I. V. NIESHCHERSKY
COLLECTION OF PROBLEMS
IN THEORETICAL
MECHANICS
Edited
by Professor A. I LURIE,
Dr. Tech. Sc.
The Supplement is written
by V I. KUZNETSOV,
Cand. Tech. Sc.
me moman scnoor punusnmo House
Moscow
Translated from the Russian
by
N. M. SINELNIKOVA
Printed in the Union of Soviet Sobalist Republics
CONTENTS
Editor’s note 5
Preface. 7
Part I. Statics of Rigid Bodies
1. Coplanar Force System
1. Collinear Forces 9
2. Concurrent Forces 10
3. Parallel Forces and Couples 19
4. Arbitrary Coplanar Force Systems 26
5. Graphical Statics. 40
11. Statics in Space
6. Concurrent Forces . . . 43
7. Reduction of a System of Forces to Its Simplest Possible Form 47
8. Equilibrium of an Arbitrary System of Forces 48
9. Centre of Gravity 56
Part I1. Kinematics
III. Motion of a Particle
10. Equation of Motion and Path of a Particle 59
ll. Velocity of a Particle . 61
12. Acceleration of a Particle 63
IV. Simplest Motions of a Rigid Body
13. Rotation of a Rigid Body about a Fixed Axis 68
14. Conversion of Simplest Motions of a Rigid Body 70
V. Composition and Resolution of Motions of a Particle
15. Equations of Motion and Path of the Resultant Motion of a Particle 74
16. Composition oi Velocities of a Particle . . . . . 76
17. Composition of Accelerations of a Particle Undergoing Translatory
Motion of Transport . . . . . . 79
18. Composition of Accelerations of a Particle Performing Rotational
Motion of Transport about a Fixed Axis 82
VI. A Rigid Body Motion in a Plane
19. Equations oi Motion of a Body and Its Particles in a Plane . 87
20. Velocity of a Point of a Body Which Performs Motions in a Plane.
Instantaneous Centres of Velocities 89
21. Space and Body Centrodes . . . . 96
22. Accelerations of a Point on a Body Which Performs Motions in
a Plane. Instantaneous Centres of Accelerations 99
23. Composition of Motions of a Body in a Plane 102
VII. Motion of a Rigid Body about a Fixed Point
24. Rotation of a Rigid Body about a Fixed Point . 10525. Composition of Rotations of a Rigid Body about Intersecting Axes l07‘
3
PREFACE
This book is an abridged translation of the latest (28th) Russian edition of Meshchersky’s Collection of Problems in Theoretical Mechanics, published in the USSR in 1962.
This Collection was compiled by a large group of Soviet professors and highly experienced instructors of the Leningrad Politechnical Institute, named after M. I. Kalinin, among whom are
S. A. Sorokov (statics), N. N. Naugolnaya and A. S. Kelson
(kinematics), A. S. Kelson (dynamics of a particle), M. I. Baty
(dynamics of a system), G. J. Djanelidze (analytical statics, dynamics of bodies having variable masses, stability of motion).
Professor A. 1. Lurie, Dr. Tech. Sc. a prominent Soviet scientist, is the general editor of this book.
The first Collection of Problems, edited by I. V. Meshchersky,
was published in 1914. With every new edition the book has been
revised and supplemented taking into consideration the developments in science and engineering for the past period.
The present edition embraces all basic principles of theoretical
mechanics usually taught during the first two years of studies in
higher and secondary technical schools.
The material in this book is presented consistently, i. e., proceeding from the particular to the general. The same method is
applied to the order of paragraphs and the arrangement of the
text. Accordingly, the initial section of the book deals with fairly
easy problems on basic concepts_ and principles of statics of rigid
bodies, while the last section of the book embraces rather complicated problems on principles of stability of motion.
It should be noted that most of the problems, chosen for this
collection, are not only an illustration of the theoretical material,
but are well in accord with the materials which serve as a bridge
between theoretical mechanics and intermediate sciences.
The primary objective of the book was to present to the reader
problems of practical value by giving the examples in such fields
as the operation of machines and mechanisms, hydrodynamics,
resistance of materials, and other branches of science and engineering. All this has made the book widely popular among the
Soviet students of technical schools.
7
The book Collection of Problems in Theoretical Mechanics is
at present one of the basic text—books for Soviet students of
theoretical mechanics.
The material collected in this book will aid students in the
practical application oi laws and methods of theoretical mechanics
in their engineering practice.
The present translation of the Collection of Problems is supplemented with solutions of certain typical problems for each paragraph to help the student to apply to specific situations the principles and theorems that he has learned.
The book is well illustrated with drawings and diagrams.