ASRJC Measurement Notes

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 / 8867 1-1 Additional Notes Topic 1: Measurement Content • Physical quantities and SI Units • Scalars and vectors • Errors and uncertainties Learning Outcomes: Candidates should be able to: Physical quantities and SI units: (a) recall the following base quantities and their SI units: mass (kg), length (m), time (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 units listed in ‘Summary of Key Quantities, Symbols and Units’ as appropriate. (c) use SI base units to check the homogeneity of physical equations (d) show an understanding of and use the conventions for labelling 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 Scalars and vectors: (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 Errors and uncertainties: (j) show an understanding of the distinction between systematic errors (includin g 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 addition of actual, fractional , percentage uncertainties or by numerical substitution (a rigorous statistical treatment is not required) * Swinfen, T.C., & Association for Science Education. (200). Signs, symbols and systematics: The ASE companion to 16 - 19 science, Hatfield, Herts: Association for Science Education Name: _______________________________ ( ) Class: 25 / ____

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 / 8867 1-2 Additional Notes A.1 Physical Quantities • Quantities that can be measured are known as physical quantities. A physical quantity consists of a numerical magnitude and a unit. For example, mass, m = 65.0 kg • A symbol may be used to represent a physical quantity. In the above example, the symbol “m” represents both the numerical magnitude and the unit. Hence, writing “Let the mass be m kilograms” is incorrect, and should be written as “Let the mass be m”. • A symbol divided by a unit represents a number. This is used in labelling of graph axes and for headings of table columns • Physical quantities can be classified into two categories: base quantities (see A.2) and derived quantities (see A.3). Consequently, units are also classified into two categories, base units and derived units. • S.I. units was adopted to put an end to more than a hundred years of disarray with a great number of units and unit systems. The S.I. system (metric system) makes a distinction between two classes of units: S.I. base units and S.I. derived units. I / A V / V 12.5 2.50 16.2 3.24 … … … … Nature of Science Physics is an experimental science. Precise 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 understand and quantify the natural world. Relating Science and Society Other sciences and society as a whole have benefited from the invention of many amazing measuring devices and techniques. Examples include • Modern engineering, in areas like design, construction, • Medical industry, where sophisticated devices like magnetic resonance imaging (MRI) scanners provide important information that aids in diagnosis and treatment decisions. A Physical Quantities and SI Units numerical magnitude physical quantity unit Unit Conversion disaster: http://mentalfloss.co m/article/25845/qui ck-6-six-unit- conversion- disasters In Singapore, the A*Star National Metrology Centre is the custodian of the national physical measurement standards, responsible for establishing and maintaining the nation’s highest level of physical measurement standards https://www.a- star.edu.sg/nmc/Ab out-NMC/National- Measurement- System I / A V / V Observe that the values in the columns do not have units as the units are in the column headings. More details on the labelling of graphs and tables will be given in the upcoming Practical Lecture. symbol

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 / 8867 1-3 Additional Notes A.2 Base Quantities and Base Units • A base quantity is one that is independent of other base quantities. • A set of 7 base (or fundamental) quantities were chosen for convenience, instead of necessity and all other units are derived from them. Their corresponding units are called base units and are independent of each other. • The seven base quantities in the S .I. convention and their corresponding base units are as below. Base Quantity Base unit Symbol for unit mass (m) kilogram kg length (l) metre m time (t) second s electric current (I) ampere A temperature (T) kelvin K amount of substance (n) mole mol luminous intensity (not in syllabus) candela cd • A mole of any pure chemical element or compound contains a definite number of molecules, the same number for all elements and compounds. • One mole is the amount of substance that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon−12. • The number of molecules in a mole is given by the Avogadro number, NA, and it is equal to 6.02 ×1023 mol−1. Check your understanding 1 Which of the following options contain all physical quantities? A gram, pressure, second B current, watt, hertz C power, velocity, density D ohm, ampere, kilogram Check your understanding 2 Which of the following options contain all units? A gram, watt, pressure B current, seconds, hertz C time, ampere, degrees D ohm, kilogram, meter Note the difference between quantities and units. Memorize Definition of the SI base units https://physics.nist. gov/cuu/Units/curre nt.html C D

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 / 8867 1-4 Additional Notes A.3 Derived Quantities and Derived Units • A derived quantity is a quantity obtained through a defining equation of base quantities. From the defining equation, a derived unit can be expressed as the product and/or quotient of the base units. • Other examples of derived quantities are shown below. • Note: o Units should be written in index form, e.g. m s−2 instead of m / s2. o There is also a space break between different unit. For example, in “m s−1” there is a space between “m” and “s−1”. Writing “ms−1” means “per millisecond”, and not “meter per second”. Example 1 Express the unit of force in terms of S.I. base units. derived quantity defining equation derived unit density density = mass volume 3 3 kg kg mm −= velocity velocity = displacement time 1m s− Derived quantity S.I. base units S.I. unit Name Symbol Area m2 - - Momentum kg m s−1 - - Pressure kg m−1 s−2 Pascal Pa Force kg m s−2 Newton N Work Done kg m2 s−2 Joule J Power kg m2 s−3 Watt W Electric Charge A s Coulomb C Potential Difference kg m2 A−1 s−3 Volt V Resistance kg m2 A−2 s−3 ohm  Frequency s−1 Hertz Hz Solution From Newton’s 2nd Law, resultant force = mass × acceleration S.I. base unit of force = S.I. ba