RI Chap 1 Quantities and Measurement Lecture Notes

1 QUANTITIES & MEASUREMENT H2 Physics 9478 Content Page 1.1 Introduction 2 1.2 Quantities and Units 2 1.3 Prefixes, Standard Form and Significant Figures 6 1.4 Estimation 7 1.5 Measuring Instruments and Methods of Measurements 8 1.6 Systematic and Random Errors 8 1.7 Accuracy and Precision 10 1.8 Calculations of Uncertainties of Derived Quantities 11 1.9 Scalars and Vectors 16 1.10 Summary 21 Learning Outcomes Candidates should be able to: (a) recall and use the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol) (b) recall and use the following prefixes and their symbols to indicate decimal sub- multiples or multiples of both base and derived units: pico (p), nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T) (c) express derived units as products or quotients of the base units and use the named units listed in ‘Summary of Key Quantities, Symbols and Units’ as appropriate (d) use SI base units to check the homogeneity of physical equations (e) make reasonable estimates of physical quantities included within the syllabus. (f) show an understanding of the distinction between random and systematic errors (including zero error), which limit precision and accuracy (g) assess the uncertainty in derived quantities by adding absolute or relative (i.e. fractional or percentage) uncertainties or by numerical substitution (rigorous statistical treatment not required). (h) distinguish between scalar and vector quantities, and give examples of each (i) add and subtract coplanar vectors (j) represent a vector as two perpendicular components

Page| 2 1.1 Introduction Physics is an experimental science. Precise and accurate measurements enable the collection of useful experimental data that can be tested against theoretical predictions to refine the development of physical theories. Experimental evidence is the ultimate authority in discriminating between competing physical theories. Scientific knowledge continues to evolve as data from new or improved measurements helps us to better understand and explain physical phenomena. Measurements are subject to uncertainties , and it is important to estimate these to understand the reliability of the measurements. Error analysis involves estimating the uncertainties in measurements and finding ways to reduce them if necessary. In an experiment, the record of measurements made should include the estimated uncertainties and an analysis of the possible sources of errors with a discussion of steps taken to reduce the uncertainties should be documented . Doing this enables better conclusions to be drawn from the experimental data. The act of measurement affects the object being measured due to the interaction between the measuring device and the object. Common examples of this include measurements made using a thermometer, voltmeter or