Unit 1

Rigid body dynamics: Review of rotational motion with fixed axis, moment of inertia, parallel and perpendicular axis theorems; combined rotations and translations – collisions involving combined translation and rotation of rigid bodies with fixed axis of rotation. [4]
Rotation of a rigid body about arbitrary axis, angular displacements, angular velocity vector, angular momentum, principal axes and moments of inertia, rotational kinetic energy; rate of change of a vector quantity in a rotating frame; Euler equation, torque-free motion of a symmetric body, gyroscope, precession of equinoxes. [5] (Refs.1, 2)

Unit 2

Accelerated frames: Linearly accelerated systems, pseudo-forces, tilted pendulum and fluid levels; rotating coordinate systems: velocity and acceleration, pseudo forces: centrifugal, Coriolis and Euler forces, forces on a bug moving on a rotating platform, weather systems and Foucault pendulum. [5] (Ref.1,2)

Elements of solid mechanics: the concept of an elastic body, internal forces – longitudinal (tension, compression) and shear stresses; deformations and strains, Hooke’s law, longitudinal and shear moduli, yield and ultimate strengths; sample application: indeterminate force problems in rigid body supports. [1.5] (Ref. 3)
Response of a solid under longitudinal stresses in 3-dimensions, uniform strain-stress relations, longitudinal and bulk moduli, Poisson’s ratio, superposition of stresses, relationship among elastic moduli and Poisson’s ratio; torsion and twists of a rod and shear modulus; beam bending theory: bending moment. [5.5] (Ref. 4)

Unit 3

Optional Topic: Introduction to theory of elasticity*: General stresses, force on an arbitrary surface and stress tensor, hydrostatic compression; Small deformations and strain tensor; generalized Hooke’s law, strain energy, elastic constants for an isotropic solid (without proof). [3] (Ref. 4)
Elements of fluid mechanics: fluid pressure and statics, pressure variation in oceans and atmosphere, force on a surface due to fluid pressure – floating objects, dam; shape of surface of a rotating fluid (Ref.3). Fluid motion: pressure gradient, continuity equation, equation of motion for incompressible flow, total derivative; incompressible, irrotational, non-viscous, and steady flows; streamlines. (Refs. 3,4) [5]

Unit 4

Bernoulli’s equation and applications; Viscosity and viscous flow, flow through a circular tube – Poiseuille equation. Elementary discussions of laminar flow vs turbulence, Reynolds number, Navier- Stokes equation; . (Refs. 3,4) [4]
Special theory of relativity: Galilean transformation and consequences; Michelson-Morley experiment, postulates, relativity of simultaneity, time, and space, Lorentz transformations, time- dilation and length contraction, velocity addition, relativistic Doppler and a few other relativistic effects. [6] (Refs. 5, 1)

Unit 5

Relativistic dynamics: collisions, laboratory and centre of mass frames, momentum, energy, transformation of energy and momentum, conservation of momentum-energy, mass-energy equivalence, Example applications including, recoil of an emission, centre of mass frame calculations, fusion of colliding nuclei, energy threshold for pair production, Compton effect. [6] (Refs. 5, 1) Transformation laws for forces; motion in uniform electric and magnetic fields.
Equivalence principle, gravitational and inertial masses, gravitational red shift and bending of light near stars. [4] (Refs. 5)

Description: In continuation with part I, the following topics are covered: rotational motion and motion in accelerated frames, special theory of relativity, and elements of continuum mechanics.

Course Outcomes: By the end of the course students will be able to develop an understanding, and be able to
CO1: Understand angular momentum, kinetic energy of a rigid body, principal moments of inertia tensor, Euler’s equation, application to torque free wobble, precession of spinning top and gyroscopes. CO2: Describe motion in linearly accelerating and rotating frames and calculate pseudo forces, explain associated phenomena.
CO3: Describe elastic properties of solids, deformations, stress, strain, their tensor nature, elastic constants, equations of elasticity, strain energy, apply to compression, elongation, shear, torsion, and bending.
CO4: Describe fluid properties, fluid statistics, floating bodies, dynamics of fluid flow, laminar and turbulent flows, incompressible, irrotational flows, ideal and viscous flows, Bernoulli’s equations, apply to simple cases, Poiseuille flow, laminar and turbulent flows.
CO5: Understand Galilean transformation, Michelson-Morley experiment and its conclusions, understand and describe postulates of relativity, simultaneity of time, Lorentz transformation, velocity addition, and few relativistic kinematic effects.
CO6: understand descriptions of collisions and laboratory and centre of mass frames, relativistic momentum, mass-energy equivalence, conservation laws, application to relativistic phenomena in atomic and nuclear physics – recoil of an atom on photon emission, pair production, Compton effect; four-vectors, describe equivalence principle, apply to collisions and other relativistic effects.

1. Kleppner and Kolenkov, Introduction to Mechanics, 2E, Ch. 7 – 9, 12 – 13.
2. Cassiday and Fowles, Analytical Mechanics, 7th Edition.
3. Resnick and Halliay, Fundamentals of Physics, 4th Edition. (Chapters on Fluid Mechanics)
4. Feynman Lectures in Physics, Vol 2, Ch. 31, 38 – 41.
5. C. Kittel et al, Mechanics – Berkeley Physics Course Vol. 1, 2E, Ch. 11 – 14, McGraw-Hill.
6. Wheeler and Taylor, Space-time Physics.
7. Patrick & Hamill, Intermediate Mechanics, Jones & Bartlett Learning.
8. J.R. Taylor, Classical Mechanics, University Science Books, (Especially for Ch. 16 on elastic solid and fluid mechanics)
9. David Morin, Introduction to Classical Mechanics, CUP, Ch. 8 – 14.
10. Marion and Thornton, Classical Dynamics of Particles and Systems, 5E.
11. Rana and Joag, Classical Mechanics, McGraw-Hill. Ch. 13, 14.