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Engineering Mechanics

Engineering Mechanics. Instructor: Professor Manoj K Harbola, Department of Physics, IIT Kanpur. In this course, we would be studying mechanical interaction between different bodies when they interact through the forces applied on each other. Topics covered in this course include Review of Newton's laws of motion and vector algebra; Equilibrium of bodies; Plane trusses; Friction; Properties of plane surfaces; Method of virtual work; Motion of particles; Momentum; Work and energy; Rotational kinematics and dynamics; Simple harmonic oscillator; and Motion in non-inertial frames. (from nptel.ac.in)

Lecture 08 - Vector Product: Kronecker-Delta and Levi-Civita Symbols (cont.)

Representing product of vectors becomes easy if we use the Kronecker-Delta and Levi-Civita symbols. In these two lectures we learn about these symbols and their use in representing vector products.

Go to the Course Home or watch other lectures:

Review of Newton's Laws of Motion and Vector Algebra

Lecture 01 - Introduction to Vectors

Lecture 02 - Addition and Subtraction of Vectors

Lecture 03 - Multiplying Vectors

Lecture 04 - Introduction to Vectors: Solved Examples I

Lecture 05 - Transformation of Vectors under Rotation

Lecture 06 - Vector Products and their Geometric Interpretation

Lecture 07 - Vector Product: Kronecker-Delta and Levi-Civita Symbols

Lecture 08 - Vector Product: Kronecker-Delta and Levi-Civita Symbols (cont.)

Lecture 09 - Introduction to Vectors: Solved Examples II

Equilibrium of Rigid Bodies

Lecture 10 - Equilibrium of Rigid Bodies - Forces and Torques

Lecture 11 - Calculating Torques and Couple Moments

Lecture 12 - Calculating Torques and Couple Moments (cont.)

Lecture 13 - Finding a Force and a Couple Equivalent to an Applied Force

Lecture 14 - Different Elements and Associated Forces and Torques

Lecture 15 - Different Elements and Associated Forces and Torques (cont.)

Lecture 16 - Solved Examples; Equilibrium of Bodies I

Lecture 17 - Solved Examples; Equilibrium of Bodies II

Lecture 18 - Forces in Different Geometric Configuration

Plane Trusses

Lecture 19 - Plane Trusses: Building a Truss

Lecture 20 - Plane Trusses: Calculating Forces in a Simple Truss and Different Types of Trusses

Lecture 21 - Plane Trusses: Calculating Forces in a Simple Truss by Method of Joints

Lecture 22 - Solved Examples for Calculating Forces in a Simple Truss by Method of Joints

Lecture 23 - Solved Examples for Calculating Forces in a Simple Truss by Method of Joints (cont.)

Lecture 24 - Plane Trusses: Method of Selection for Calculating Forces in a Simple Truss

Friction

Lecture 25 - Dry Friction: Introduction with an Example

Lecture 26 - Dry Friction: A Solved Example

Lecture 27 - Dry Friction: Dry Thrust Bearing and Belt Friction with Demonstration

Lecture 28 - Dry Friction: Screw Friction and Rolling Friction

Lecture 29 - Dry Friction: Solved Examples

Properties of Plane Surfaces

Lecture 30 - Properties of Plane Surfaces: First Moment and Centroid of an Area

Lecture 31 - Centroid of an Area Made by Joining Several Plane Surfaces

Lecture 32 - Centroid of a Distributed Force and its Relation with Centre of Gravity

Lecture 33 - Solved Examples of Calculation of First Moment and Centroid of Distributed Forces

Lecture 34 - Second Moment and Product of an Area and Radius of Gyration

Lecture 35 - Parallel Axis Transfer Theorem for Second Moment and Product of an Area

Lecture 36 - Transformation of Second Moment and Product of an Area under Rotation of Coordinate Axes

Lecture 37 - Second Moment and Product of an Area, Solved Examples

Method of Virtual Work

Lecture 38 - Degrees of Freedom, Constraints and Constraint Forces

Lecture 39 - Virtual Displacement, Virtual Work and Equilibrium Condition in Terms of Virtual Work

Lecture 40 - Method of Virtual Work: Solved Examples

Motion of Particles

Lecture 41 - Motion of a Particle in a Plane in terms of Planar Polar Coordinates

Lecture 42 - Planar Polar Coordinates: Solved Examples

Lecture 43 - Description of Motion in Cylindrical and Spherical Coordinate Systems

Lecture 44 - Using Planar Polar, Cylindrical and Spherical Coordinate Systems: Solved Examples

Lecture 45 - Motion with Constraints, Constraint Forces and Free Body Diagram

Lecture 46 - Motion with Constraints - Solved Examples

Lecture 47 - Motion with Constraints - Solved Examples (cont.)

Lecture 48 - Motion with Constraints - Solved Examples (cont.)

