# CHAPTERS BY WACEK KIJEWSKI

# # Chapter 01 - A History of Measurement

Living in the twentieth century, we are familiar with the accurate measurement of time, distance, weight, volume, and so on. But imagine life in Stone Age times, many thousands of years ago, when there were no sophisticated instruments in use. Months were measured by noting the changing shape of the moon and then notching a piece of wood in order to record that change. The Egyptians several thousand years ago used a shadow stick to measure the passage of time. This gave rise to the sundial which was in universal use before clocks were invented in the thirteenth century. (Personal clocks did not come into use for another two hundred years!) The Egyptians also used the position of stellar constellations to draw up a calendar, and held celebrations when notable changes occurred.

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# # Chapter 02 - The "Power of Ten" Notation

*Basic and applied sciences are interwoven, they are like a tree whose roots correspond to basic science. If the roots are cut, the tree will degenerate. Basic science fosters a kind of attitude that will be most productive in whatever work will finally end up with...Training in basic science often produces the best candidates for applied work.*

Victor Weisskopf, the recipient of the International

Commission on Physics Education award, speaking

at the AAAS in Boston, 1993.

# # Chapter 03 - Physical Quantities, Units, Symbols and Prefixes

>Many experiments carried out in physics and chemistry are quantitative. They involve assigning numbers to length, mass, time, current, density etc. The thing which can be measured is called the physical quantity. Each quantity has its own symbol, a letter. Most quantities have units and each unit has a name and its own symbol. The symbol for a unit is either a letter or a series of letters.

# # Chapter 04 - The International System Of Units

What does it mean to take a measurement? It means that for a physical quantity we assign a certain number followed by the unit. The number expresses the ratio of the measured quantity to a certain standard and the unit is the name for the standard. Over the years, human beings have used many systems of units and many standards for physical and chemical measurements. Before 1960, three systems of units were in existence: cgs, mks and fps (the British, imperial or often called in USA, the inch-pound) systems.

# # Chapter 05 - The Characteristics of the SI System

**1.** The SI system is a decimal system with each component a multiple or submultiples of 10. All calculations and conversions are therefore simplified.

E.g: 1 km = 10^{3} m = 10^{5}cm = 10^{6} mm.

# # Chapter 06 - Conversion of Units

*It is a great nuisance that knowledge can be acquired by hard work.*

Somerset Maugham

The method presented below is based on knowledge of power of ten notation, knowledge of SI prefixes and manipulation of exponents. Once you have mastered these important skills, you will find out that this method employs logical steps that are easy to use in any combination of units. It is recommended instead of a unit factor method which is still widely used and which requires remembering unit factors. The unit factor method is inefficient and therefore, not suitable to use in more complex conversions encountered in physics.

# # Chapter 07 - Measurement: Accuracy, Significant Figures, Uncertainties

Science cannot proceed far without availing itself of measurement, i.e. reading numbers from an instrument designed for that purpose. Whatever you measure, the accuracy of your measurement is limited by the instrument you use and also by the measured object itself. Most instruments require an estimate of the fraction of the smallest division on a scale.

This means that your result is, to some extent, uncertain. If you are using a good quality instrument and the quantity that you are measuring is consistent, then your result may be quite accurate; i.e. the uncertainty of your result may be small. If your instrument is not of a very good quality or if the measured quantity varies, or if you are not careful in taking readings, then your result will be less accurate and the uncertainty of your result will be greater.

In either case there is nearly always some limitation in the number of meaningful digits when reporting the measured quantity. Let us consider an example relating to the measurement of length...

# # Chapter 08 - Types of Errors and Uncertainties in Measurement

The errors and uncertainties in measurement can be categorized as: systematic uncertainty, random uncertainty, mistake error and other errors.

Systematic uncertainty is related to the measuring instrument used. Each measuring instrument has its own, built-in uncertainty or error due to the way it is manufactured or calibrated. The accuracy of the measurement results in systematic error (SU) and is often referred to as the average uncertainty value (AUV) of the instrument. SUs have always the direction and often the same magnitude. In some cases corrections can be made to the data of the measurements to compensate for systematic errors. However, the best way of minimizing SU is to use better quality, more sensitive instruments, and you should not forget to check the zero error!

# # Chapter 09 - Compound Errors

When finding the sum of, or the difference between the values of two (or more) measurements, the absolute error of the result is found by taking the sum of the absolute errors of the measurement.

# # Chapter 10 - Estimation

We are surrounded by numbers. We count, measure, calculate, compute, estimate... Numbers quantify information; there are essential to understand facts events, processes, laws... Once information is quantified, they can carry specific meaning. They are becoming interesting or puzzling or shocking. We should develop a habit to use numbers in our judgment or assessment to verify information quickly and efficiently.

# # Chapter 11 - Presentation of a Laboratory Report

Generally there are some variations in the presentation of laboratory reports in different science subjects. However all laboratory reports have 5 parts:

A title, Some introductory remarks, A description of the procedure or method's used, A record of results, Concluding remarks.

# # Chapter 12 - Various Stages in Practical Work

*Sine experiential nihil sapienter sciri potest.
(“Without experience one cannot understand anything”)*

In scientific work you are often faced with problems to which you have to find the answer by doing experiments, i.e. by observations and measurements. The practical work should be carried out in an organized way.

# # Chapter 13 - Problems

Here are examples of some problems involving basic measurements. Remember, it is your task to design and plan the experiments.

# # Chapter 14 - Physical Constants

*π* = 3.14159

e = 2.71828

1 radian ==57.2958 degrees

# # Chapter 15 - Formulae for Area and Volume

area of a square | = a^{2} |

area of a rectangle | = a × b |

area of a triangle | = ½ (a × h) |