativeMotion

Constrained Motion

vA

vBvB/A

Coordinates Used for Curvilinear Motion

x

y

z

i

j

k

r

en

et

eb

Center of curvature

Path of P

P

C

r

re e

Path of P

P

r

Rectangular coordinates

Normal-Tangential coordinates

Polar coordinate

s

Kinematics of Rigid Bodies

Kinetics of Particles

F1

F2

F3

F4

=

ma

P P

Some Relevant Concepts Particle: A body of negligible dimensions (or when its

dimensions are irrelevant to the description of its motion or the action of the forces on it). Bodies of finite size, such as rockets, projectiles, or vehicles.

Rigid Body: A system of particles for which the distances between the particles remain unchanged when it moves. It 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.

Constrained Motion: When a body is confined to move along a certain path.

Unconstrained Motion: When a body has no physical guides to move in and it follows a path determined by its initial motion and by the forces applied to it.

Some Relevant Concepts (Cont.)

Newton’s Laws: Law I: A body remains at rest or continues to move with

uniform velocity if there is no unbalanced force acting on it.

Law II: The acceleration of a body is proportional to the resultant force acting on it and is in the direction of this force (F = ma).

Law III: The forces of action and reaction between interacting bodies are equal in magnitude, opposite in direction, and collinear.

Units & Notation

QuantitySymbolSI UnitUS UnitConversionForm US to SI

Massmkgslug1 slug = 14.594 kg

Lengthlmft1 ft = 0.3048 m

Timetssec------

ForcefNlb1 lb = 4.4482 N

Gravitational acceleration (g) = 9.81 m/s2 = 32.2 ft/s2

ScalarVector

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