# Mechanics

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# Code(Credit) : CUTM1484(3-2-1)

## Course Objectives

• This course would empower the student to acquire skills and practical knowledge, which help the student in their everyday life.
• This syllabus will cater the basic requirements for their higher studies.
• This course will provide a theoretical basis for doing experiments in related areas.
• This is an introductory course for undergraduate science students.

## Learning Outcomes

• Understand the analogy between translational and rotational dynamics and application of both motions simultaneously in analyzing rolling without slipping.
• Understand the phenomena of collisions and idea about center of mass frames of reference and laboratory frames of reference and their correlation.
• Understand the non-inertial systems and the fictitious forces.
• Understand the principles of elasticity and principle of fluid flow.
• Apply Kepler’s  law  to  describe  the  motion  of  planets  and  satellite  in  circular  orbit, through the study of law of gravitation.
• Explain  the  phenomena  of  simple  harmonic  motion  and  the  properties  of  systems executing such motions.

## Course Syllabus

Module I

Work and energy: Work and kinetic energy theorem, conservative and non-conservative forces, potential Energy, force as gradient of potential energy, work & potential energy, work done by non-conservative forces, law of conservation of energy.

Practice-1: To verify work energy theorem using Newton's second law simulator. (Vlab)

Module II

Collisions: Elastic and inelastic collisions between particles, centre of mass, centre of mass and laboratory frames, two dimensional elastic collision in centre of mass frame, advantage of centre of mass frame of reference.

Practice-2: To measure the speed of a bullet and to verify the law of conservation of momentum by ballistic pendulum simulator.(Vlab)

Practice-3: Verification of elastic and inelastic collision. (Virtual lab)

Module III

Rotational dynamics: Angular momentum 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.

Practice-4:To determine the moment of inertia of a flywheel

Module IV

Non-inertial systems: Frames of reference, inertial frames, non-inertial frames and fictitious forces, uniformly rotating frame, laws of physics in rotating coordinate systems, centrifugal force, Coriolis force and its application.

Module V

Elasticity: Relation between elastic constants, twisting couple in a cylinder or wire.

Practice-5:To determine the Young's modulus of a wire by Searle’s method.

Practice-6To determine the modulus of rigidity of a wire by static torsion method.

Practice-7:To determine the modulus of rigidity of a wire by torsional pendulum/Maxwell needle.

Fluid motion: Kinematics of moving fluids, Poiseuille’s equation for flow of a liquid.

Practice-8:To determine coefficient of viscosity of water by capillary flow method (Poiseuille’s method).

Practice-9:To determine coefficient of viscosity of oil by falling ball viscometer.

Module VI

Gravitation 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).

Module VII

Oscillations: 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. compound pendulums.

Practice-10:To determine the value of g using bar pendulum.

Practice-11: To determine the value of g using Kater's pendulum

Practice-12: To determine the moment of inertia of a torsion pendulum

Text Book:

1. Mechanics, D.S. Mathur, S. Chand and Company Limited.

Reference Books:

1. An introduction to mechanics, D. Kleppner, R.J. Kolenkow, 1973, McGraw-Hill.
2. Physics, Resnick, Halliday and Walker 8/e. 2008, Wiley
3. Physics for scientists and Engineers with Modern Phys. ,J.W. Jewett, R.A. Serway, 2010, Cengage Learning

## Session 1

Work, Kinetic Energy, Work-energy theorem.

Animation : physclip

You tube video: Work and Energy

Study material: Mechanics-1

## Session 2

Practice-1 ( 2hrs):

To verify work energy theorem using Newton's second law simulator. (Vlab)

Manual: Newtons law of motion

Virtual lab: Vlab

## Session 3

Conservative and non-conservative forces,  Potential Energy

Animation: Physclip

You tube video: Conservative force

## Session 4

Force as gradient of potential energy, Work & Potential energy

Coursera video:  Work and Potential Energy

You tube video: MIT OpenCourseWare

Study Material: https://slideplayer.com/slide/13088136/

## Session 5

Work done by non-conservative forces, Law of conservation of energy

Coursera video: Conservation of energy

Web text: openstax

You tube video: Conservation of energy

## Session 6

Flip class-1:

Elastic and inelastic collisions between particles, One dimensional collision.

Animation: Physclip

Coursera video: Momentum and Collisions

Web text: openstax

You tube video: Elastic and inelastic collision

PPT: Mechanics-5

## Session 7

Practice-2 (2 hrs.):

To measure the speed of a bullet and to verify the law of conservation of momentum by Ballistic Pendulum simulator.

Virtual lab: vlab

## Session 8

Practice-3(2 hrs.):

Verification of elastic and inelastic collision

Virtual lab: vlab

## Session 9

Centre of mass, centre of mass frames and laboratory frames.

Animation: Physclip

Coursera video: Centre of Mass, Elastic and Inelastic Collisions

You tube video: MIT OpenCourseWare

PPT: Mechanics-6

## Session 10

Two dimensional elastic collision in centre of mass frame, Advantage of centre of mass frame of reference.

Animation: Physclip

You tube video: MIT OpenCourseWare

Study material: 10-Mech-Collision and CM frame

## Session 11

Angular momentum of a particle and system of particles.

Animation: Physclip

Web text: libretext

You tube video: Angular momentum

Study material: 11-Rotational dynamics

## Session 12

Torque, torque acting on a system of particles.

Animation: Physclip

Web text: libretext

You tube video: Torque

Study Material: https://www.slideshare.net/RajalPandya2/torque-93897788

## Session 13

Flip class-2:

Principle of conservation of angular momentum, Examples.

