MA1301: Classical Mechanics
School | Cardiff School of Mathematics |
Department Code | MATHS |
Module Code | MA1301 |
External Subject Code | 100400 |
Number of Credits | 10 |
Level | L4 |
Language of Delivery | English |
Module Leader | Dr Usama Kadri |
Semester | Spring Semester |
Academic Year | 2024/5 |
Outline Description of Module
Mechanics is a scientific discipline that is concerned with the characteristics and behaviour of a substance or physical objects when displaced, or experienced a force.
There are two broad objectives of the module. The first is to bridge between the physical world and the mathematical derivations we employ to better understand how things work, in classical mechanics. The second, is to develop critical thinking.
The module is strongly recommended to all those who intend to pursue further study in applied mathematics, as well as to those interested in the roots of mathematics.
Free Standing Module Requirements: A pass in A-Level Mathematics of at least Grade A
On completion of the module a student should be able to
On completion of the module the students will be familiar with the laws of motion, including circular and planetary motion. They will know how forces are used and be introduced to the concepts of energy and angular momentum and their conservation laws. The key feature of the module is that every new concept and technique is reinforced by fully worked examples, so that, at the end of the module, the students will be able to:
- Solve simple problems in particle kinematics involving the motion of a particle in space and time, including circular motion;
- Apply Newton’s laws of dynamics and the law of gravitation to determine the motion of a particle under the action of forces, including motion through a resisting medium, and simple oscillatory motions;
- Apply the concept of mechanical energy and its conservation law to calculate the motion and equilibrium positions of a particle in a conservative force field;
Use conservation of angular momentum and energy to determine the orbit of a particle in a central force field.
How the module will be delivered
You will be guided through learning activities appropriate to your module, which may include:
- Weekly face to face classes (e.g. labs, lectures, exercise classes)
- Electronic resources to support the learning (e.g. videos, exercise sheets, lecture notes, quizzes)
Students are also expected to undertake at least 50 hours of self-guided study throughout the duration of the module, including preparation of formative assessments.
Skills that will be practised and developed
Modelling of a physical system by differential equations;
Use of units of measurement;
Solving elementary differential equations;
Use of vector algebra and calculus;
Assessment Breakdown
Type | % | Title | Duration(hrs) |
---|---|---|---|
Exam - Spring Semester | 90 | Classical Mechanics | 2 |
Written Assessment | 10 | Coursework | N/A |
Syllabus content
- Units and dimensions (self-study)
- Introduction to kinematics
- Vectors: dot & cross products
- The motion of projectiles: 3D kinematics
- Uniform circular motion: centripetal forces & perceived gravity.
- Newton’s first, second, and third laws
- Weight, perceived gravity, and weightlessness
- Frictional forces
- Hooke’s law: simple harmonic oscillator
- Work, energy, and universal gravitation
- Resistive forces: viscosity, air drag
- Potential energy and harmonic oscillators
- Elastic and Inelastic Collisions
- Momentum of individual objects
- Rotating rigid bodies & angular momentum
- Orbits and escape velocity
- Conservation of Momentum & centre of mass
- Torque and physical pendulum
- Rolling motion, gyroscopes
- Static equilibrium, stability: rope walker
- Gases and incompressible liquids
- Hydrostatics, Archimedes’ principle, and fluid dynamics
- Harmonics & resonance