# CLASSICAL DYNAMICS - 2020/1

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

Module Leader

DEANE Jonathan (Maths)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 4

JACs code: G100

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

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 |
---|---|---|

School-timetabled exam/test | IN-SEMESTER TEST (50 MINS) | 25 |

Examination | EXAMINATION (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 (three of four best answers contribute to exam mark, with Question 1 compulsory) at the end of Semester 1; worth 75% module mark.

· In semester test worth 25% module mark.

__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 biweekly 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

Overall student workload

Independent Study Hours: 112

Lecture Hours: 33

Seminar Hours: 5

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.

Programmes this module appears in

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

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

Mathematics with Statistics MMath | 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 2020/1 academic year.