PAPER CODE - 101101
BSC PHYSICS (MECHANICS & MECHANICS OF SOLIDS)

CREDIT:5.5

MODULE 1: VECTOR MECHANICS OF PARTICLES
TRANSFORMATION OF SCALARS AND VECTORS UNDER ROTATION TRANSFORMATION; FORCES IN NATURE; NEWTON’S LAWS AND ITS COMPLETENESS IN DESCRIBING PARTICLE MOTION; FORM INVARIANCE OF NEWTON’S SECOND LAW; SOLVING NEWTON’S EQUATIONS OF MOTION IN POLAR COORDINATES; PROBLEMS INCLUDING CONSTRAINTS AND FRICTION; EXTENSION TO CYLINDRICAL AND SPHERICAL COORDINATES; POTENTIAL ENERGY FUNCTION; F = - GRAD V, EQUIPOTENTIAL SURFACES AND MEANING OF GRADIENT; CONSERVATIVE AND NON-CONSERVATIVE FORCES, CURL OF A FORCE FIELD; CENTRAL FORCES; CONSERVATION OF ANGULAR MOMENTUM; ENERGY EQUATION AND ENERGY DIAGRAMS; ELLIPTICAL, PARABOLIC AND HYPERBOLIC ORBITS; KEPLER PROBLEM; APPLICATION: SATELLITE MANOEUVRES; NON- INERTIAL FRAMES OF REFERENCE; ROTATING COORDINATE SYSTEM: FIVE-TERM ACCELERATION FORMULA. CENTRIPETAL AND CORIOLIS ACCELERATIONS; APPLICATIONS: WEATHER SYSTEMS, FOUCAULT PENDULUM; HARMONIC OSCILLATOR; DAMPED HARMONIC MOTION – OVER-DAMPED, CRITICALLY DAMPED AND LIGHTLY-DAMPED OSCILLATORS; FORCED OSCILLATIONS AND RESONANCE.

MODULE 2: PLANAR RIGID BODY MECHANICS
DEFINITION AND MOTION OF A RIGID BODY IN THE PLANE; ROTATION IN THE PLANE; KINEMATICS IN A COORDINATE SYSTEM ROTATING AND TRANSLATING IN THE PLANE; ANGULAR MOMENTUM ABOUT A POINT OF A RIGID BODY IN PLANAR MOTION; EULER’S LAWS OF MOTION, THEIR INDEPENDENCE FROM NEWTON’S LAWS, AND THEIR NECESSITY IN DESCRIBING RIGID BODY MOTION; EXAMPLES. INTRODUCTION TO THREE-DIMENSIONAL RIGID BODY MOTION — ONLY NEED TO HIGHLIGHT THE DISTINCTION FROM TWO-DIMENSIONAL MOTION IN TERMS OF (A) ANGULAR VELOCITY VECTOR, AND ITS RATE OF CHANGE AND (B) MOMENT OF INERTIA TENSOR; THREE-DIMENSIONAL MOTION OF A RIGID BODY WHEREIN ALL POINTS MOVE IN A COPLANAR MANNER: E.G. ROD EXECUTING CONICAL MOTION WITH CENTER OF MASS FIXED — ONLY NEED TO SHOW THAT THIS MOTION LOOKS TWO-DIMENSIONAL BUT IS THREE- DIMENSIONAL, AND TWO-DIMENSIONAL FORMULATION FAILS.

