APL100W25
APL 100: Engineering Mechanics (Winter semester 2025)
Course Info
Credit: 4 units (3-1-0)
Instructors: Prof. Rajdip Nayek
Course-related email: apl100w25@gmail.com
Class timings: Mon & Thu (2:00 - 3:30 PM) at LHC 108
Tutorial Session: Tue & Fri (9:00 - 10:00 AM)
Office Hours: Thu 4:00 - 5:00 PM (in Block 4 Room B-24)
Intended audience: All first-year BTech students
Course Policy (in pdf format): Course policy PDF
List of student IDs who were caught for getting proxy attendance here
Table of Contents
- Lecture Schedule
- Tutorial Schedule
- Course Content
- Course References
- Grading
- Lecture Attendance
- Miscellaneous Information
Lecture Schedule
| Sl# | Topics | Lecture Notes |
|---|---|---|
| 0. | Index notation / Einstein summation convention (ESC) | ESC (Self Study) |
| 1. | (Kinematics) Definitions, Reference frames, Coordinate systems Position vector, Velocity, and Acceleration of a Point/Particle |
Lecture 1 |
| 2. | (Kinematics) Kinematics of a Particle/Point in Cartesian, Cylindrical, and Path Coordinate System | Lecture 2-3 |
| 3. | (Kinematics) Motion of a Particle w.r.t. to Rotating Ref. Frame | Lecture 4 |
| 4. | (Kinematics) Velocity and Acc. Transfer Relationships in Multiple Reference Frames | Lecture 5 , Lecture Video |
| 5. | (Kinematics) Kinematics of rigid bodies | Lecture 6 |
| 6. | (Dynamics) Definitions of Force, Moment, COM, Linear Momentum, Angular Momentum, Euler Axioms | Lecture 7 |
| 7. | (Dynamics) Equivalent Force Systems, Wrench, Coplanar and Parallel Force systems | Lecture 8 |
| 8. | (Dynamics) Center of Parallel force systems, Distributed force systems, Newton’s 3rd law, Coulomb friction, and FBDs | Lecture 9 |
| 9. | (Dynamics) Support reactions, Momentum transfer rule, Euler’s second axiom about a moving reference point | Lecture 10 |
| 10. | (Dynamics) Inertia Tensor derivation and its properties, components of Inertia Tensor, Parallel Axis Theorem | Lecture 11 |
| 11. | (Dynamics) Inertia matrix for RBs with plane of symmetry, Transformation of Inertia Matrix, and Principal axes of Inertia matrix | Lecture 12 |
| 12. | (Dynamics) Inertia matrix relative to its body frame, Euler’s 2nd axiom in terms of Inertia tensor, Simplified cases of Euler’s axioms | Lecture 13, Lecture Video |
| 13. | (Dynamics) Applications of Euler’s axioms (Csys coincide with p-axes, rotation about body axis) through Examples - Part 1 | Lecture 14 |
| 14. | (Dynamics) Applications of Euler’s axioms (Plane 2D motion, Rotor balancing) through Examples - Part 2 | Lecture 15 |
| 15. | (Energy) Kinetic Energy of an RB, Work done by a force on moving a particle, Work-energy theorem for particle | Lecture 16 |
| 16. | (Energy) Mechanical power of an RB, Work-energy theorem for an RB, Conservative forces and Potential Energy | Lecture 17 |
| 17. | (Energy) PE + KE of an RB for Conservative Forces, Potential energy due to Gravity and Linear Spring, General Work-Energy Principle | Lecture 18, Lecture 18 video |
| 18. | (Impulse-Momentum relation) Impulse of a force/moment, Impulse-momentum relation, Angular impulse-angular momentum relation | Lecture 19 |
| 19. | (Collision of two RBs) Collision of two unconstrained RBs, Planar 2D collision, Collision of constrained RBs | Lecture 20 |
| 20. | (Statics) Static Equilibrium, Belt friction, Structures (intro) | Lecture 21 |
| 21. | (Statics) Analysis of Frames, Trusses (intro) | Lecture 22 |
| 22. | (Statics) Analysis of Truss: Method of joints and method of sections) | Lecture 23 |
| 23. | (Statics) Principle of Virtual Work for particles and rigid bodies | Lecture 24 |
| 24. | (Statics) Principle of Virtual Work for Conservative Forces | Lecture 25 |
Tutorial Schedule
-
Tutorial sheets will be uploaded on the course MOODLE (and this webpage) a week prior to the tutorial session.
- Each sheet will be divided into Part-A and Part-B:
- Part-A:
Solutions will be uploaded on MOODLE (and this webpage) along with the tutorial sheet.
Students are required to review both the problems AND their solutions before attending the tutorials.
