# CLASSICAL DYNAMICS - 2023/4

Module code: MAT1036

## Module Overview

Much of the way that mathematicians model the physical world today relies on basic concepts that were set out by Newton in the 17th century. In this module we take as our starting point Newton’s laws of motion and examine how they may be applied.

### Module provider

Mathematics & Physics

### Module Leader

ROULSTONE Ian (Maths & Phys)

### Number of Credits: 15

### ECTS Credits: 7.5

### Framework: FHEQ Level 4

### Module cap (Maximum number of students): N/A

## Overall student workload

Independent Learning Hours: 74

Lecture Hours: 33

Seminar Hours: 5

Guided Learning: 5

Captured Content: 33

## Module Availability

Semester 2

## Module content

Indicative content includes:

- Introduction. Vectors, vector differentiation. Frames of reference. Derived physical quantities (e.g. displacement, velocity, acceleration, momentum). Units.
- Newton’s laws of motion. Inertial reference frames. Examples of forces: gravity; friction; springs & tension. Dynamics under these forces, e.g. projectile motion, simple harmonic motion. Conservation of momentum.
- Dimensional Analysis and its application in physical problems.
- Energy and Work. Work done and its relationship to kinetic and potential energy. Conservation of energy. Conservative forces and potentials.
- Systems of particles. Elastic and inelastic collisions. Centre of mass, frames of reference and collisions.
- Angular Motion. Polar coordinates. Angular momentum. Central forces. Planetary orbits.
- Non-inertial reference frames. Rotating frames. Centrifugal force, apparent gravity, spinning tops. Coriolis force.

## Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

Coursework | Coursework 1 | 5 |

Coursework | Coursework 2 | 10 |

Coursework | Coursework 3 | 10 |

Examination | Exam (2 hours) | 75 |

## Alternative Assessment

N/A

## Assessment Strategy

The __assessment strategy__ is designed to provide students with the opportunity to demonstrate

- Understanding of and ability to interpret physical problems, and to translate them into a mathematical language.
- Subject knowledge through the recall of key concepts and their relation to Newton's laws.
- Analytical ability through the solution of unseen problems in the test and exam.

Thus, the

__summative assessment__for this module consists of:

- One two hour examination at the end of the semester; worth 75% module mark.
- Three courseworks, worth 5%, 10% and 10% module mark, respectively. The assessed courseworks will each consist of a sheet of questions covering the recent module content. A selection of these questions will need to be submitted for marking.

__Formative assessment and feedback__

Students receive written feedback via a number of marked coursework assignments over an 11 week period. In addition, verbal feedback is provided by lecturer/class tutor at seminars.

## Module aims

- introduce the basic concepts of classical dynamics including Newton's laws, forces, work and energy, dimensional analysis and reference frames.
- enable students to use Newton's laws to turn problems of the physical world into differential equations
- solve differential equations and physically interpret the resulting solution

## Learning outcomes

Attributes Developed | ||

1 | Understand the concepts of force, momentum, torque, angular momentum, work and power, kinetic and potential energy | K |

2 | Understand Newton's laws of motion and be able to apply them to simple mechanical systems | C |

3 | Calculate simple solutions to the equations of motion, such as projectile trajectories and the motion of a mass on a spring. Be able to calculate dynamics of collisions for systems of particles. | CT |

4 | Understand dynamics of non-inertial reference frame. Describe examples such as the Coriolis force; centrifugal force and apparent gravity | KC |

5 | Use dimensional analysis to identify parameters in simple situations. | CT |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

## Methods of Teaching / Learning

The __learning and teaching__ strategy is designed to give:

- A detailed introduction to classical dynamics, Newton's laws, forces and related concepts (work, energy, collisions and reference frames).
- Experience at methods of problem solving in classical dynamics

The

__learning and teaching__methods include:

- 3x1 hour lectures per week x 11 weeks, with lecture notes to supplement the lectures, as well as supplementary exercises and background reading for independent study
- 5x1 hour seminars guiding students through problem solving

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

## Reading list

https://readinglists.surrey.ac.uk

Upon accessing the reading list, please search for the module using the module code: **MAT1036**

## Programmes this module appears in

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

Mathematics with Statistics MMath | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics with Statistics BSc (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics BSc (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics MMath | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2023/4 academic year.