Course

Unit 1

Examples of motion in 1D; Vector kinematics: displacement, velocity and acceleration from trajectories, vector form of uniform circular motion, formal solutions to kinematic equations. Motion in polar coordinates, tangential and normal accelerations, radius of curvature; sample applications: motion of a bead on circular, elliptical, spiral, and other types of trajectories; bead on a rotating spoke. (Ref.1, Ch.1, Ref.2, Ch.2) [6]

Unit 2

Dynamics: Newton’s laws, the notion of inertial mass, inertial systems; applications to spring forces; sample applications to constrained motion – simple pendulum, conical pendulum or a bead on a rotating hoop, whirling block; motion of charged particles in magnetic fields, circular and helical orbits, mass spectrometer, crossed electric and magnetic fields – velocity selection, lateral drift. (Ref.1-Ch.2,3, Ref.2-Ch.3, Ref.3-Ch.4) [6]

Unit 3

Energy: First integral of motion and work-energy theorem, First integral of motion, line integral of force, conservative forces and path independence of work, work in central and non-central forces, conservative and non-conservative forces. Potential energy function, energy diagrams. [6] Momentum: Review of motion of system of particles, centre of mass motion, momentum and conservation; Mass flow: mass and momentum transport, momentum flux, damping force on a disc moving through a fluid. [3]

Unit 4

Angular momentum: angular momentum of a particle and system of particles, conservation of angular momentum in central forces, application to Kepler’s II law, distance of minimum approach in a nuclear scattering; Gravitational and electrostatic force and potential and potential energy of spherical objects. [4]
Central force motion (1-body problem): first integrals and constants of motion, energy diagrams, bounded and unbounded orbits, radial equation of motion and elliptical orbits, orbital speed and period, geosynchronous orbits. (Refs.1,2) Two-body problem: Centre of mass and relative motion: Centre of mass and relative coordinates, reduced mass, Correction to orbital periods in the planetary motion; molecular vibrations. [5] (Ref.2).

Unit 5

Review of vector calculus for physics: Coordinate systems, functions of many variables, partial and total derivatives, differentials; position vector and unit vectors in curvilinear coordinates, infinitesimal line, surface and volume elements, solid angle. Scalar and vector fields; simple examples of line, surface and volume integrals; current and flux, continuity equation; Gradient in cartesian and curvilinear coordinates, divergence and curl, integral theorems; selected applications to electrodynamics and fluid flow. [10]

Description: Building upon the first introductory course on mechanics, this course is the first part of the two courses that introduces advanced techniques in mechanics covering topics of vector kinematics and dynamics, energy methods, momentum and angular momentum, central force and damped and forces oscillatory motion, coupled oscillations and mechanical waves in elastic media from an intermediate level book on mechanics.

Course Outcomes: After successful completion of this course, students shall be able to
Apply concepts in kinematics in one, two and three dimensions in Cartesian, polar, cylindrical and spherical coordinates, integrate equations for simple cases;
Apply Newton’s law for a few simple cases including under constant electric and magnetic fields.
Apply energy and momentum methods in one and higher dimensions to solve of equations of motion and related mechanical aspects
Apply the principles of angular momentum and its conservation, Newton’s laws in the application to Kepler’s laws.
Apply methos of vector calculus to analyse basic electrostatics and fluid flow.

1. Kleppner and Kolenkov, Introduction to Mechanics, 2E (Ch. 1 – 7.)
2. C. Kittel et al, Mechanics – Berkeley Physics Course Vol. 1, 2E, McGraw-Hill. Ch. 1 – 7.
3. Cassiday and Fowles, Analytical Mechanics, 7th Edition.
4. Berkeley Physics Vo. 3, Waves. Wiley India.
5. H.J. Pain, Vibrations and Waves, 6th Edition.
6. Patrick Hamill, Intermediate Dynamics, Jones and Bartlett Publishers
7. David Morin, Introduction to Classical Mechanics, CUP, Ch. 1 – 7.
8. R.P. Feynman et al, Feynman Lectures in Physics, Narosa publications.
9. R. Shankar, Basic Training in Mathematics: Fitness Program for Science Students.