Momentum

Lecture 49 - Equation of Motion in terms of Linear Momentum and the Principle of Conservation of Linear Momentum

Lecture 50 - Linear Momentum and Centre of Mass

Lecture 51 - Momentum Transfer, Impulse and Force due to a Stream of Particles Hitting an Object

Lecture 52 - Momentum and the Variable Mass Problem

Lecture 53 - Linear Momentum - Solved Examples

Work and Energy

Lecture 54 - Work Energy Theorem; Conservative and Non-conservative Force Fields

Lecture 55 - Definition of Potential Energy for Conservative Forces; Total Mechanical Energy and the Principle of Conservation Energy

Lecture 56 - Work and Energy Two Solved Examples using Conservation Principles

Lecture 57 - Further Discussion on Potential Energy

Lecture 58 - Work and Energy - Solved Examples

Lecture 59 - Applying Conservation Principles to Solve a Collision Problem

Lecture 60 - Work and Energy - Solved Examples

Rigid Body Motion

Lecture 61 - Degrees of Freedom and Number of Variables Required to Describe Motion of a Rigid Body

Lecture 62 - Equation of Motion for a Single Particle in terms of Angular Momentum and Torque; Motion of a Conical Pendulum

Lecture 63 - Conservation of Angular Momentum; Angular Momentum for a Collection of Particles

Lecture 64 - Applying Angular Momentum Conservation, a Solved Example

Rigid Body Motion (Fixed Axis Rotation)

Lecture 65 - Some Demonstrations of Conservation of Angular Momentum about Fixed Axis

Lecture 66 - Some More Demonstrations and Related Problems

Lecture 67 - Kinetic Energy and Moment of Inertia for Fixed Axis Rotation and Some Solved Examples

Lecture 68 - Solved Examples for Calculating Moment of Inertia and Conservation of Angular Momentum

Lecture 69 - Rigid Body Motion: Fixed Axis Rotation - Solved Examples

Lecture 70 - Rotation and Translation with Axis Moving Parallel to Itself

Lecture 71 - Solved Examples for Rotation and Translation with Axis Moving Parallel to Itself

Rigid Body Dynamics

Lecture 72 - Some Demonstrations on General Motion of Rigid Bodies

Lecture 73 - Infinitesimal Angles as Vector Quantities and Change of a Vector when Rotated by an Infinitesimal Angle

Lecture 74 - Angular Velocity and the Rate of Change of a Rotating Vector; Relating Change in Angular Velocity to an Applied Torque

Lecture 75 - Relationship between Angular Momentum and Angular Velocity

Lecture 76 - Rigid Body Dynamics - Solved Examples

Lecture 77 - A Review of the Relation between Angular Momentum and Angular Velocity

Lecture 78 - Solved Examples for Calculating Rate of Change of Angular Momentum and Torque

Lecture 79 - Understanding Demonstrations Shown Earlier using Equation of Motion

Lecture 80 - Understanding Demonstrations Shown Earlier using Equation of Motion: Euler Equations

Lecture 81 - Euler Equations, Solved Examples

Simple Harmonic Oscillator

Lecture 82 - Expanding Potential Energy about the Equilibrium Point and the Corresponding Force

Lecture 83 - Solving the Equation of Motion with Given Initial Conditions

Lecture 84 - Simple Harmonic Oscillator - Solved Examples

Lecture 85 - Representing Simple Harmonic Motion on a Phasor Diagram; Energy of an Oscillator

Lecture 86 - Simple Harmonic Oscillator - Solved Examples

Lecture 87 - Solving the Equation of the Motion with Constant Friction in the System

Lecture 88 - Harmonic Oscillator with Velocity-Dependent Damping (Heavy Damping)

Lecture 89 - Harmonic Oscillator with Velocity-Dependent Damping (Critical Damping)

Lecture 90 - Simple Harmonic Oscillator - Solved Examples

Lecture 91 - Harmonic Oscillator with Velocity-Dependent Damping (Light Damping)

Lecture 92 - Simple Harmonic Oscillator - Solved Examples (Light Damping)

Lecture 93 - Oscillations of an Undamped Harmonic Oscillator Subjected to an Oscillatory Force

Lecture 94 - Oscillations of a Forced Damped Harmonic Oscillator

Lecture 95 - Oscillations of a Forced Damped Harmonic Oscillator (cont.)

Lecture 96 - Energy and Power in a Forced Damped Harmonic Oscillator

Lecture 97 - Solved Examples (Forced Damped Harmonic Oscillator)

Motion in Non-inertial Frames

Lecture 98 - Equation of Motion in a Uniformly Accelerating Frame

Lecture 99 - Equation of Motion in a Uniformly Accelerating Frame; Solved Examples I

Lecture 100 - Equation of Motion in a Uniformly Accelerating Frame; Solved Examples II