 COURSE SUMMARY
Course Title:
Mechanics
Course Code:
18PHY103
Year Taught:
2018
2019
Semester:
1
Degree:
Integrated Degree
School:
School of Arts and Sciences
Campus:
Mysuru

'Mechanics' is a course offered at the School of Arts and Sciences, Amrita Vishwa Vidyapeetham, Mysuru campus.

#### Scope and Objectives

To enable students to understand Newtonian mechanics and apply Newton’s laws to explain natural physical phenomena.

#### Syllabus

Unit I:

Vector Analysis: Integrals (line, surface and volume), Physical significance of Gradient, Divergence and curl, statement of Gauss’s and Stroke’s theorems.

Particle dynamics (review): Review of the equations of motion, projectile motion, Newton’s First, Second and Third Law of Motion, Newton’s I Law as a basic kinematical law defining a frame of reference, Newton’s II Law as a basic dynamical law of mechanics and Newton’s III law as an interaction law, Frames of reference, inertial and non inertial, pseudo forces, Force laws, weight and mass, Application of Newton’s law, importance of free body diagrams representing forces on the body in a free body diagram and frictional forces. Discussion of importance of friction in daily life.

Unit II:

Work and Energy: Work done by a constant force and by a variable force – one and two dimensional cases. Kinetic energy and work-energy theorem, Significance of the work-energy theorem, power. The importance of language in Physics to be highlighted by differentiating the meaning of ‘work’, ‘power’, ‘energy’ as defined in Physics and in daily life.

Conservation Laws: Introduction, conservative forces, potential energy, complete solution for one, two and three dimensional systems, non-conservative forces, conservation of energy, conservation of energy to be seen as a spreading out and appearing in different forms, mass and energy.

Conservation of Linear Momentum: Centre of mass, motion of the center of mass, linear momentum of a particle, linear momentum of a system of particles, conservation of linear momentum, some applications of momentum principle, systems of variable mass – Rocket equation.

Collisions: Elastic and Inelastic, Collision in one and two dimensions.

Unit III:

Gravitation: Historical Introduction, Newton’s law of Universal Gravitation, Universal Gravitation constant ‘G’, inertial and gravitational mass, variation in acceleration due to gravity with altitude and depth, motion of planets and satellites, gravitational field and potential, gravitational potential energy, potential energy for many particle systems, calculations of field and potential for (a) a spherical shell, (b) a sphere, energy consideration in the motion of planets and satellites.

Central Force: Kepler’s laws of planetary motion, the inverse square law, Rutherford’s problem, derivation of Kepler’s Law from Universal law of Gravitation.

Unit IV:

Rotational Kinematics: Rotational variables, angular velocity, angular acceleration. Rotation with constant angular acceleration, Linear and angular variables, kinetic energy of rotation, rotational inertia, calculation 70  of rotational inertia – of a rod, sphere and cylinder, torque, Newton’s laws of rotation, work, power and work – kinetic energy theorem.

Unit V:

Dynamics of Rigid bodies: Angular momentum and moment of inertia, Theorem on moment of inertia, moment of inertia for (i) solid cylinder, (ii) rectangular slab, (iii) solid sphere and (iv) circular hoop.

Fluid Mechanism: Ideal fluids, Equation of Continuity, Viscous fluids, critical velocity, Derivation of Poiseuille’s Equation.

#### Textbook / References

Textbooks:

1. J C Upadhyaya, “Classical Mechanics”, Himalaya Publishing house, Reprint-2013.
2. D S Mathur, “Mechanics”, S Chand and company, New Delhi, Reprint-2001.
3. BrijLal, N Subrahmanyam, “Properties of matter”, 6th edition, Eurasia publishing house Ltd.New Delhi, Reprint-1993.

References:

1. Halliday, Resnick, Jearl Walker, “Principles of Physics” 9th edition, Wiley, 2013.
2. Berkeley Physics Course, Vol-1 “Mechanics”, 2nd edition, Charles Kittle, Walter D Knight, Malvin A Ruderman, Carl A Helmholz, Burton J Moyer, Tata McGraw Hill Education Private Limited, New Delhi, (SIE)-2011.
3. D S Mathur, “Elements of properties of matter”, S Chand and company, New Delhi, Reprint 2007.

#### Practicals

(A minimum of ten experiments to be done from the list given below)

1. To Determine the Momentum of Inertia and Mass of a Flywheel.
2. Study of the motion of an air bubble.
3. Study of the motion of a freely falling body.
4. Study of the acceleration of a body subjected to different unbalanced forces.
5. Study of accelerations of different masses under a constant unbalanced force.
6. Study of conservation of energy and momentum in head-on-collision between two spheres of equal mass.
7. Conservation of momentum in an explosion.
8. Determination of Surface tension of liquid by capillary rise method.
9. To study the relation between length and time period of a simple pendulum.
10. Study of the rate of flow of water through a capillary tube under different pressure heads.
11. Momentum of inertia of a rod by torsional oscillation.
12. Determination of Acceleration due to Gravity and radius of gyration by Bar Pendulum.