CLASSICAL DYNAMICS - 2024/5

Module code: MAT1036

Module Overview

Much of the way that mathematicians model the physical world today relies on the mathematical framework 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 to study the dynamics of particles and mechanical systems. This module provides a foundation for MAT3008 Lagrangian and Hamiltonian Dynamics.

Module provider

Mathematics & Physics

ROULSTONE Ian (Maths & Phys)

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

Independent Learning Hours: 64

Lecture Hours: 33

Seminar Hours: 5

Guided Learning: 15

Captured Content: 33

Semester 2

None.

Module content

Indicative content includes:

• Introduction: Vectors and vector differentiation. Frames of reference. Displacement, velocity, acceleration and momentum. Units.

• Forces: Newton’s laws of motion. Inertial reference frames. Examples of forces such as gravity, normal forces, friction, air resistance and spring tension. Dynamics under forces, e.g. projectile motion, simple harmonic motion and damped simple harmonic motion.

• Dimensional Analysis: Applications of dimensional analysis in physical real-world systems.

• Work and Energy: Work done. Kinetic and potential energy. Conservation of energy. Conservative forces and potentials.

• Systems of Particles: Conservation of momentum. Elastic and inelastic collisions.

• Angular motion: Polar coordinates. Angular momentum and torque. Central forces. Circular motion.

• Non-inertial reference frames (if time permits): Newton’s second law in accelerating reference frames. Rotating reference frames. Coriolis and centrifugal forces.

Assessment pattern

Assessment type Unit of assessment Weighting
Coursework Assessed Coursework 1 5
Coursework Assessed Coursework 2 10
Coursework Assessed Coursework 3 10
Examination End-of-Semester Examination (2 hours) 75

N/A

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• Understanding of subject knowledge, and recall of key definitions and results in Classical Dynamics.

• The ability to identify and use the appropriate methods to solve real-world problems in Classical Dynamics.

Thus, the summative assessment for this module consists of:

• Three assessed courseworks, with the first coursework worth 5%, and the second and third courseworks each worth 10% of the module mark. The first coursework will correspond to Learning Outcomes 1 and 2. The second coursework will correspond to Learning Outcomes 3 and 4. The third coursework will correspond to Learning Outcomes 5 and 6.

• A synoptic examination (2 hours), worth 75% of the module mark, corresponding to all Learning Outcomes 1 to 6.

Formative assessment

Students will receive formative feedback at biweekly seminars on problem sheets, provided to students in advance and designed to consolidate student learning.

Feedback

Students will receive feedback on the three assessed courseworks. The feedback is timed such that the feedback from the three assessed courseworks assists students with preparation for the synoptic examination. This feedback is complemented by verbal feedback at biweekly seminars and at office hours.

Module aims

• This module aims to (1) Introduce students to the mathematical concepts and results in Classical Dynamics including Newton's laws of motion, forces, work and energy, dimensional analysis and reference frames and (2) to enable students to use Newton's laws to analyse physical real-world problems, and solve the resulting ordinary differential equations of motion and interpret the solutions.

Learning outcomes

 Attributes Developed 001 Students will understand the concepts of force and momentum. They will understand Newton's laws of motion and be able to apply them to simple mechanical systems. KC 002 Students will be able to calculate simple solutions of the equations of motion, such as projectile motion and the motion of a mass on a spring. KC 003 Students will use dimensional analysis to identify parameters in simple physical real-world systems. KCT 004 Students will understand the concepts work and power, and kinetic and potential energy. They will be able to calculate the work done by a force using line integrals. KC 005 Students will be able to calculate the dynamics of collisions for systems of particles. KC 006 Students will understand the concepts of torque and angular momentum. They will be able to apply Newton's laws of motion for angular motion in rotating systems. KC

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:

• Provide students with a thorough introduction to Classical Dynamics, including applications of Newton's laws of motion in a variety of physical real-world problems.

• Provide students with experience of methods used to understand and solve real-world problems in Classical Dynamics, and interpret the resulting solutions.

The learning and teaching methods include:

• Three one-hour lectures per week for eleven weeks, in which students will be encouraged to take lecture notes to facilitate their learning and engagement with the module material. These lectures provide a structured learning environment and opportunities for students to ask questions and to practice methods taught.

• Five seminars for guided discussion of solutions to problem sheets (provided to students in advance) to reinforce their understanding and guide their learning.

• Three assessed courseworks to provide students with further opportunity to consolidate learning. Students receive feedback on these courseworks as guidance on their progress and understanding.

• Lectures may be recorded or equivalent recordings of lecture material provided. These recordings are intended to give students an opportunity to review parts of lectures which they may not fully have understood and should not be seen as an alternative to attending lectures.

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.

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

Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourceness and Resilience, and Sustainability. This module is designed to allow students to develop knowledge, skills and capabilities in the following areas:

Digital Capabilities: The SurreyLearn page for MAT1036 features a dynamic discussion forum where students can pose questions and engage with others using e.g. LaTeX and MathML tools. This enhances their digital competencies while facilitating collaborative learning and information sharing.

Employability: The module MAT1036 equips students with skills which significantly enhance their employability. The mathematical proficiency gained hones critical thinking and problem-solving abilities. Students learn to interpret and evaluate physical real-world problems, model these mathematically using ordinary differential equations, and hence deduce and interpret solutions. Mathematical modeling is a highly sought after skill in many professions.

Global and Cultural Capabilities: Student enrolled in MAT1036 originate from a variety of countries and have a wide range of cultural backgrounds. Students are encouraged to work together during problem-solving teaching activities in seminars and lectures, which naturally facilitates the sharing of different cultures.

Resourcefulness and Resilience: MAT1036 is a module which demands the ability to understand physical real-world problems, formulate and solve these complex problems mathematically, and interpret the results. Students will gain skills in analysing real-world problems using creative and lateral thinking, and will complete assessments which challenge them and build resilience.

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 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

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 2024/5 academic year.