## MA105-4-SP-CO:Mechanics and Relativity

The details
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Current
Monday 13 January 2025
Friday 21 March 2025
15
22 May 2024

Requisites for this module
(none)
(none)
(none)
(none)

MA222, MA225

## Key module for

BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
MMATG198 Mathematics,
BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC G1F5 Mathematics with Physics (Including Foundation Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad),
MSCIG199 Mathematics and Data Science

## Module description

This module introduces Newtonian Dynamics and develops the application of simple mathematical ideas to study it.

## Module aims

The aims of this module are:

• To enhance the skills and knowledge of specialist mathematicians in the second year, in the context of fundamental physical ideas, which have been central both to the development of mathematics over the last three hundred years, to the analysis of aspects of modern technology, and to the understanding of the Universe.

## Module learning outcomes

By the end of this module, students will be expected to be able to:

1. Develop an understanding of the dynamical insights of Galileo.

2. Develop a good working knowledge of Newton’s law of motion.

3. Understand the equation of simple harmonic motion and write down its solution.

4. Analyse the motion of a simple pendulum for small and large displacements.

5. Understand the conservation of energy and momentum.

6. Understand central forces.

7. Understand special relativity.

## Module information

Indicative Syllabus

• Newton's Laws of Motion.

• Newton's Law of Gravitation. Hooke's law. Friction.

• Newton's Second Law as a differential equation.

• Constant acceleration problems in one, two and three dimensions. Projectiles.

• Simple harmonic motion. Damped simple harmonic motion.

• Definitions of work and energy and their relation to Newton's Laws of Motion.

• Conservative forces; potential energy.

• Conservation of Energy.

• Circular orbits for a single particle in a central field of force.

• Centrifugal force.

An important part of this module is for students to learn how to use Matlab to assist their investigations, to develop skills in writing laboratory reports and in working with a partner.

## Learning and teaching methods

Teaching in the School will be delivered using a range of face to face lectures, classes, and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.

## Bibliography*

The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.

## Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   Coursework 1
Coursework   Coursework 2
Exam  Main exam: In-Person, Open Book (Restricted), 90 minutes during Summer (Main Period)
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 90 minutes during September (Reassessment Period)

### Exam format definitions

• Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
• In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
• In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
• In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Coursework Exam
20% 80%

### Reassessment

Coursework Exam
20% 80%
Module supervisor and teaching staff
Dr Tao Gao, email: t.gao@essex.ac.uk.
Dr Tao Gao & Dr Amanatidis
maths@essex.ac.uk

Availability
Yes
No
No

## External examiner

No external examiner information available for this module.
Resources
Available via Moodle
Of 33 hours, 33 (100%) hours available to students:
0 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s), module, or event type.

Further information

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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