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1.4.1 Bearings

In the following subsections, we apply the vector ideas introduced so far to displacements and velocities. The examples will feature directions referred to points of the compass, known as bearings.

The direction of Leeds relative to Bristol can be described as ‘15° to the East of due North’, or N 15° E. This is an instance of a bearing. Directions on the ground are typically given like this, in terms of the directions North (N), South (S), East (E)
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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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Learning outcomes

On completion of this unit you should be able to:

  • convert a vector from geometric form (in terms of magnitude and direction) to component form;

  • convert a vector from component form to geometric form;

  • understand the use of bearings to describe direction;

  • understand the difference between velocity and speed;

  • find resultant displacements and velocities in geometric form, via the use of components.


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Introduction

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as shown in Section 2, in which you will also work with bearings.

This unit is an adapted extract from the Open University course
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Acknowledgements

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


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1.3.2 Search engines and subject gateways

Although both search engines and subject gateways will help you find the resources that you need, the types of information that you find will differ.

Search engines such as Google and Yahoo! search the internet for keywords or phrases, and then show you the results. These results are not mediated by the search engines, and therefore you need to use your own judgement on the reliability of the results. You may, for example, find websites written by experts, alongside websites written by
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4.3.2 Complementary currencies

Complementary currencies also demand a rethink of our economy, but have a more imaginative and radical edge. Because of the difficulties with conventional monetary systems, various alternatives are being tried. These are usually restricted to a particular group of people, and so are called ‘local’ or ‘complementary’ currencies. They are generally based in a local community and enable people to exchange goods and services without resorting to ‘traditional’ currency. Some are
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4.3.1 Ecological tax reforms

Communities such as Findhorn already behave as if natural resources need careful management: they work hard to reduce fossil fuel use. A central assumption of this way of thinking is that people need to root economies more locally (Figure 15). To see the same impulse spread through the mainstream economy would require that th
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2.2 Vibrant civil societies and a networked globe

One thing is common to all three attempts to find a route to a sustainable economy and society: in different ways they all assume that people will get actively involved in making human societies more sustainable. But this transformation will not take place through the corporate world's promises, by local protectionism, a return to ‘strong states’ or the publication of numerous indicators. Any of the three positions outlined above requires interactions and feedbacks created by a vibrant
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2.1 Political responses to climate change and the environment

Not for the first time in this book, you are faced with a term that is important but difficult to define precisely. Although the fact that plenty of people from different standpoints are using the term ‘globalisation’ is some measure of its importance, it can be confusing to find that there are different ways of framing what it means for humans and the environment today and in the future. In this section, the range of political responses to climate change and environment–economy interac
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4 The end of the last ice age: the Holocene

I have already noted that the great ice sheets took about 100,000 years to form and only about 10,000 years to decay. So what happened at the end of the last ice age? Figure 15 shows the EPICA ice core CO2 concentration and air temperature for the most recent 20 000 years, which is within the last ice
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1.4 An overview of the global energy budget

Figure 12 incorporates the additional factors considered in Section 1.3, including the non-radiative energy transfers across the surface-air boundary (green arrow). Essentially a more detailed version of Figure 7, this figure gives quantified estimates of the globally averaged energy budget for the whole Earth-atmosphere system, and its component parts. Question 3 should help you to find your way around Figure 12, and to draw together many of the key points developed so far in this chapter. M
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1.3.4 The role of convection in the atmosphere

We come now to our final refinement to the simple picture in Figure 7. Recall that the troposphere is heated from below, with temperature then falling with increasing altitude. This situation sets the scene for the onset of convection – the bulk flow or circulation of a fluid driven by differences in temperature. Convection in the atmosphere plays a vital role in two further mechanisms – quite apart from the emission of longwave radiation – whereby energy is transferred from the
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Learning outcomes

By the end of this unit you should be able to:

  • understand why systems thinking might be useful and know something about how it can be applied in the context of environmental responsibility;

  • describe the significance of environmental pragmatism and cognitive justice as tools for supporting environmental policy and action.


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References

Anon (2002) ‘The Windicator’, Windpower Monthly, January, p. 50.
Blake, William (1994) The Marriage of Heaven and Hell, Dover Publications.
Boyle, G. (1966, 2003) Renewable Energy, Oxford, Oxford University Press in association with the Open University.
BP (2002) BP Statistical Review of World Energy [on
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Acknowledgements

Author

This unit was prepared by Tom Power with guidance from Dr Arlene Hunter.

Tom Power is a lecturer in science education at The Open University. His research interests include teacher education in the global south (www.open.ac.uk/deep) and the CASE intervention. He has been a teacher and an advisory teacher in East Sussex and a specialist adviser to the TTA teacher research panel.

Dr Arlëne Hunter, Staff Tutor in Science in Ireland
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7.1 Climate models

To understand climate change it is necessary to construct climate models, to explore and predict interactions between different factors. Models are tested for accuracy against known sets of data, before being run forward to predict future changes.


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2 A 4.6 billion-year history

Climate change is a natural process of warming and cooling that has occurred all through the Earth's history. Throughout geological time there have been ‘hot-house’ periods and ice ages. In order to understand the current situation, it is necessary to have some sense of context and perspective, from historical and geological time-scales. The document below shows a chart showing a generalised temperature history of the Earth.

Click on 'View document' to see the chart

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1 Natural climate change?

The chart below shows a record of the global mean surface temperature of the Earth compiled for the past 140 years. Clearly there is an upward trend, but what does a chart like this really show?

5.3.4 Plan testing and validation

It is one thing to have a plan; it is another thing to have a plan that you can rely on to work. There is an old military maxim that ‘A plan only gets you into first contact with the enemy. After that, you fly by the seat of your pants’ (Anon). A 1993 IBM report on business continuity planning confirmed this when it revealed that ‘half of the plans failed completely or substantially when they were first tested’ (IBM, 1993, p. 5).

The IBM report identified three categories of pla
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