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Dynamics MDB 2043

Introduction to Dynamics

May 2016 Semester

Lesson Outcomes

At the end of this lecture you should be able to:

Identify classifications of dynamics

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Why Dynamics So Important?

Statics VS. Dynamics

Bodies at RESTor in equilibrium

Bodies in MOTION

Dynamics of

Solid Bodies

Dynamics of

Gasses/Air

Dynamics of

Liquids

e.g. Hydrodynamicse.g. Robotics

e.g. Aerodynamics

Introduction

Mechanics

Mechanics: The action and effects of forces on bodies

Statics

Dynamics

Bodies at rest, or in equilibrium

Bodies in motion, or out of equilibrium

In Equilibrium Be static or move with constant velocity

v=0 mv=0.2 m/s

m

Static Move with v=constant

Out of Equilibrium Accelerate with the change of velocity

θ

a=0.5 m/s2m

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Dynamics

Kinematics

Kinetics

Study of motion without reference to the forces producing motion: Relations applied only between position, velocity, acceleration and time

Relation between unbalanced forces and the change in motion they produce

A

B

va

Kinematics: e.g. Motion of rocket from position A to B

Kinetics:e.g. Motion of pendulum

ball applied by F

F

θ

Kinematics: how fast, how far and how long

the motion takes

Kinetics: What forces were involved to

produce the motion?

- Weight- Friction- Tension- Spring Force- Support Force

How about the resulting acceleration?

Basic Concepts

Particles: - a body of negligible dimensions- a body with dimensions irrelevant to the motion or

the action of forces upon it

A

B

A

BEquivalent Particle

= Rigid Body: - important overall dimensions of the body or changes

in position of the body - negligible deformation (change in shape) of the body

Flexible Body: - deformed body under loads - beyond the scope of this course

Negligible spring deformation

=Rigid body

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Newton’s Laws of Motion

These are fundamental laws relating forces and motion.

Law I. A particle remains at rest or continues to move in a straight line with a constant velocity if there is no unbalanced force acting on it.

Sir Isaac Newton(1643-1727)

Law II. The acceleration of a particle is proportional to the resultant force acting on it and is in the direction of this force.

∑F=0 In equilibrium

∑F=ma Out of equilibrium

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

F= F'F F'

Laws I and II are strictly true only in an absolute frame of reference (i.e. A particle does not accelerate for Law I and does not rotate for Law II)

Law II (Most commonly used in dynamics)

∑F=ma

Where ∑F: resultant force acting on a body (vector)

m: mass of the body (scalar)

a: the resulting acceleration of the body (vector)

∑F

m=∑F=F1+F2+F3+F4+…..Fn-1+Fn=ma

F1Fn

F2

F3F4

Fn-1

m

This equation relates applied forces (∑F) to the motion of a body (a).

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Motion can be constrained (forced to follow a specific path: e.g. car trip, train

on tracks)

or unconstrained (can move in any direction: e.g. aircraft flight path, trajectory

of a ball after it is thrown)

Tennis Ball BouncingUnconstrained Motion

Train Running on TracksConstrained Motion

2-D Coordinate Systems to Describe Motion:

• Rectangular coordinate (x, y)

• Polar coordinate (r,θ)

• Normal (perpendicular) and Tangent (along the path) coordinates

y P

x

r

θ

t

n

An Overview of Mechanics

Statics: The study of bodies in equilibrium.

Dynamics:1. Kinematics – concerned with the geometric aspects of motion2. Kinetics - concerned with the forces causing the motion

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

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Kinematics & Kinetics

Kinematics study of geometrical aspect of motion

Parameters: position, distance, speed velocity & acceleration (linear or

angular).

Kinetics study of force or torque driving or generated by the motion

Parameters: force, torque, impulse, momentum, work, energy.

Dynamics = Kinematics + Kinetics

Particle vs Rigid Body Dynamics

Dynamics of Particles

Dynamics of Rigid Bodies

Rotation of the bodyabout its centre ofmass is neglected

Rotation of a bodyabout its centre ofmass is accountedfor.

Only the mass isconsidered. Thesize and shape ofthe body areignored.

Besides its mass, thebody size and shape areconsidered in analysingits motion

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Rectilinear vs Curvilinear Motion

Rectilinear Motion

Planar Motion

Motion along a straight line (1-

D)

Motion within a

plane (2-D).

Spatial Motion

Motion within a volume (3-

D)

Curvilinear Motion

Tips for solving dynamics problems

1. Read the problem carefully and try to correlate the actual physical situation with the theory you have studied.

2. Draw any necessary diagrams and tabulate the problem data.

3. Establish a coordinate system and apply the relevant principles, generally in mathematical form.

4. Solve the necessary equations algebraically as far as practical; then, use a consistent set of units and complete the solution numerically. Report the answer with no more significant figures than the accuracy of the given data.

5. Study the answer using technical judgment and common sense to determine whether or not it seems reasonable.

6. Once the solution has been completed, review the problem. Try to think of other ways of obtaining the same solution

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References:

R.C. Hibbeler, Engineering Mechanics: Dynamics, SI 13th Edition, Prentice-Hall, 2012.