Animation: Physclip

Web text: libreText

Web text: Openstax

You tube video: Angular Momentum

Study material: 13-Conservation of angular momentum

## Session 14

Rotation about a fixed axis, Moment of inertia.

Animation: Physclip

Web text: libreText

Study material: 14-Moment of inertia

## Session 15

Calculation of moment of inertia for rectangular, cylindrical bodies.

You tube video: Moment of inertia of rectangular body

Study material: 15-MI of rectangular bodies

## Session 16

Calculation of moment of inertia for spherical bodies.

Web text: M.I. of spherical shell

Web text: M.I. of solid sphere

You tube video: You tube

Study material: 16-MI spherical bodies

## Session 17

Practice-4(2 hrs.):

To determine the moment of inertia of a flywheel.

Virtual lab: vlab

## Session 18

Frames of reference, Inertial frames, Non-inertial frames

Coursera video: Coursera

You tube video: Frame of refernce

## Session 19

Non-inertial frames and fictitious forces, Centrifugal force.

Web text: openstax

Web text: libretext

You tube video: MIT OpenCourseWare

## Session 20

Coriolis force and its application.

Web text: openstax

You tube video: Coriolis force

## Session 21

Flip class-3:

Elasticity, Hooke’s law, elastic constants.

Web text: Openstax

Web text: Theconstructor.org

You tube video: Elasticity

Study material: 21-Elastic constants

## Session 22

Relation between elastic constants, relation between Y, η and σ; relation between Y, K and σ.

You tube video: Relation-elastic constants

Study material: 22-Relation between elastic constant

## Session 23

Twisting couple in a cylinder or wire.

You tube video: Twisting couple on a cylinder

Study material: 23-twisting couple

## Session 24

Practice-5(2 hrs.):

To determine the Young's modulus of a wire by Searle’s method.

You tube video: Young's modulus - MeitY OLabs

## Session 25

Practice-6(2 hrs.):

To determine the modulus of rigidity of a wire by static torsion method.

Virtual lab: vlab

## Session 26

Practice-7(2 hrs.):

To determine the modulus of rigidity of a wire by torsional pendulum/Maxwell needle.

Virtual lab: vlab

## Session 27

Kinematics of moving fluids.

Web text: openstax

You tube video: Viscosity

Study material: 27 -fluid kinematics

## Session 28

Poiseuille’s equation for flow of a liquid.

Web text: openstax

You tube video: Rate of flow of liquid

Study material: 28-Poiseuille

## Session 29

Practice-8(2 hrs.):

To determine coefficient of viscosity of water by capillary flow method (Poiseuille’s method).

## Session 30

Practice-9(2 hrs.):

To determine coefficient of viscosity of oil by falling ball viscometer.

You tube video: Viscosity - MeitY OLabs

## Session 31

Flip class-4:

Law of gravitation, gravitational potential energy, Inertial and gravitational mass.

Animation: Physclip

Web text: LibreText

You tube video: MIT OpenCourseWare

Study material: 31-Gravitation

## Session 32

Potential and field due to spherical shell.

Animation: Physclip

You tube video: Edu point

## Session 33

Flip class-5 :

Potential and field due to solid sphere.

You tube video: Solid sphere

## Session 34

Motion of a particle under a central force field.

You tube video: Central force

## Session 35

Two-body problem and its reduction to one-body problem and its solution.

You tube video: Central force

## Session 36

The energy equation and energy diagram.

Web text: http://coffee.ncat.edu

Web text: libretexts

## Session 37

Kepler’s Laws

Animation: Physclip

## Session 38

Flip class-6:

Satellite in circular orbit and applications.

You tube video: Satellite in circular orbit

## Session 39

Geosynchronous orbits.  Basic idea of global positioning system (GPS).

You tube video: Geosynchronous orbits

## Session 40

Simple Harmonic Oscillations,  Differential equation of SHM and its solution.

Animation: Physclip

You tube video: SHM

Study material: 40-SHM

## Session 41

Flip class-7:

Kinetic energy, potential energy, total energy and their time-average values.

Animation: Physclip

You tube video: Energy

## Session 42

Damped oscillation (General solution)

Animation: Physclip

Study material: 41-DHM

## Session 43

Damped oscillation(Continued)

Underdamped, overdamped and critical damped motion

Animation: Physclip

## Session 44

Forced oscillations.

You tube video: Forced oscillation

## Session 45

Flip class-8:

You tube video: Transient

## Session 46

Resonance, sharpness of resonance.

Animation: Physclip

You tube video: Resonance

## Session 47

Power dissipation and quality factor.

You tube video: Q factor

## Session 48

Flip class-9 (2 hrs.):

Bar pendulum

You tube video : Compound pendulum

## Session 49

Flip class-10( 2 hrs.):

Kater's pendulum

You tube video: Kater's pendulum

You tube video: Kater's pendulum2

## Session 50

Practice-10(2 hrs.):

To determine the value of g using Bar Pendulum.

Virtual lab: Vlab

## Session 51

Practice-11(2 hrs.):

To determine the value of g using Kater's Pendulum.

## Session 52

Practice-12(2 hrs.):

To determine the moment of inertia of the given disc using Torsion pendulum, with identical masses.

### Mr. Gouri Kumar Sahu

##### Assistant Professor
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I am an Assistant Professor of Physics in the School of Applied Science, Paralakhemundi Campus of Centurion University of Technology and Management, Odisha. I have started teaching Physics from the year 1995 just after completion of my Post Graduate Degree from Berhampur University. I have more than six years of teaching experience at +2 level […]