68414 Advanced Mechanics
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Credit points: 6 cp
Result type: Grade and marks
Requisite(s): (68201 Physics 2 OR 68037 Physical Modelling) AND (33230c Mathematics 2 OR 68038 Advanced Mathematics and Physics OR 33290 Statistics and Mathematics for Science)
The lower case 'c' after the subject code indicates that the subject is a corequisite. See definitions for details.
Description
This subject builds upon the foundation studies of mechanics as well as mathematical methods, undertaken in introductory subjects. The subject covers advanced topics of classical mechanics, such as dynamics in force fields, coupled oscillators, and rotational motion. The subject also provides an introduction to Lagrangian formalism in mechanics. The emphasis is on the development of advanced problem-solving skills.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | Develop problem solving skills in the area of statics and dynamics of particles and solid bodies, oscillating systems, motion in potential and force fields |
|---|---|
| 2. | Apply mathematical skills to understand mechanical systems, including analysis of rotational motion of solid bodies and Lagrangian method for mechanical systems |
| 3. | Develop problem solving presentation skills in a peer audience environment |
| 4. | Communicate physics concepts and problem solving arguments in a structured way |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Demonstrate coherent understanding of physics and related knowledge applied to diverse contexts. (1.1)
- Evaluate the reliability of scientific evidence and apply effective experimental design, analysis and critical thinking to predict the behaviour of real-world systems using physical models (2.1)
- Apply effective and appropriate communication methods for discussing physics concepts, data and analysis with diverse audiences. (5.1)
Contribution to the development of graduate attributes
1. Disciplinary knowledge
Develop an understanding of the essence and practical applications of physics, as well as application of mathematical modelling to analyse the motion of particles and bodies. Develop a critical thinking approach and ability to predict the behaviour of mechanical systems.
2. Research, inquiry and critical thinking
Develop problem solving, organisational and quantitative skills, for predicting analytically the behaviour of a physical system, specifying underlying assumptions. Ability to work efficiently within a scientific team.
5. Communication
Develop the required skills for professional communication of the solutions of physics problems in writing, as well as delivering professional presentations to the peer audience.
Teaching and learning strategies
Two 2-hour advanced learning sessions a week, combining the elements of a lecture and a workshop.
The tutorials combine the features of a lecture, outlining the key concepts of the relevant topics in mechanics, and explaining the problem-solving techniques, as well as of a practical workshop, targeting the development of problem-solving skills.
Regular assessbile assignments for homework serve to strengthen and assess problem-solving skills and mathematical methods. Successful training in problem-solving is crucial for the success in this subject.
The required learning materials will be provided at Canvas, but students are encouraged to consult the recommended literature for further self-study.
Content (topics)
The subject addresses a range of advanced topics in mechanics, and trains solid problem-solving skills in the classical areas of statics, kinematics and dynamics; energy and momentum conservation; rotational motion of solid bodies, and oscillations. The subject also introduces the basics of Lagrangian formalism, in application to classical mechanical problems. Finally, a brief introduction to special relativity theory is given.
A brief outline of the subject contents is as follows:
Introduction
Problem-solving basics, dimensional and qualitative analysis.
Statics
Translational and rotational equilibrium.
Dynamics
Advanced motion in 2D/3D, rotational kinematics, usage of polar coordinates.
Momentum and energy conservation
Conservation laws, elastic and inelastic collisions, motion with variable mass.
Oscillations
Harmonic motion, damped oscillations, driven oscillations, coupled oscillators.
Rotational motion
Angular momentum, moments of inertia, tensor of inertia calculations, rotational dynamics.
Lagrangian formalism
Lagrangian function, Euler-Lagrange equations, constraints, conservation of generalised momentum.
Introduction to special relativity
Postulates, Lorentz transformations, introduction to relativistic dynamics.
The required mathematical skills are also being addressed in parallel to the relevant mechanical problems.
Assessment
Assessment task 1: Problem-solving test
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge 2. Research, inquiry and critical thinking 5. Communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3 and 4 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1 and 5.1 |
| Type: | Exercises |
| Groupwork: | Group, group and individually assessed |
| Weight: | 10% |
| Criteria: | Marks will be awarded based on students' application of appropriate problem-solving strategies, argued and documented in a scientifically rigorous manner. |
Assessment task 2: Class Test 1
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge 2. Research, inquiry and critical thinking 5. Communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2 and 4 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1 and 5.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 30% |
| Length: | 110 minutes |
| Criteria: | Marks will be awarded based on students' application of appropriate problem-solving strategies, argued in a scientifically rigorous manner. |
Assessment task 3: Class Test 2
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge 2. Research, inquiry and critical thinking 5. Communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2 and 4 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1 and 5.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 30% |
| Length: | 110 minutes |
| Criteria: | Marks will be awarded based on students' application of appropriate problem-solving strategies, argued in a scientifically rigorous manner. |
Assessment task 4: Class Test 3
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge 2. Research, inquiry and critical thinking 5. Communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2 and 4 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1 and 5.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 30% |
| Criteria: | Marks will be awarded based on students' application of appropriate problem-solving strategies, argued in a scientifically rigorous manner. |
Minimum requirements
In order to pass the subject, the students must achieve an overall mark of at least 50%.
At least 40% success must be achieved with the class tests.
Recommended texts
- D. Morin, Introduction to Classical Mechanics, Cambridge University Press 2008 or earlier
- G.R. Fowles, Analytical Mechanics, Saunders 2004 or earlier edition
- V. Barger and M. Olsson, Classical mechanics: a modern perspective, McGraw-Hill 1995
- R.D. Gregory, Classical mechanics: an undergraduate text, Cambridge Univ. Press 2006
- H. Goldstein, Classical mechanics, Addison-Wesley 2001 or earlier edition