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Introduction

This unit lays the foundations of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. In particular, this unit – Modelling static problems – considers why objects stay put.

Please note that this unit assumes you have a good working knowledge of vectors.

This is an adapted extract from the Open University course Author(s): The Open University

First-order differential equations

This unit introduces the topic of differential equations. The subject is developed without assuming that you have come across it before, but it is taken for granted that you have a basic grounding in calculus. In particular, you will need to have a good grasp of the basic rules for differentiation and integration.

This unit is an adapted extract from the course Mathematical methods and
Author(s): The Open University

Acknowledgements

All materials included in this unit are derived from content originated at the Open University.


Author(s): The Open University

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1.3: Summing vectors given in geometric form

The following activity illustrates how the conversion processes outlined in the preceding sections may come in useful. If two vectors are given in geometric form, and their sum is sought in the same form, one approach is to convert each of the vectors into component form, add their corresponding components, and then convert the sum back to geometric form.

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1.2: Converting to geometric form

You have seen how any vector given in geometric form, in terms of magnitude and direction, can be written in component form. You will now see how conversion in the opposite sense may be achieved, starting from component form. In other words, given a vector a = a 1 i + a 2 j, what are its magnitude |a| and direction θ?

The first part of this question is dealt with using Pythagoras’ Theorem: the magnitude of a v
Author(s): The Open University

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Acknowledgements

All materials included in this unit are derived from content originated at the Open University.


Author(s): The Open University

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Acknowledgements

The material acknowledged below is Proprietary and used under licence, see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Grateful acknowledgement is made to the following:

Figures

Figur
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1 A climate change icon

The polar bear has become an international climate change icon. But how much is known about this bear, its habitat and life? This unit will talk about the role of language, but by way of introduction how about the name of this bear? To me it is the polar bear; to a German it is an Eisbär (ice bear) and to a French person it is an ours blanc (white bear). In these three examples the bear is referred to as polar, white, or an ice bear – eminently sensible. The Latin name for th
Author(s): The Open University

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Introduction

The scientific theory of plate tectonics suggests that at least some of these Arctic lands were once tropical. Since then the continents have moved and ice has changed the landscape. This unit will concentrate on evidence from the last 800,000 years using information collected from ice cores from Greenland and Antarctica, and will use this evidence to discuss current and possible future climate. The cores show that there have been nine periods in the recent past when large areas of the Earth
Author(s): The Open University

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6.1 ‘I’, ‘we’ or ‘they’?

We must abandon the conceit that individual, isolated, private actions are the answer. They can and do help. But they will not take us far enough without collective action.

(Al Gore, 2007)

There are some things that we can do as individuals: making this an energy-efficient house and making smart transport choices. Then there a
Author(s): The Open University

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