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# Engineering Mechanics

### Overview

COURSE OUTLINE: In this course, we would be studying mechanical interaction between different bodies when they interact through the forces applied on each other. This would consist of 2 parts: statics and dynamics.

### Syllabus

Introduction to Vectors.
Multiplying vectors.
Introduction to vectors: solved examples I.
Transformation of vectors under rotation.
Vector products and their geometric interpretation.
Vector Product: Kronecker Delta and Levi-Civita symbols-I.
Vector Product: Kronecker Delta and Levi-Civita symbols-II.
Introduction to vectors: solved examples II.
Equilibrium of rigid bodies – Forces and torques.
Calculating torques and couple moments - I.
Calculating torques and couple moments - II.
Finding a force and a couple equivalent to an applied force.
Different elements and associated forces and torques - I.
Different elements and associated forces and torques - II.
Solved examples; equilibrium of bodies – I.
Solved examples; equilibrium of bodies – II.
Forces in different geometric configurations.
Plane trusses I - Building a truss and condition for it to be statically determinate.
Plane trusses II - Calculating forces in a simple truss and different types of trusses.
Plane trusses III - Calculating forces in a simple truss by method of joints.
Plane trusses IV - Solved examples for calculating forces in a simple truss by method of joints.
Plane trusses V - Solved examples for calculating forces in a simple truss by method of joints.
Plane trusses VI: Method of sections for calculating forces in a simple truss.
Dry friction I - introduction with an example.
Dry friction II - a solved example.
Dry friction III - Dry thrust bearing and belt friction with demonstration.
Dry friction IV - Screw friction and rolling friction.
Dry friction V: Solved examples.
Properties of plane surfaces I - First moment and centroid of an area.
Properties of plane surfaces II - Centroid of an area made by joining several plane surfaces.
Properties of plane surfaces III - Centroid of a distributed force and its relation with centre....
Properties of plane surfaces IV - solved examples of calculation of first moment and centroid....
Properties of plane surfaces V- Second moment and product of an area and radius of gyration.
Properties of plane surfaces VI - Parallel axis transfer theorem for second moment and product of an.
Properties of plane surfaces VII - transformation of second moment and product of an area under rota.
Properties of plane surfaces VIII - second moment and product of an area, solved examples.
Method of virtual work I - degrees of freedom, constraints and constraint forces.
Method of virtual work II - virtual displacement, virtual work and equilibrium condition in terms of.
Method of virtual work III - solved examples.
Motion of a particle in a plane in terms of planar polar coordinates.
Planar polar coordinates: solved examples.
Description of motion in cylindrical and spherical coordinate systems.
Using planar polar, cylindrical and spherical coordinate systems: solved examples.
Motion with constraints, constraint forces and free body diagram.
Motion with constraints – solved examples.
Motion with dry friction – solved examples.
Motion with drag – solved examples.
Equation of motion in terms of linear momentum and the principle of conservation of linear momentum.
Linear momentum and centre of mass.
Momentum transfer, impulse and force due to a stream of particles hitting an object.
Momentum and the variable mass problem.
Linear momentum – solved examples.
Work and energy I - work energy theorem; conservative and non-conservative force fields.
Work and energy II - Definition of potential energy for conservative forces; total mechanical energy.
Work and energy III - Two solved examples using conservation principles.
Work and energy IV – Further discussion on potential energy.
Work and energy V - Solved examples.
Work and energy VI – Applying conservation principles to solve a collision problem.
Work and energy VII - Solved examples.
Rigid body motion I - degrees of freedom and number of variables required to describe motion of a ri.
Rigid body motion II - Equation of motion for a single particle in terms of angular momentum and tor.
Rigid body motion III - Conservation of angular momentum; angular momentum for a collection of parti.
Rigid body motion IV - applying angular momentum conservation, a solved example.
Rigid body motion V (fixed axis rotation) - some demonstrations of conservation of angular momentum.
Rigid body motion VI (fixed axis rotation) - Some more demonstrations and related problems.
Rigid body motion VII (fixed axis rotation) - Kinetic energy and moment of inertia for fixed axis ro.
Rigid body motion VIII (fixed axis rotation) - solved examples for calculating moment of inertia and.
Rigid body motion –IX (fixed axis rotation): solved examples.
Rigid body motion X - rotation and translation with axis moving parallel to itself.
Rigid body motion XI - solved examples for rotation and translation with axis moving parallel to its.
Rigid-body dynamics XII - Some demonstrations on general motion of rigid bodies.
Rigid-body dynamics XIII - Infinitesimal angles as vector quantities and change of a vector when rot.
Rigid-body dynamics XIV - Angular velocity and the rate of change of a rotating vector; relating cha.
Rigid-body dynamics XV - Relationship between angular momentum and angular velocity – the moment of.
Rigid-body dynamics XVI: Solved examples.
Rigid body motion XVII – A review of the relation between angular momentum and angular velocity, mom.
Rigid body motion XVIII- Solved examples for calculating rate of change of angular momentum and torq.
Rigid body dynamics XIX: understanding demonstrations shown earlier using equation of motion.
Rigid body dynamics XX - understanding demonstrations shown earlier using equation of motion (Euler.
Rigid body dynamics XXI - Euler equations, solved examples.
Simple harmonic motion I - expanding potential energy about the equilibrium point and the correspond.
Simple harmonic motion II : solving the equation of motion with given initial conditions.
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