Syllabus (PHYSICS)

Course Type: MAJ-1

Semester: 1

Course Code: BPHSMAJ01C

Course Title: Mechanics and Properties of Matter

(L-P-Tu): 4-2-0

Credit: 6

Practical/Theory: Combined

Course Objective: The objective of this course is to provide students with a comprehensive understanding of mechanics and properties of matter. Through theoretical concepts, problem-solving exercises, and practical applications, students will develop a strong foundation in Mechanics and Properties of Matter, enabling them to analyze and interpret complex physical phenomena related to motion, forces, and material behavior of real world.

Learning Outcome: By achieving the course objectives, students will be well-prepared to solve complex problems in classical mechanics, understand the fundamental properties of materials, and interpret various physical phenomena, providing a solid foundation for further studies in physics, engineering, and related fields.

Theory

Vector Differentiation

Directional derivatives and normal derivatives, Gradient of a scalar field and its geometrical interpretation, Divergence and curl of a vector field with their physical significances, Del and Laplacian operators, Vector identities. (6 Lectures)

Fundamentals of Dynamics

Reference frames. Inertial frames; Review of Newton’s Laws of Motion. Equation of motion of a particle, Galilean transformations; Galilean invariance. Momentum of variable-mass system: motion of rocket. Motion of a projectile in uniform gravitational field. Dynamics of a system of particles. Centre of Mass. Motion of Centre of Mass, Principle of conservation of momentum with applications. (6 Lectures)

Work and Energy

Work and Energy, Work Energy Theorem. Conservative and non-conservative forces. Potential energy. Qualitative study of one-dimensional motion from potential energy curves. Stable and unstable equilibrium. Elastic potential energy. Force as gradient of potential energy. Work and potential energy. Work done by non-conservative forces. Law of conservation of energy. (4 Lectures)

Collisions

Collisions, Centre of mass frame and Laboratory frames, Elastic and inelastic collisions between particles. Elastic collision in two-dimensional case, coefficient of restitution. (3 Lectures)

Rotational Dynamics

Angular momenta of a particle and system of particles. Torque. Principle of conservation of angular momentum. Rotation about a fixed axis. Moment of inertia. Calculation of moment of inertia for rectangular, cylindrical, and spherical bodies, rod, lamina, ring, disc, spherical shell, solid sphere. Kinetic energy of rotation, rolling along a slope, Application to compound pendulum. Motion involving both translation and rotation. (10 Lectures)

Gravitational and Central Force Motion

Law of gravitation. Gravitational potential energy. Inertial and gravitational mass. Potential and field due to spherical shell and solid sphere. Motion of a particle under a central force field. Two-body problem and its reduction to one-body problem and its solution. The energy equation and energy diagram. Kepler’s Laws. Satellite in circular orbit and applications. Geosynchronous orbits. Weightlessness. Basic idea of global positioning system (GPS). (8 Lectures)

Non-Inertial Systems:

Non-inertial frames and fictitious forces. Uniformly rotating frame. Laws of Physics in rotating coordinate systems. Centrifugal force and its effect on g. Coriolis force and its applications. Geophysical effects of coriolis force, Components of velocity and acceleration in Cylindrical and Spherical coordinate systems. (6 Lectures)

Elasticity

Elastic constants, Relation between elastic constants. Twisting torque on a cylinder or wire. Bending of beam, bending moment, Cantilever: shear force and torque, Cantilever loaded at any distance from the fixed end, Beam supported at both end and loaded at the centre, shape of Girders/ rail tracks. (7 Lectures)

Fluid Motion

Kinematics of moving fluids: equation of continuity, Poiseuille’s equation for flow of a liquid through a capillary tube, Euler’s equation, Bernoulli’s theorem and its applications. (4 Lectures)

Oscillations
SHM: Simple Harmonic Oscillations. Differential equation of SHM and its solution. Kinetic energy, potential energy, total energy and their time-average values. Damped oscillation. Forced oscillations: Transient and steady states; Resonance, sharpness of resonance; power dissipation and Quality Factor. (6 Lectures)

List of Practicals (Any six)

1. Measurements of length (or diameter) using vernier caliper, screw gauge and travelling microscope.

2. To study the random error in observations.

3. To determine the Moment of Inertia of a Cylinder.

4. To determine Coefficient of Viscosity of water by Capillary Flow Method (Poiseuille’s method).

5. To determine the Young's Modulus of a Wire by Flexural/ Optical Lever Method.

6. To determine the value of g using Kater’s Pendulum.

7. To determine the Modulus of Rigidity of a Wire by Maxwell’s needle/dynamical method

8. To determine the elastic Constants of a wire by Searle’s method.

9. To study the Motion of Spring and calculate, (a) Spring constant, (b) g and (c) Modulus of rigidity and (d) unknown mass.

Reading References

Theory

1. An Introduction to Mechanics, D Kleppner and R J Kolenkow, McGraw Hill.

2. Physics, R Resnick, J Halliday and D Walker, 8^th Edition, Wiley.

3. Mechanics, Berkeley Physics, Vol.1, C. Kittel, W. Knight, et. al. Tata McGraw Hill.

4. Introduction to Classical Mechanics, D Morin, Cambridge University Press.

5. Mechanics and Properties of Matter, A B Gupta, 5^th Edition, Books and Allied Pvt Ltd.

6. Mechanics, D S Mathur and P S Hemne, S. Chand and Company Pvt Ltd.

7. Theory and Problems of Theoretical Mechanics, M R Spiegel, McGraw Hill.

8. A Treatise on General Properties of Matter, Sengupta and Chatterjee, NCBA.

9. Properties of Matter, Brij Lal and N Subrahmanyam, S. Chand and Company Pvt Ltd.

10. The Physics of Waves and Oscillations, N K Bajaj, Tata McGraw Hill.

11. Vibrations and Waves, A P French, CBS Publishers.

​​Practical

1. Advanced Practical Physics for Students, B L Flint and H T Worsnop, Asia Publishing House

2. An Advanced Course in Practical Physics, D Chattopadhyay and P C Rakshit, NCBA

3. Advanced Level Physics Practicals, M Nelson and J M. Ogborn, 4th Edition, Heinemann Educational Publishers

4. A Text Book of Practical Physics, I Prakash, R Krishna and A K Jha, Kitab Mahal

5. Laboratory Manual of Physics, Vol 1, M Jana, Books and Allied Pvt Ltd