Table Of ContentM. Movnin, A. Izrayelit
LL
AASS
CC
CC
II
II
NN
TT
AA
EE
RRHH
w
o
OOCC sc
o
M
EEEE
s
r
e
h
HHMM s
i
l
b
u
P
TT
r
i
M
M. MOVNIN, A. IZRAYELIT
Theoretical Mechanics
Translated from the Russian by M. Konyaeva
Mir Publishers • Moscow 1970
UDC 531.01 (075.3) =20
Ha ansAuucKOM sabuce
FROM THE AUTHORS
The new international system of units (SI) is used through
out the text. However, taking into account that the engi
neers’ system (mkgfs) still finds wide use, the units of this
system are also given. Moreover, wherever necessary the rela
tions are indicated between the units of the international and
engineers’ systems. Normative and design data are given in
both systems of units.
In the presentation of the material primary emphasis is
placed on the practical significance of conclusions.
To gain a better understanding of theoretical propositions,
the solutions of sample problems are given. All solutions
are first carried out in algebraic form and then numerical data
are substituted.
Although the book is mainly intended for full-time vocatio
nal schools, the large number of detailed and specially selec
ted examples makes it handy for their evening and correspon
dence departments as well.
CONTENTS
From the Authors..................................................... 5
Notation......................................................................... 12
Introduction ................................................................. 15
Part 1. Statics
Chapter I. Basic Definitions and Axioms of Statics 17
1. Fundamentals ............................................................. 17
2. Axioms of Statics ....................................................... 22
3. Constraints and Their Reactions. Axioms of
Constraints ................................................................. 25
Chapter II. Systems of Concurrent Forces in a Plane................ 28
4. Analytic Determination of the Resultant of Two
Forces Applied at the Same P oint........................ 28
5. Resolution of a Force into Two Components Ap
plied at the Same Point ......................................... 30
6. Addition of Concurrent Forces in a Plane. Force
Polygon......................................................................... 32
7. Projection of a Force on an A x is............................ 33
8. Projection of a Vector Sum on an A x is..................... 36
9. Analytic Determination of the Resultant of a Sys
tem of Concurrent Forces (Method of Projections) 37
10. Conditions and Equations of Equilibrium for a Sys
tem of Concurrent Forces......................................... 39
11. Procedure for Solving Equilibrium Problems . . 40
12. Theorem of Concurrence of Three Mutually
Balanced Non-Parallel Forces ................................. 49
Chapter III. Couple......................................................................... 52
13. Addition of Two Parallel Forces of the Same Sense 52
14. Addition of Two Parallel Forces of Opposite Sense 53
15. Moment of a Couple................................................. 56
16. Equivalence of Couples. Translation of a Couple
in Its Plane of A ction............................................ 58
17. Theorem of Equivalent Couples......................... . 60
18. Addition of Couples Acting in the Same Plane . 61
8 CONTENTS
Chapter IV. Two-Dimensional Systems of Arbitrarily Located
Forces ......................................................................... 65
19. Moment of a Force About a P oint........................ 65
20. Equilibrium of a Lever . 67
21. Reduction of a Force to a Given Point . . . . 69
22. Reduction of a Two-Dimensional Force System to
a Given P oint............................................................. 70
23. Resultant of a Two-Dimensional Force System . . 72
24. Theorem of the Moment of a Resultant (Varignon’s
Theorem) ................................................................. 73
25. A Case of the Reduction of a Two-Dimensional
Force System to a Couple........................................ 79
26. Conditions and Equations of Equilibrium for
a Two-Dimensional Force System .................... 80
27. Three Forms of Equilibrium Equations................ 82
28. Supporting Devices of Beam System s................ 85
29. Classification of Loads............................................ 88
30. Practical Solution of Equilibrium Problems
for Two-Dimensional Force System s.................... 89
31. Equilibrium of a System of Connected Bodies . . 101
Chapter V. Friction......................................................................... 106
32. Types of Friction......................................................... 106
33. The Laws of Sliding Friction.................... 107
34. Angle and Cone of Friction........................................ 109
35. Experimental Determination of Coefficients of
Friction ..................................................................... 114
36. The Laws of Rolling Friction................................ 116
Chapter VI. Three-Dimensional Force Systems 120
37. Force Parallelepiped .................................................... 120
38. Equilibrium of a System of Concurrent Forces in
Space ......................................................................... 121
39. Moment of a Force About an Axis ........................ 123
40. Equilibrium of an Arbitrary Three-Dimensional
Force System ............................ 128
Chapter VII. Centroids and Centres of Gravity........................ 134
41. Centre of Parallel Forces......................................... 134
42. Co-ordinates of the Centre of Parallel Forces 135
43. Centroid of a Volume ............................................. 139
44. Centroid of an Area. Static Moments of an Area 141
45. Centroid of a L in e.................................................... 147
