HCI 2023-24 H2 Physics Complete Lecture Notes

Hwa Chong Institution (College Section) H2 Physics C1 2023 1 Chapter 1 Measurement An indication of the range over which physical measurements are made.

Hwa Chong Institution (College Section) H2 Physics C1 2023 2 TOPIC 1: MEASUREMENT H2 Physics Syllabus 9749 SECTION I: Measurement Measurement Learning Outcomes Students 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 (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 addition of actual, fractional, percentage uncertainties or by numerical substitution (a rigorous statistical treatment is not required). Playlist of teaching videos and lecture examples: https://youtube.com/playlist?list=PL_b5cjrUKDlY0aQFdGFfOKuFJQTiXzIeY

Hwa Chong Institution (College Section) H2 Physics C1 2023 3 Contents TOPIC 1: MEASUREMENT ................................ ................................ ......................... 2 1.1 Introduction ................................ ................................ ................................ ........... 4 1.2 Physical Quantities and Units ................................ ................................ ................ 4 1.2.1 Base Quantities and Units ................................ ................................ ............. 5 1.2.2 Derived Quantities and Units ................................ ................................ ......... 5 1.2.3 Homogeneity of equations ................................ ................................ ............. 7 1.2.4 Prefixes ................................ ................................ ................................ ......... 9 1.3 Estimation ................................ ................................ ................................ ........... 10 1.4 Errors and Uncertainties ................................ ................................ ...................... 12 1.4.1 Significant Figures and Decimal Places ................................ ....................... 14 1.4.2 Combining Uncertainties ................................ ................................ ............. 15 1.4.3 Precision and Accuracy ................................ ................................ ............... 19 1.4.4 Systematic and Random Errors ................................ ................................ ... 21 1.5 Scalars and Vectors ................................ ................................ ............................ 26 1.5.1 Adding and Subtracting Coplanar Vectors ................................ ................... 26 1.5.2 Resolution of Vectors ................................ ................................ ................ 322 Appendix I International System of Units (SI) ................................ ............................... 35 Appendix II Summary of Key Quantity, Symbols and Units ................................ ....... 37 Appendix III SI Prefixes ................................ ................................ .............................. 39 Tutorial 1 Measurement ................................ ................................ ................................ .. 40 Self-Review Questions ................................ ................................ ................................ 40 Discussion Questions ................................ ................................ ................................ .. 42

Hwa Chong Institution (College Section) H2 Physics C1 2023 4 1.1 Introduction Measuring our observations objectively is an important task that differentiates science from the arts. The scientific method involves making observations that are repeatable by another person. For this reason, the study of physical quantities and their units is the starting point of our learning of science. 1.2 Physical Quantities and Units A physical quantity is a physical property that can be measured and/or calculated and expressed in numbers. For example, "length" is a physical quantity that can be expressed by stating a number and a measurement unit such as metres or inches. Hence the value of a physical quantity is expressed as a numerical value and a unit of measurement. For example, the length of a football field = 100 m This has a few implications. 1. Using the unit “metre” helps us to define a particular property of the football field – its length. Using other units could allow us to define other properties (for example, square metres describe the area) of a football field. 2. We can only compare propert ies of the same unit. Using the “metre” allows us to compare the length of one object with another. We cannot compare a “metre” with a “kilogram”. 3. The numerical value of the physical quantity is dependent on the unit it is expressed in. The length of the same football field above will have a value of 330 when expressed in the unit “foot”. Physical Quantity Numerical value Unit

Hwa Chong Institution (College Section) H2 Physics C1 2023 5 1.2.1 Base Quantities and Units Through the centuries, scientists in different parts of the world have used different units at different times to measure the same physical quantities. However standardised definitions and units are needed in the modern world. The current International System of Units a, universally abbreviated SI (from the French Le Système International d'Unités), is the modern metric system of measurement. Seven well-defined and independent base quantities are chosen. Their corresponding SI base units are indicated: Base Quantity SI Base Unit Name Symbol Name Symbol Mass m kilogram kg Length l metre m Time t second s Electric current I ampere A Thermodynamic temperature T kelvin K Amount of substance n mole mol Luminous intensity Iv candela cd Note: 1. The units, when written in full , are in small letters . Ampere and Kelvin are names of scientists. 2. The kilogram is the only SI unit with a prefix as part of its name and symbol. 3. Luminous intensity is not in the Learning Objectives(a) of the Syllabus. 4. Definitions of the units are not required in the Syllabus but are provided in Appendix I at the end of the lecture notes for your reference. SI base units were chosen based on their mutual independence. They are the simplest units that cannot be expressed in terms of other SI base units. 1.2.2 Derived Quantities and Units There are a lot of other physical properties that we come across in our daily lives. These quantities and units used scientifically are included in the SI as