Table of Contents

Chapter 1: VECTORS • Introduction • Scalar or dot product • Vector or cross product • Examples of scalar and vector products in physics • Multiple products • Vector derivatives • Scalar and vector fields • The gradient of scalar field • The concept of divergence and Gauss’s theorem • Green’s theorem in the plane • The curl of a vector field and stokes theorem • Successive applications of the operator • Curvilinear coordinates • Applications to hydrodynamics • The equation of heat flow in solids • The gravitational potential

Chapter 2: PHYSICAL FUNDAMENTALS OF MECHANICS • Introduction • Frame of reference and coordinate systems • Newton’s laws of motion • Space-time symmetry • Galileo’s principle of relativity and Galilean transformations • Fundamental interactions in nature • Elastic forces • Friction forces

Chapter 3: NON-INERTIAL FRAMES • Non-inertial frames • Reference frame with translational acceleration and fictitious or pseudo or inertial force • Coriolis and centrifugal forces • Motion relative to the earth • Equation of motion and deviation of freely falling bodies on earth • Effect of coriolis force on nuclear and molecular motion • Satellite motion

Chapter 4: CONSERVATION LAWS • Introduction • Law of conservation of mass • Conservation of energy • Work-energy theorem • Conservative forces • Potential energy • Rectilinear motion under conservative force • Non-conservative forces • Principle of conservation of momentum • Centre of mass (or centre of inertia) • Collisions • Collision in centre of mass frame • Relations between scattering angles in Lab and CM frames • Kinetic energy in collision • Systems with variable mass • Angular momentum (or moment of momentum) • Angular momentum of a system of particles or an extended system • Angular momentum of two particles relative to their C.M. or C-Frame • Law of conservation of angular momentum • Angular momentum of the extended system about an arbitrary point • Rutherford Scattering: Scattering of charged particles by heavy nuclei

Chapter 5: DYNAMICS OF RIGID BODIES • Introduction • Moment of inertia • Theorems of moment of inertia • Calculation of moment of inertia • Energy of a rotating rigid body • Gyroscopes • Spin precession in constant magnetic field • Fly wheel • Angular momentum in quantum mechanics • Molecular rotations

Chapter 6: MOTION UNDER CENTRAL FORCES: THE UNIVERSAL GRAVITATION • Introduction • Nature of central forces • Motion under central force • Newton’s law of universal gravitation • Inertial and gravitational mass • Motion in gravitational field (Inverse square law field) • Kepler’s laws • Rutherford scattering • Gravitational field and potential • Three particles system • Inter-planetary flights • Binary stars • Gravitation and intermolecular forces • Gravitational red shift

Chapter 7: ELASTIC PROPERTIES OF MATTER • Introduction • Some definitions • Different types of co-efficients of elasticity • Theorems on stress and strain • Relations between elastic constants • Bending of beams • The cantilever-depression of its loaded end • Transverse vibration of a cantilever • Beam supported at both ends and loaded in the middle • Torsion of a cylinder • Torsional oscillations • Determination of elastic constants • Origin of elastic forces • Determination of Y by bending • Determination of Poisson’s ratio of rubber • Engineering materials

Chapter 8: FLUID MECHANICS • Introduction • Properties of fluids • Archimedes’ principle • Euler’s equation of motion for a moving fluid • Torricelli’s theorem: Speed of efflux of a fluid from a large vessel • Irrotational continuous flow of inviscid fluids • The continuity equation • Bernoulli’s equation: Steady flow of fluids • Venturimeter • Laminar and turbulent flows • Coefficient of viscosity • Limiting or terminal velocity • Reynolds’ number • Flow of a liquid in a round pipe: Poiseuille’s formula • Lift

Chapter 9: SURFACE TENSION • Introduction • Surface tension • Molecular theory of surface tension • Surface energy • Shape of liquid drops • shape of liquid in contact with a solid • Angle of contact • Equilibrium of a liquid drop on a solid surface • Equilibrium of liquid drop resting on the surface of another liquid • Determination of angle of contact and surface tension by Quincke’s drop method • Pressure Difference Across a curved Surface • Expression for excess of pressure on the curved surface • Excess pressure inside a spherical drop and buble • Excess pressure inside an air bubble in a liquid • Excess pressure inside an air bubble in a liquid • Surface tension of soap solution • Water film between two glass plates • Capillary Action (capillarity) • Determination of surface tension • Variation in surface tension • Saturation vapour pressure and shape of meniscus

