Spring semester

Unit(s) of Assessment	Weighting Towards Module Mark( %)
50 minute class test (test 1)	12.5
50 minute class test (test 2)	12.5
2 hour unseen examination	75
Qualifying Condition(s)     An aggregate mark of 40% is required to pass this module.

Much of the way that mathematicians model the physical world today relies on basic concepts that were set out by Newton in the 17^th century.  In this module we  take as our starting point Newton’s laws of motion and examine how they may be applied.

MAT1015 Calculus; MAT1016 Linear Algebra

This module introduces the basic concepts of classical dynamics and shows how to use them to build simple mathematical models of mechanical systems.

At the end of the module a student should:

    * Understand the concepts of force, momentum, torque, angular momentum, work and power, kinetic and potential energy

    * Understand Newton ’s laws of motion and be able to apply them to simple mechanical systems

    * Be able to calculate simple solutions to the equations of motion, such as projectile trajectories and the motion of a mass on a spring

    * Understand Newton ’s gravitational law, Kepler’s laws and their application to planetary motion

    * Be able to use dimensional analysis to identify parameters in simple situations.

Module Content

Introduction  Basic physical attributes (length, time, mass), derived physical quantities (e.g. velocity, acceleration, momentum, density); S.I. units.

Newton ’s laws of motion  The modelling of different types of force including gravity close to the Earth’s surface, contact forces, spring forces and tension. The dynamics of systems under these forces, for example, projectile motion with and without air resistances and  simple harmonic motion.

Conservation of momentum and collisional dynamics.  Work done and its relatiionship to kinetic and potential energy; conservation of energy.

Velocity and acceleration in polar coordinates. Torque and angular momentum.

Newton ’s gravitational law  and  planetary/satellite motion.

Dimensional analysis.

Teaching is by lectures and tutorials. Learning takes place through lectures, tutorials, exercises and background reading.

3 lecture/tutorial hours per week for 12 weeks.

Recommended reading:     A.P. French and M.G. Ebison, Introduction to Classical Mechanics, Kluwer (1986).     Background reading:     M.W. McCall, Classical Mechanics: a modern introduction, Wiley (2001).

September 10