SUGGESTED REFERENCE BOOKS

ENGINEERING MECHANICS, 2ND ED. — MK HARBOLA
INTRODUCTION TO MECHANICS — MK VERMA
AN INTRODUCTION TO MECHANICS — D KLEPPNER& R KOLENKOW
PRINCIPLES OF MECHANICS — JL SYNGE & BA GRIFFITHS
MECHANICS — JP DEN HARTOG
ENGINEERING MECHANICS - DYNAMICS, 7TH ED. - JL MERIAM
MECHANICAL VIBRATIONS — JP DEN HARTOG
THEORY OF VIBRATIONS WITH APPLICATIONS — WT THOMSON

MECHANICS OF SOLIDS
PREREQUISITES: (I) PHYSICS (MECHANICS) ALL MODULES AND (II) MATHEMATICS COURSE
WITH ORDINARY DIERENTIAL EQUATIONS

MODULE 3: STATICS
FREE BODY DIAGRAMS WITH EXAMPLES ON MODELLING OF TYPICAL SUPPORTS AND JOINTS; CONDITION FOR EQUILIBRIUM IN THREE- AND TWO- DIMENSIONS; FRICTION: LIMITING AND NON-LIMITING CASES; FORCEDISPLACEMENT RELATIONSHIP; GEOMETRIC COMPATIBILITY FOR SMALL DEFORMATIONS; ILLUSTRATIONS THROUGH SIMPLE PROBLEMS ON AXIALLY LOADED MEMBERS LIKE TRUSSES.

MODULE 4: MECHANICS OF SOLIDS
CONCEPT OF STRESS AT A POINT; PLANET STRESS: TRANSFORMATION OF STRESSES AT A POINT, PRINCIPAL STRESSES AND MOHR’S CIRCLE; DISPLACEMENT FIELD; CONCEPT OF STRAIN AT A POINT; PLANE STRAIN: TRANSFORMATION OF STRAIN AT A POINT, PRINCIPAL STRAINS AND MOHR’S CIRCLE; STRAIN ROSEOE; DISCUSSION OF EXPERIMENTAL RESULTS ON ONE- DIMENSIONAL MATERIAL BEHAVIOUR; CONCEPTS OF ELASTICITY, PLASTICITY, STRAIN HARDENING, FAILURE (FRACTURE / YIELDING); IDEALIZATION OF ONEDIMENSIONAL STRESS-STRAIN CURVE; GENERALIZED HOOKE’S LAW WITH AND WITHOUT THERMAL STRAINS FOR ISOTROPIC MATERIALS; COMPLETE EQUATIONS OF ELASTICITY; FORCE ANALYSIS — AXIAL FORCE, SHEAR FORCE, BENDING MOMENT AND TWISTING MOMENT DIAGRAMS OF SLENDER MEMBERS (WITHOUT USING SINGULARITY FUNCTIONS); TORSION OF CIRCULAR SHAFTS AND THIN-WALLED TUBES (PLASTIC ANALYSIS AND RECTANGULAR SHAFTS NOT TO BE DISCUSSED); MOMENT CURVATURE RELATIONSHIP FOR PURE BENDING OF BEAMS WITH SYMMETRIC CROSS-SECTION; BENDING STRESS; SHEAR STRESS; CASES OF COMBINED STRESSES; CONCEPT OF STRAIN ENERGY; YIELD CRITERIA; DEFLECTION DUE TO BENDING; INTEGRATION OF THE MOMENT-CURVATURE RELATIONSHIP FOR SIMPLE BOUNDARY CONDITIONS; METHOD OF SUPERPOSITION (WITHOUT USING SINGULARITY FUNCTIONS); STRAIN ENERGY AND COMPLEMENTARY STRAIN ENERGY FOR SIMPLE STRUCTURAL ELEMENTS (I.E. THOSE UNDER AXIAL LOAD, SHEAR FORCE, BENDING MOMENT AND TORSION); CASTIGLIANO’S THEOREMS FOR DEFLECTION ANALYSIS AND INDETERMINATE PROBLEMS.

REFERENCE BOOKS:

AN INTRODUCTION TO THE MECHANICS OF SOLIDS, 2ND ED. WITH SI UNITS — SH CRANDALL, NC DAHL & TJ LARDNER
ENGINEERING MECHANICS: STATICS, 7TH ED. — JL MERIAM
ENGINEERING MECHANICS OF SOLIDS — EP POPOV