# Mechanics 1

## Unit aims

- To introduce the basic principles and laws of classical mechanics.
- To develop mathematical tools of kinematics and dynamics.
- To illustrate the ideas of mechanics by applying them to certain classical problems.

## Unit description

The development of the theory of mechanics is associated with many of the greatest names in mathematics, physics, and engineering. For example, problems in mechanics motivated Newton to invent calculus. Mechanics has developed continuously since then, and is now the foundation for all mathematical physics.

This unit is an introduction. It is designed to be accessible to motivated students with no previous exposure to mechanics. However, the material will progress fast beyond the A-levels, and the viewpoint based on calculus and linear algebra will be prevalent and essential. At the same time, the physics principles underlying not only mechanics, but the whole conceptual body of modern physics, from which such names as Galileo, Newton, and Einstein are inseparable, will be continuously emphasised throughout the course.

The unit begins with a brief discussion of the basic concepts of mechanics, such as the basic properties of space and time, inertial frame of reference and point particle. Newton's laws are introduced, followed by the laws of conservation of momentum, angular momentum, and energy, followed by the notion of work and conservative and conservative forces. Classical particle motion problems in one and two dimensions are studied in some detail.

## Relation to other units

This unit is an essential part of the Year 1 core curriculum. It uses the methods of Linear Algebra and Geometry and Calculus 1 (and partially some methods systematically taught later in Multivariable Calculus), as well as introduces some techniques of the analysis of ordinary differential equations (taught in Year 2: Ordinary Differential Equations 2).

## Learning objectives

- To create a solid foundation for understanding of basic principles of mechanics and some of its classical problems.
- To be able to use calculus and linear algebra to approach these problems.
- To open ways to further study of Applied Mathematics

## Transferable skills

Mechanics 1 is a pre-requisite for studying any further mathematical physics. Even if you plan to further specialise in Pure Mathematics or Statistics, Mechanics will provide you with a rich source of mathematical techniques and intuition for advancing in your studies.

## Syllabus

- Basic concepts of mechanics. Space, time, coordinates.
- Trajectory, velocity and acceleration.
- Newton's laws and the concept of force.
- Equation of motion, examples in 1D.
- Momentum. Impulse. Conservation of momentum.
- Angular momentum, torque, pendulum.
- Kinetic energy. Work done, power. Path-independence, potential energy, conservative forces.
- Oscillations and phase plane analysis
- Two-body problem and polar coordinates.

## Reading and References

There is no one standard text for the course. Online notes will be available on Blackboard. There are many excellent texts for this subject. The following books are suggested:

- D. Kleppner & Robert J. Kolenkow,
*An Introduction to Mechanics*, McGraw-Hill, 1973 - G.R. Fowles & G.L. Cassiday,
*Analytical Mechanics*, 6th ed. Saunders College Publishing (1993). This book covers the same ground as Kleppner and Kolenkow, except for special relativity. - Charles Kittel, Walter D. Knight, & Malvin A. Ruderman,
*Mechanics (Berkeley Course)*. This is a good physics book with less emphasis on mathematics than Kleppner and Kolenkow. - P. Smith, and R.C. Smith,
*Mechanics*. Chichester: Wiley, 1990.

**Unit code:** MATH11009

**Level of study:** C/4 (Honours)

**Credit points:** 10

**Teaching block (weeks):** 2 (13-24)

**Unit director:** Professor Richard Kerswell, FRS

**Lecturer:** Professor Richard Kerswell, FRS

## Pre-requisites

First teaching block of Linear Algebra and Geometry and Calculus 1.

## Co-requisites

None.

## Methods of teaching

Lectures, homework, problem-solving and tutorials. Motivation and independent reading.

## Methods of Assessment

The pass mark for this unit is 40.

The final mark is calculated as follows:

- 90% from a 1 hour 30 minute exam in May/June*
- 10% from selected homework questions.

**There are two parts to the exam; Part A consists of 5 shorter questions, Part B consists of 2 longer questions. ALL questions will be used for assessment. Part A contributes 40% and Part B contributes 60% of the overall mark for the paper.*

NOTE: Calculators are NOT allowed in the examination.

For information resit arrangements, please see the re-sit page on the intranet.

Please use these links for further information on relative weighting and marking criteria.

Further exam information can be found on the Maths Intranet.