# Engineering Mechanics

## Lecture notes

Introductory lecture - motion of a point in Cartesian and Cylindrical Coordinate [Video lecture] [Lecture notes][lecture notes (video)]

Path coordinate and radius of curvature [Video lecture] [Lecture notes][lecture notes (video)]

Index notation and motion of a moving frame [Video lecture] [Lecture notes][lecture notes (video)]

Motion of a particle with respect to a fixed reference frame [Video lecture] [Lecture notes][lecture notes (video)]

Kinematics of rigid body [Video lecture] [Lecture notes][lecture notes (video)]

Force, moment, momentum, moment of momentum and Euler Axioms [Video lecture][lecture notes][lecture notes video]

Equivalent force system and simplest resultant [video lecture][lecture notes][lecture notes video]

Work Energy Theorem [video lecture][lecture notes][lecture notes video]

Free body diagram [video lecture][lecture notes][lecture notes video]

Impulse, Angular impulse, Conservative force and dry friction [video lecture][lecture notes][lecture notes video]

Belt friction and some problems on friction [video lecture][lecture notes]

Problem solving [lecture video][lecture notes]

Intertial Tensor and coordinate transformation of inertia tensor [lecture video][lecture notes]

Principal Moment of inertia and Parallel axis theorem [lecture video][lecture notes]

Euler's equation [lecture video][lecture notes]

Balanced rotor and Work Energy principal for rigid bodies [lecture video][lecture notes]

Problem solving on dynamics [lecture video][lecture notes]

Gyroscopic moment and center of percussion [lecture video][lecture notes]

Impact [lecture video][lecture notes]

Problems on impact [lecture video][lecture notes]

Statics - 1 [lecture video][lecture notes]

Statics - 2 [lecture video][lecture notes]

Internal forces in beams [lecture video][lecture notes]

Variational mechanics - 1 (Hamiltonian) [lecture video][lecture notes]

Variational mechanics - 2 (Lagrangian) [lecture video][lecture notes]

Looking back at the course [lecture video][lecture notes]

## Syllabus

Introduction & Kinematics: Moving point in different coordinate systems; Rigid bodies; Translation and Rotation; Relative motion for translating systems; Angular velocity; General motion of a rigid body; General relative motion

Axioms and Force Systems: Mass and centre of mass; Resultant force systems; centre of parallel forces; Work, power and kinetic energy; Euler’s Axioms; Equations of Equilibrium; Impulse and Angular Impulse; Impulse-momentum relations; Dry friction; Gravitational force; Free body diagrams; Conservative forces; workless forces; Belt friction, thrust bearing & clutch. Central force motion.

Dynamics of a Rigid body: Inertia tensor; Principal axes; Angular Impulse-momentum relations; general equations of motion of a rigid body; motion of a rigid body with a fixed axis; Euler’s equations; work-energy relation; Balancing of rotors; Plane motion with examples; Centre of percussion; Impact of rigid bodies.

Statics: Equations of equilibrium; static determinacy; frames, mechanisms and constraints; Friction and impending motion (rolling and tipping); Journal bearing; Bars, beams and trusses.

Variational Mechanics: Hamilton’s principle; Lagrange’s equations; the principle of virtual work; potential energy & Stability.

## References

Dumir, P. C., Sengupta, S., and Veeravalli, S. V. “Engineering Mechanics”, Universities Press

Beer, F. P., Johnston, E. R. Jr., Cornwell, P. J., Self, B. P., Mazurek, D. F., and Sanghi, S. “Vector Mechanics for Engineers - Statics and Dynamics”

## Grading Policy

Major (40%), Minor (30%), Quiz (20%), Tutorial (10%).

3 quizzes (centrally) will be conducted and the best 2 will be considered for grading. Quiz dates: 27-11-2022, 07-01-2023, and 29-01-2023

There will be no re-quiz.

Re-minor will be held towards the end of the semester with the complete syllabus.

In case, a student fails to keep 75% attendance, one grade will be reduced.

For getting an 'E' grade, 75% attendance is mandatory.

## Minor solution

Solution of minor [solution]

## Course info

Credit: 4 Units (3-1-0)

Lectures: Monday (8:00 - 9:30 AM) and Thursday (8:00 - 9:30 AM) OR Monday (2:00 - 3:30 PM) and Thursday (8:00 - 9:30 PM)

Venue: LHC 114 (8:00 - 9:30 AM) OR LHC 111 (2:00 - 3:30 PM)

Instructor: Prof. S. Pradyumna and Prof. Souvik Chakraborty (Block IV, 342-C)

Teaching Assistants: Navaneeth N. (navaneeth.n@am.iitd.ac.in), Tapas Tripura (tapas.t@am.iitd.ac.in), Shailesh Garg (shailesh.garg@am.iitd.ac.in), Tushar (tushar@am.iitd.ac.in), Sawan Kumar (sawan.kumar@am.iitd.ac.in), Vagish Kumar (vagish.kumar@am.iitd.ac.in)

Course Objective: This is a fundamental course on Engineering Mechanics where the students are exposed to the concept of statics, kinematics, and dynamics.

Intended audience: First-year UG students