H201 Measurements - 1. Notes (1718) [For Upload]

Measurement CONTENT 1. Physical Quantities and SI Units 2. Errors and Uncertainties 3. Scalars and vectors LEARNING OUTCOMES Candidates should be able to: a. recall the following base quantities and their units: mass (kg), length (m), (s), current (A), temperature (K), amount of substance (mol). b. express derived units as products or quotients of the base units and use the named listed in ‘Summary of Key Quantities, Symbols and Units’ as appropriate. c. Use of SI base units to check homogeneity of physical equations. d. show an understanding and use the conventions for labeling graph axes and table columns as set out in the ASE publication Signs, Symbols and Systematics (The ASE companion to 16-19 Science, 2000). e. 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). f. make reasonable estimates of physical quantities included within the syllabus. g. distinguish between scalar and vector quantities, and give examples of each. h. add and subtract coplanar vectors. i. represent a vector as two perpendicular components. j. Show an understanding of the distinction between systemic errors (including zero error) and random errors. k. show an understanding of the distinction between precision and accuracy. l. assess the uncertainty in a derived quantity by simple addition of actual, fractional or percentage uncertainties or by numerical substitution (a rigorous statistical treatment is not required). Physics Books for further reading : Physics for Scientists and Engineers. Serway. College Physics. Sears and Zemansky. Physics. Robert Hutchings. Physics. Tom Duncan.

1.0 Quantities and Units The science of physics is based upon taking measurements. All scientific theories and laws must be tested experimentally, and all experiments necessitate making measurements. 1.1 Physical Quantities: Base Quantities and Derived Quantities In Physics, quantities that can be measured are known as physical quantities. Each quantity consists of a numerical magnitude and a unit. (For vectors, there are directions as well.) Base quantities are physical quantities that are the most fundamental and they are independent of each other. The corresponding units for the base quantities are called the base units. It is important at all times to think of and write the value and the unit of any quantity together. The metric system of units was introduced at the time of the French Revolution to rationalise the chaos of units that existed at that time. It has been modified since then and now most countries use the metric system of units called the Systeme International (SI). The advantage of the SI system of units is that any quantity has only one unit in which it can be measured.  Quantities can be classified as base quantities or d