Classical Mechanics, Volume 5: Conservation Laws and Rotational Motion

159 Pages·2019·30.967 MB·English

by  Gregory A. DiLisi

Classical Mechanics, Volume 5
Conservation laws and rotational motion

Classical Mechanics, Volume 5
Conservation laws and rotational motion
Gregory A DiLisi
John Carroll University, University Heights, Ohio, USA
Morgan & Claypool Publishers
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ISBN 978-1-64327-398-3(ebook)
ISBN 978-1-64327-395-2(print)
ISBN 978-1-64327-396-9(mobi)
DOI 10.1088/2053-2571/ab1cb2
Version:20190801
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 x
Author biography xv
Part I Conservation laws
1 Motivation 1-1
2 Getting ready 2-1
2.1 Anticipatory set 2-1
2.2 Objective 2-4
2.3 Purpose 2-4
3 Giving information 3-1
3.1 Instructional input 3-1
3.1.1 Multiplying vectors by scalars 3-1
3.1.2 Multiplying vectors by vectors: the vector ‘dot’-product 3-2
3.2 Modeling 3-4
3.3 Instructional input 3-7
3.3.1 Work or energy 3-7
3.4 Modeling 3-10
3.5 Instructional input 3-12
3.5.1 Work done by a non-constant force 3-12
3.5.2 The ‘work-energy theorem’ or the ‘law of 3-13
conservation of energy’
3.6 Modeling 3-19
3.7 Checking for understanding 3-23
3.8 Instructional input 3-27
3.8.1 Linear momentum 3-27
3.8.2 The ‘law of conservation of momentum’ 3-30
3.9 Modeling 3-35
3.10 Checking for understanding 3-40
3.10.1 What if an object’s mass changes? 3-40
vii
ClassicalMechanics,Volume5
4 Keeping information 4-1
4.1 Closure 4-1
4.1.1 LCE and LCP 4-1
4.2 Independent practice 4-6
4.2.1 The law of conservation of energy 4-6
4.3 Independent practice 4-10
4.3.1 The law of conservation of momentum 4-10
4.4 Peer teaching 4-11
4.4.1 Gravitational potential energy 4-12
4.4.2 Work done by ‘other’ forces 4-12
Part II Rotational motion
5 Motivation 5-1
6 Getting ready 6-1
6.1 Anticipatory set 6-1
6.2 Objective 6-2
6.3 Purpose 6-3
7 Giving information 7-1
7.1 Instructional input 7-1
7.1.1 The Center-of-Mass 7-1
7.2 Modeling 7-8
7.3 Checking for understanding 7-10
7.3.1 Where is the human body’s Center-of-Mass? 7-10
7.4 Instructional input 7-15
7.4.1 The moment of inertia about an axis of rotation 7-15
7.5 Modeling 7-20
7.6 Instructional input 7-23
7.6.1 Multiplying vectors by vectors: the vector ‘cross’-product 7-23
7.6.2 Representing vectors ‘out of’ and ‘into’ this book 7-26
7.7 Modeling 7-30
7.8 Checking for understanding 7-33
7.8.1 All vector operations 7-33
viii
ClassicalMechanics,Volume5
7.9 Instructional input 7-35
7.9.1 Torque 7-35
7.10 Modeling 7-40
7.11 Instructional input 7-44
7.11.1 Angular displacement 7-44
7.11.2 Linear-to-angular transformations 7-46
7.12 Checking for understanding 7-51
7.13 Modeling 7-56
8 Keeping information 8-1
8.1 Closure 8-1
8.2 Independent practice 8-4
8.2.1 The Center-of-Mass 8-4
8.2.2 Moment of Inertia 8-7
8.2.3 Torque 8-7
8.2.4 Rotational motion 8-9
ix