Come prepared to discuss any doubts with the tutorial teachers. - Part-B:
This section contains the homework assignments.
Please do not ask tutorial teachers to provide solutions or hints for Part-B during the tutorials (or even outside of tutorials).
You are encouraged to work independently on these assignments to enhance your learning.
- Part-A:
- Additional Requirements:
Students must bring the relevant text/problem sets and a calculator to every tutorial session.
| Tutorial Questions | Tutorial (Part A) Solutions |
|---|---|
| Tutorial 1 | Solution |
| Tutorial 2 | Solution |
| Tutorial 3 | Solution |
| Tutorial 4 | Solution |
| Tutorial 5 | Solution |
| Tutorial 6 | Solution |
| Tutorial 7 | Solution |
| Tutorial 8 | Solution |
| Tutorial 9 | Solution |
| Tutorial 10 | Solution |
| Tutorial 11 | Solution |
All tutorials will be held in LH413.3
| Day | Faculty | Group |
|---|---|---|
| Monday | Prof. Arghya Samanta | 11-12 |
| Tuesday | Prof. Rajdip Nayek | 13-14 |
| Wednesday | Prof. Ritabrata Thakur | 15-16 |
| Thursday | Prof. Sabyasachi Chatterjee | 17-18 |
| Friday | Prof. Rajdip Nayek | 19-20 |
Course Content
-
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 center of mass; Resultant force systems; center of parallel forces; Work, power and kinetic energy; Euler’s Axioms; Equations of Equilibrium; Impulse and Angular Impulse; Impulse-momentum relations; Dry friction; Belt friction; Free body diagrams; Conservative forces; workless forces.
-
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 of rotation; Euler’s equations; work-energy relation; Balancing of rotors; Plane motion with examples; Impact of rigid bodies; Gyroscopic torque.
-
Statics: Equations of equilibrium; static determinacy; frames, mechanisms, and constraints; Friction and impending motion (rolling and tipping); Journal bearing; Bars, trusses, and beams.
-
Variational Mechanics: Hamilton’s principle; Lagrange’s equations; principle of virtual work.
Course References
This course is based on three textbooks:
- Course Textbook: “Engineering Mechanics” by P. C. Dumir, S. Sengupta, and S. V. Veeravalli, Universities Press, 2020.
- “Vector Mechanics for Engineers, Statics & Dynamics” by F. P. Beer et al. McGraw Hill, 7th Ed. 2005
- “Engineering Mechanics, Statics and Dynamics” by I.H. Shames, Prentice Hall, (Third or Fourth edition).
Use the last two reference books for practicing problem-solving. The notation/development followed in the reference books is very different from that of the main text and our lectures. It is mandatory that all students follow the notation used in lecture notes in all exams/quizzes/tutorial sessions. The use of any other notation leads to massive confusion and ambiguity. If you do not follow the notations used in the lecture notes, your work will not be evaluated.
Grading
A single make-up exam will be arranged for students who miss the minor exam due to medical reasons. Only medical certificates issued by the IIT Hospital will be accepted. The best two out of three quizzes will be counted. There will be no re-quiz for a missed quiz.
To earn an A grade, a student must have more than 80% marks AND must be within the top 10% of the class. Below 30% will be an F grade. All exams, quizzes, and final grading will be common for the Morning and Afternoon batches.
| Component | Scores | Solutions |
|---|---|---|
| Quiz #1 | 10 | Sol |
| Minor | 30 | Sol |
| Quiz #2 | 10 | Sol |
| Quiz #3 | 10 | |
| Major | 40 | [PartA Sol], [PartB Sol] |
| Re-Major | 40 | PartA Sol, PartB Sol |
| Tutorial Attendance | 10 | Tut Attd |
| Total | 100 |
Formula sheet for minor exam can be found here
Lecture Attendance
Students are required to maintain a minimum attendance of 75% in lecture classes. If a student’s lecture attendance falls below 75%, their grade in the course may be reduced, in line with the institute’s policy on attendance. Any student who is caught signing on the attendance sheet for another student in any lecture/tutorial session will get a zero on the tutorial attendance part (zero on 10%).
Miscellaneous Information
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Cases of plagiarism will be dealt with sternly, and all parties involved will receive identical punishment. Finding any evidence of plagiarism will lead to zero being awarded to all parties on that entire exam.
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Classroom doors close at 2:05 PM. If you arrive after the classroom door has been closed, do not knock and disturb, just leave.
-
All course-related material (including lecture notes) will be uploaded to this website and the Moodle course page. Some short-notice announcements may also be posted on this page. Your IITD email will be used to broadcast short-notice announcements. Students are advised to frequently (i) visit the Moodle course webpage, and (ii) their IITD mail inbox for the up-to-date information/activities related to this course.