CLASSICAL DYNAMICS - 2019/0

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

DEANE Jonathan (Maths)

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

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

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.