46. Stability of Equilibrium ......................................... 147
Part 2. Kinematics
Chapter VIII. Fundamentals.................... 154
47. Subject of Kinematics ............................................ 154
48. Space and Time ......................................................... 155
CONTENTS 9
49. Basic Definitions ..................................................... 156
V
Chapter IX. Kinematics of Particles#........................................ 160
50. Methods of Specifying the Motion of a Particle 160
51. Velocity of a Particle ............................................. 162
52. Acceleration of a Particle .................................... 167
53. Types of Motion of a Particle as Related to Acce
leration ................................ 174
54. Uniformly Variable Motion of a Particle . . . . 176
55. Kinematic Graphs and Relationship Between Them 180
Chapter X. Simple Motions of Rigid Bodies ........................ 185
56. Translation of a Rigid B od y.................... 185
57. Rotation of a Rigid Body About a Fixed Axis . . 186
58. Velocities and Accelerations of Points of a Rotating
Body ............................................................................. 191
Chapter XI. Methods of Transmission of Rotary Motion 198
59. Classification of Transmission Mechanisms . . . 198
60. Gear Ratio ................................................................ 198
61. Cylinder Friction Drives ........................................ 200
62. Face Friction D rives.................................... 202
63. Cone Friction Drives ............................................ 203
64. Belt Drives: Fundamental Concepts ............. 205
65. Gear Drives: General Considerations ............ 206
66. Gear Ratio of a Spur Gear D rive................ 207
67. Gear Trains.................................................... 208
68. Worm Gearing ........................................................ 212
Chapter XII. Complex Motion of Particles............................ 216
69. Base, Relative and Absolute M otions................ 216
70. Theorems on Addition of the Velocities and
Accelerations of a Particle in Complex Motion 219
Chapter XIII. Plane M otion......................................................... 225
71. Concept of Plane Motion of a Rigid Body . . . 225
72. Determination of the Velocity of Any Point of a
Body in Plane Motion ............................................. 226
73. Instantaneous Centre of Zero Velocity . . . . 228
74. Determination of the Acceleration of Any Point of
a Body in Plane M otion........................................ 240
75. Planetary Gearing ................................................ 244
76. Differential Gearing ............................................. 247
Part 3. Dynamics
Chapter XIV. Basic Concepts and Axioms of Dynamics 251
77. Subject of Dynamics 251
78. Principle of Inertia 252
10 CONTENTS
79. Fundamental Law of Dynamics of Particles 252
80. Systems of Units .................................................... 254
81. Axiom of Superposition .................................... 256
82. Axiom of Interaction ............................................ 258
83. Two Basic Problems of Dynamics........................ 259
Chapter XV. Motion of Particles. Method of Kinetostatics 268
84. Ideal and Real Constraints ................................ 268
85. D’Alembert’s Principle ........................................ 269
86. Inertia Force for a Particle in Rectilinear Motion 271
87. Inertia Force for a Particle in Curvilinear Motion 271
88. Inertia Force for a Rigid B ody............................ 274
89. Solution of Problems by the Method of Kineto
statics ......................................................................... 275
Chapter XVI. Work and Power..................................................... 280
90. Work of a Constant Force in Rectilinear Motion 280
91. Work of a Variable Force in Curvilinear Motion 282
92. Work of a Resultant Force.................................... 283
93. Work of a Force of Gravity................................. 285
94. Work of an Elastic Force.................................... 286
95. Concept of Mechanical Efficiency........................ 289
96. Efficiency of a System of Mechanisms Connected in
Series ......................................................................... 290
97. Efficiency of a System of Mechanisms Connected
in Parallel................................................................ 291
98. Power ......................................................................... 296
99. Work and Efficiency for Bodies Sliding Along
an Inclined Plane............................................ 298
100. Work and Power in Rotation................................ 306
101. Work in Rolling M otion........................................ 308
Chapter XVII. The Laws of Dynamics.................................... 315
102. Concept of a System of Particles............................ 315
103. Law of Momentum for a Particle .................... 317
104. Law of Momentum for a System of Particles . . 322
105. Potential and Kinetic Energy ............................ 324
106. Kinetic Energy of a Body in Various Types of
Motion......................................................................... 325
107. Moments of Inertia of Homogeneous Bodies of
Simple Shape ............................................................. 327
108. Law of Kinetic Energy for a Particle................ 330
109. Law of Kinetic Energy for a System of Particles 333
110. Fundamental Equation of Dynamics for a Rigid
Body in Rotation ................................................ 338
Chapter XVIII. Application of the Laws of Kinematics and
Dynamics to the Analysis to Mechanisms 345
111. Principles and Definitions.................................... 345
112. Fundamentals of Kinematics of Mechanisms . . 350
