Dynamics (동역학)Syllabus and Ch.1

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Syllabus - Course Course Objectives:

To develop a firm understanding of the basic principles of engineering dynamics

• Describing the motion of particles and rigid bodies under accelerating conditions

• Constructing mathematical formulations of dynamics problems To become familiar/proficient in applying these principles to practical

problems.

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Syllabus – Textbook & Grading Policy Textbook

English version: Dynamics, Engineering Mechanics, by Benson H.Tongue, Wiley (2nd edition), 2011

Translated version: 동역학 (Tongue 지음), 최연선, 기창두, 백윤수등 Wiley (2판), 2011

Students need to purchase the either English or translated version based on his/her English skills and experience

Previous versions of the textbook will be also acceptable Be cautious on homework or other assignments

Grading Policy: The following weighting basis will be applied. Two midterm exams: 45% Final exam: 40% Homework: 10% Instructor’s opinion of you as an (dynamics)

engineer: 5%

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SyllabusWeeks Topics Readings1-2 Background & Roadmap,

Motion of Translating BodiesCh.1 & 2

3-4 Inertial Response of Translating Bodies (Newton’s Law Momentum)

Ch.3

5-6 Energetics of Translating Bodies (Energy)

Ch. 4

7-8 Multibody Systems Ch. 59 Midterm week10-11 Kinematics of rigid bodies

(Plane motion)Ch. 6

12-13 Kinetics of rigid bodies(Forces and acceleration)

Ch. 6 & 7

14-15 Kinetics of rigid bodies(Energy and momentum)

Ch. 7

16 Final Week

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Introduction- Overview of Mechanics

Mechanics: The study of how bodies react to force acting on them

Statics: The study of bodies in

equilibrium – Force with no motion

Dynamics: Describing the motion of an object subjected applied forces • Kinematics – concerned with

the geometric aspect of motions

• Kinetics – concerned with the force causing the motion

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What is Dynamics?

Solid Mechanics

Dynamics: Kinetics

Dynamics: Kinematics

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Introduction - Dynamics Kinematics:

describes the motion of bodies without reference to the forces which either cause the motion or result from the motion.

study of the “geometry of motion”. Kinematics is used to relate displacement, velocity, acceleration, and time.

This is a Math. There is no physical laws here. Kinetics:

study of the relations existing between the forces acting on a body, the mass of the body, and the motion of the body.

These relations are in accordance with Newton’s Laws of Motion.

Kinetics is used • To predict the motion caused by given forces, or • To determine the forces required to produce a

given motion, or• Some combination of the above two.

If the rocket accelerates at a certain rate, how can we determine its position and velocity at some instant?

If the engine of the rocket produces a certain amount of thrust (force), how can we determine its position and velocity at some instant?

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What is Dynamics?

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What is Dynamics?

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1.1 Newton’s Laws

Law 1: A body at rest (or moving in a straight line at a particularspeed) will remain at rest (or continue moving in a straight line atthat speed) unless acted on by a nonzero net force.

Law 2: When a body is acted on by a nonzero net force, the netforce is equal to the time rate of change of the body’s linearmomentum. When a force is applied to a body having a constant mass m the

relationship simplifies to F = ma.

Law 3: For every action, there is an equal and opposite reaction. This means if we act on a mass by pushing it, the mass reacts with

a force that is equal in magnitude and opposite in direction.

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Space and Time Space: the environment in

which physical phenomena happen.

Often use a right-handed Cartesian coordinate system to locate points in space (point P).

Time: a scalar variable that allows us to order sequences of events.

Dynamics approach will be understanding the motion of the object over long periods of time. Doing so requires an understanding of what’s going on in a system for lengthy blocks of time, not for simply an instant.

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Force, Mass, and Inertia A force acting on an object is the interaction between that object and

its environment. Forces have magnitude and direction—we use vectors to

mathematically represent forces. The mass of an object is a measure of the amount of matter in it.

Force and mass are primitive concepts, i.e., not explainable using more elementary ideas.

Inertia: a body’s resistance to changing its state of motion in response to the application of a force system. The inertia properties of an object are its mass and a description of how its mass is distributed.

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Vectors and Their Cartesian Representation

Vectors are denoted by an arrow over a letter (or written in bold).

A symbol with no arrow generally denotes a scalar.

Unit vectors are denoted by a “hat” over a letter.

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Cartesian Vector Representation The expression is the position of

P relative to the origin O. When there is no ambiguity, we denote

position by and write

rx and ry are the (scalar) Cartesian components:

For the position of A with respect to Bwe write

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Vector Operations Multiplication by scalar:

Vector addition:

Dot or scalar product:

Cross product: referring to the lower right figure, given vectors the vector

has the direction shown and magnitude

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Units We will use SI units. F = ma, provides for the formulation of a consistent and

unambiguous system of units. Each system has three base dimensions and a fourth

derived dimension.

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Define the following Terms. Mechanics: Dynamics: Kinetics: Kinematics: Force: Equilibrium: Mass: Inertia: Vectors: