2005/06 Undergraduate Module Catalogue

MATH2591 Dynamics of Particles and Rigid Bodies

10 creditsClass Size: 200

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2005/06

Pre-requisites

MATH1382 or MATH1410 or equivalent.

This module is approved as an Elective

Objectives

To explore the dynamics of bodies which are modelled as particles. To introduce the idea of a rigid body and determine its dynamics using the principle of linear momentum and the conservation of energy. On completion of this module, students should be able to: (a) solve a variety of problems in inertial frames; (b) solve a variety of problems of motion under a central force; (c) apply concepts of rigid-body dynamics, culminating with energy principles, to mechanical problems

Syllabus

This module is a natural follow on from MATH 1382 and is concerned with the dynamics of both particles and rigid bodies. In the first part there are more sophisticated illustrations of particle motion in one and two dimensions including planetary motion where Kepler?s three observational laws are derived from basic principles. The second part is concerned with the idea of a rigid body having finite size and a centre of mass. Its motion can be regarded as the motion of the centre of mass together with rotation about that point. The principle of linear momentum (essentially Newton's second law) describes the motion of the mass centre whereas conservation of energy provides a second equation for problems in which mechanical energy is conserved. Topics covered include: Inertial frames and rotating axes: angular velocity, accelerating and rotating axes, inertial forces, bead on a rotating circular wire. Motion in 2-D: motion under a central force, angular momentum, planetary motion, conics, orbit equation, Kepler?s laws. Dynamics of rigid bodies: centres of mass, moments and couples, reduction of systems of forces to force and a couple, 2-D statics, toppling and sliding. Rigid-body rotation: about a fixed axis with speed and kinetic energy. Moments of inertia about an axis through a fixed point, and centre of mass. Perpendicular- and parallel-axis theorems. Energy: potential energy of a rigid body, translational and rotational components of Kinetic energy, energy equation and conditions for its validity; applications.

Teaching methods

Lectures (22 hours) and tutorials (11 hours).

Methods of assessment

15% coursework, 85% 2 hour written examination at end of semester.

Reading list

The reading list is available from the Library website

Last updated: 13/05/2005

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