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Chapter 1
Essential Mathematics and Physics
Chapter contents
Matter, energy, power and heat
Units and prefixes used in radiography
Radiological units
Useful mathematics
Proportions and the inverse square law
Introduction
This chapter introduces and explores the principles of mathematics and physics that will make following chapters and the principles of radiography easier to understand. Although many of the concepts introduced in this chapter are only for revision, they are relevant to later chapters.
Matter, energy, power and heat
Matter
The entire world is made up of matter. Anything that occupies space can be termed ‘matter’. Matter is a collection of atoms, the basic building blocks. All matter has mass, that is, the measure of matter in an actual object. If gravity is involved, this mass is known as the weight of an object. If an object is placed in a lesser gravitational field, such as the atmosphere on the moon, the mass will remain the same, but the weight will decrease. The weight will also change if the object changes form, but, again, the mass will remain the same. An example of this is water in its three forms – solid (ice), liquid (water) and gas (steam). In these three forms, the mass is the same throughout, but the weight changes considerably.
| Matter | A collection of atoms and molecules |
| Mass | The measure of matter in an object |
| Weight | Mass under the influence of gravity |
Energy
The process of matter altering its state or form produces energy. Any object, however large or small, that is able to do ‘work’ is said to have energy. Energy has a number of different forms. Energy can be neither created nor destroyed, although it can change from one form to another (Table 1.1).
Total energy is measured in joules (J):
Table 1.1 Energy types, definitions and examples.
| Potential | The amount of work an object could do because of its position | An axe raised, ready to be brought down to chop, has potential energy |
| Kinetic | As an object leaves its state of potential energy, it gains kinetic energy | An apple gains kinetic energy as it falls out of a tree |
| Electrical | The movement of electrons inside a conductor after the application of a potential difference | The movement of electrons in a cable produces the electrical energy needed to make a bulb light up |
| Nuclear | Nuclear energy is the energy stored within the nucleus of an atom | This energy is formed when the nucleus of an atom is split |
| Thermal | The energy of a hot object. This is caused by the vibration of molecules within matter | A hot bath has faster moving molecules than a cool bath |
| Sound | The energy produced by sound vibrations | A musical instrument, engine noise, speech, thunder, diagnostic ultrasound, sonar |
| Chemical | The energy generated when a reaction occurs between two substances | Thermal energy produced when water is added to hot oil |
| Electromagnetic | Electric and magnetic energy moving in waves | X-ray production, radio waves, infrared light |
Energy conversion
As energy cannot be created or destroyed, it changes form, and this process is known as energy conversion.
In radiography, the X-ray tube is an example where energy is converted from one form (electrical) into other forms (X-rays, heat, light). We also use ultrasound where an ultrasound transducer converts electrical energy into sound ene...
