Classical Mechanics, Volume 3: Newton's Laws and Uniform Circular Motion

125 Pages·2019·40.203 MB·English

by  Gregory A. DiLisi

Classical Mechanics, Volume 3
Newton’s laws and uniform circular motion

Classical Mechanics, Volume 3
Newton’s laws and uniform circular motion
Gregory A DiLisi
John Carroll University, University Heights, Ohio, USA
Morgan & Claypool Publishers
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ISBN 978-1-64327-314-3(ebook)
ISBN 978-1-64327-311-2(print)
ISBN 978-1-64327-312-9(mobi)
DOI 10.1088/2053-2571/ab1894
Version:20190701
IOPConcisePhysics
ISSN2053-2571(online)
ISSN2054-7307(print)
AMorgan&ClaypoolpublicationaspartofIOPConcisePhysics
PublishedbyMorgan&ClaypoolPublishers,1210FifthAvenue,Suite250,SanRafael,CA,
94901,USA
IOPPublishing,TempleCircus,TempleWay,BristolBS16HG,UK
This book is dedicated to my family:
to my grandparents, Tommaso and Carmela Frate,
to my parents, Richard and Mary DiLisi,
to my siblings, Rick DiLisi, Carla Solomon, and Jennifer Newton,
to my wife, Linda,
to my daughter, Carmela,
and
to the wonderful creatures who inhabit our home.

Contents
Preface ix
Author biography xiv
Part I Newton’s laws of motion
1 Motivation 1-1
2 Getting ready 2-1
2.1 Anticipatory set 2-1
2.1.1 Who should (or should not) use the product 2-2
2.1.2 How should the product be used 2-2
2.1.3 What problems should users expect to encounter 2-2
2.2 Objective 2-3
2.3 Purpose 2-3
3 Giving information 3-1
3.1 Instructional input 3-1
3.1.1 Newton’s first law of motion 3-3
3.1.2 Newton’s second law of motion 3-11
3.1.3 Newton’s third law of motion 3-15
3.1.4 Problem-solving 3-20
3.1.5 Category #1: applied forces 3-20
3.1.6 Category #2: contact forces 3-28
3.1.7 Category #3: field forces 3-31
3.2 Modeling 3-38
3.3 Checking for understanding 3-51
4 Keeping information 4-1
4.1 Closure 4-1
4.2 Independent practice 4-3
4.2.1 Challenge problems 4-6
4.3 Peer teaching 4-8
4.3.1 General laws 4-8
4.3.2 Forces: Tension 4-9
vii
ClassicalMechanics,Volume3
4.3.3 Forces: Spring Force 4-9
4.3.4 Forces: Frictional Force 4-9
4.3.5 Axes 4-9
4.3.6 Solving 4-10
Part II Uniform circular motion
5 Motivation 5-1
6 Getting ready 6-1
6.1 Anticipatory set 6-1
6.2 Objective 6-4
6.3 Purpose 6-4
7 Giving information 7-1
7.1 Instructional input 7-1
7.1.1 What is ‘uniform’ about ‘uniform circular motion’? 7-1
7.1.2 Acceleration during uniform circular motion 7-6
7.1.3 Putting it all together 7-12
7.2 Modeling 7-13
7.3 Checking for understanding 7-17
8 Keeping information 8-1
8.1 Closure 8-1
8.2 Independent practice 8-2
8.3 Peer teaching 8-3
8.3.1 Centripetal acceleration 8-4
8.3.2 Newton’s laws of motion 8-4
viii
Preface
We derive the word ‘physics’ from the Greek word ‘physika,’ which translates into
‘pertainingtonaturalthings.’Therefore,aswebeginourstudyof‘physics,’wequite
literally begin our study of ‘natural things.’ When I was in high school, my physics
teacher, Mr Lamovsky, once asked me: ‘Who is the greatest physicist? Newton?
Einstein?Galileo?’Ithoughtforamomentandgavehimananswerthatabsolutely
flooredhim.‘Batman,’Isaid,‘becausehisentirelifeisdedicatedtofiguring-outhow
and why things move … grapplings, cables, levers, cars, projectiles, etc.’
In short, that’s what this book is about—figuring out how and why things move.
Instead of viewing physics as the study of ‘natural things’ (from its literal Greek
translation), a good way to view physics is to simply think of it as the study of
motion. In fact, Albert Einstein once said: ‘Nothing happens until something
moves.’ Think about it … you cannot generate a thought without some electrical
signalmovinginyourbrain.Evenyouremotionsinvolvethecomplexmovementof
chemical and electrical signals throughout your body. I think we can all agree with
Einstein that indeed nothing happens until something moves! Pay careful attention
and you will notice that every problem you will encounter in this book involves
somethingmoving.Therefore,thegoalofanygoodphysicsbookisquitesimple:to
develop problem-solving techniques that handle different types of motion. The
situations we encounter in everyday life vary considerably and so our problem-
solvingtechniques mustvaryaccordingly.Wewill discoverthatthe techniquesthat
defeat the Joker may not work well on the Riddler or Penguin. Therefore, we will
developanentirearsenalofproblem-solvingtactics—allofwhicharemeanttohelp
us understand the behavior or movement of objects in motion!
Before developing these problem-solving techniques, I will describe how I
designed thisseriesofbooksandhowtheycametobecreated.First,Iwilldescribe
the structure and topics covered in a typical introductory physics sequence of
courses. This overarching structure will provide the context for which these texts
were designed. Next, I will describe the format of how each topic is presented. The
formatwilldemonstratehoweachsectioniswrittenandhoweachtopicinthetextis
arranged.Finally,Iwillmorethoroughlydescribetheoverallpurposeoftheseriesof
books.
1. Structure of the typical introductory physics sequence of classes: The intro-
ductory physics sequence of classes is typically divided into three distinct
courses. This series of books focuses on only the first course, ‘Classical
Mechanics.’ However, the distinctions among these three courses are useful
to see because they frame the context under which ‘Classical Mechanics’ is
housed. The distinctions among these three courses are briefly described
below:
1. ‘Classical Mechanics’—The term ‘Classical Mechanics’ describes the
motion or behavior of objects whose dimensions and/or speeds are
familiar to all of us. The objects we examine must have mass. Your
intuition from everyday experiences will be generally correct because,
ix