Chapter 10: OSCILLATORY MOTION • Introduction • Oscillations in a potential well • Simple harmonic motion (SHM) • Some examples of free vibrations • Superposition of two simple harmonic motions • Superposition of mutually perpendicular two SHMs • Coupled oscillators • Anharmonic oscillations • Damped oscillations • Power dissipation in damping oscillations • Auto-oscIllations • Forced oscillations • Fourier Analysis of periodic motion

Chapter 11: FUNDAMENTALS OF ANALYTICAL MECHANICS • Introduction • Generalized coordinates • Lagrangian-hamilton’s variation principle • Hamiltonian formalism

Chapter 12: NON-LINEAR OSCILLATIONS, CHAOS AND FRACTALS • Introduction • Singular points of trajectories • Non-linear oscillations • Chaos • Logistic map • Fractals

Chapter 13: RELATIVISTIC MECHANICS • Introduction • Inertial frames of reference • Galilean transformations • Velocity of light • The search for the ether • Michelson-Morley experiment • Lorentz and Fitzgerald hypothesis • Einstein’s special theory of relativity • Lorentz transformations • Proper frame, proper length and proper time • Experimental verification of time dilation • Relativistic velocity transformation equations • Relativity of mass • Mass-energy equivalence • Relation between momentum and energy • Particles with zero rest mass • Speed limit for material particles • Space and time in relativity • Four-vector notation • The velocity four vector • The momentum four-vector • The four-force vector • Electromagnetic interaction • The current density `Four-Vector’ • Aberration of light from stars • The relativistic doppler effect

Chapter 14: QUANTUM MECHANICS • Introduction • Wave equation • Fundamental postulates of quantum mechanics • Important theorems relating to basic postulates • Operators • Eigen functions and eigen values of operators • Operator for momentum • Importance of hamiltonian operator • Operator for angular momentum • Rules for setting up a quantum mechanical operators • Complete set of eigen functions • Completeness relation • Hermitian operators • Adjoint of an operator • Simultaneous measurement and commuting operators • Equation of motion for operators • Unitary operators • Degeneracy • Forbidden transitions • Particle in a potential well (one-dimensional box) • Potential barrier • Emission of a-particles from a radioactive element • Particle in a rectangular three-dimensional box • Relativistic wave equation • Dirac equation (for a free particle)

About the Author

Professor Dr S.L. Kakani, M.Sc (Phys.), Ph.D., former Executive Director, Institute of Technology and Management, Bhilwara, is an internationally renowned physicist and has had a distinguished career spanning more than four decades of teaching, research and administration. He has authored several standard books. His two research monographs on superconductivity have been published by NOVA Science, New York, and recently four of his books have also been published by Anshan Ltd., UK. He has authored a large number of research papers in the fields of superconductivity, nanomaterials, condensed matter physics, material science, etc. He has supervised Ph.D. theses in the field of superconductivity and thin films. Prof Kakani served as the Chairman, BOS and Research Board, MDS University, Ajmer. He is Visiting Professor at several prestigious institutions. He has received several national and international awards and honours for his outstanding academic contributions and achievements. He is life member of IAPT, Vigyan Parishad and Hith-T update.

Dr C. Hemrajani, Head (Retd.), Physics Department, MLV Government PG College, Bhilwara. A Ph.D. from MDS University, Ajmer, he is the co-author of several UG and PG textbooks. He has put in thirty-six years of service teaching Physics right from UG to PG.

Dr Mrs. Shubhra Kakani, M.Sc. (Phys.), Ph.D., received her M.Sc. in Physics and Ph.D from MDS University, Ajmer. She has co-authored more than nine books: Problems on Advanced Quantum Physics, Thermal Physics, Superconductivity, Modern Physics, Nuclear and Particle Physics, Mechanics, Engineering Physics, A Textbook of Engineering Physics and ICSE Physics. Presently, she is pursuing post-doctoral research.