NJC 2025 H2 Physics Quantities & Measurement (Student)

National Junior College Science Department | Physics 1 1. Quantities & Measurement Content Page 1.1 Physical Quantities and SI Units ................................ ................................ ................................ ........ 3 1.1.1 Importance of SI Base Units ................................ ................................ ............................... 3 1.1.2 Physical Quantities: Base Quantities and Derived Quantities ................................ .............4 Base Units ................................ ................................ ................................ .......................4 S.I. Derived Units ................................ ................................ ................................ ............5 1.1.3 Prefixes ................................ ................................ ................................ .............................. 7 1.1.4 Homogeneity of Physical Equations ................................ ................................ ...................8 Dimensional Consistency ................................ ................................ ................................ 8 Homogeneous equations ................................ ................................ ................................ .8 Reasonable estimations ................................ ................................ ................................ 10 1.2 Errors and Uncertainties ................................ ................................ ................................ .................. 11 1.2.1 Systematic Errors ................................ ................................ ................................ .............11 1.2.2 Random Errors ................................ ................................ ................................ .................12 1.2.3 Distinction between Systematic Errors and Random Errors................................ ..............13 1.2.4 Precision and Accuracy ................................ ................................ ................................ ....13 1.2.5 Experimental uncertainties ................................ ................................ ............................... 16 Expressing measurements with its uncertainty ................................ .............................. 16 Fractional and Percentage Uncertainties ................................ ................................ .......17 1.2.6 Consequential Uncertainty ................................ ................................ .............................20 Asymmetric Uncertainty ................................ ................................ ................................ .24 1.3 Scalars and vectors ................................ ................................ ................................ ......................... 25 1.3.1 Vector addition ................................ ................................ ................................ .................26 Sketching Techniques for Vector addition of vectors 𝑨 and 𝑩: ................................ .......26 1.3.2 Scalar multiplication of a vector ................................ ................................ .....................31 1.3.3 Vector subtraction ................................ ................................ ................................ ............32 Change in a vector ................................ ................................ ................................ ........32 Relative velocity ................................ ................................ ................................ ............34 1.3.4 Scalar Product of two vectors (dot product) ................................ ................................ ......36 Additional Reading Materials ................................ ................................ ................................ ................. 37 1. The Importance of Indicating Physical Units in Data ................................ ..............37

National Junior College Science Department | Physics 2 2. The importance of accounting for experimental uncertainty. ................................ ..38 Appendix ................................ ................................ ................................ ................................ ............... 39 Learning Objectives 1.1 Physical quantities and SI units (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. 1.2 Errors and uncertainties (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). 1.3 Scalars and vectors (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. All videos in this lecture notes can be found in this playlist:

National Junior College Science Department | Physics 3 1.1 PHYSICAL QUANTITIES AND SI UNITS 1.1.1 Importance of SI Base Units The International System of Units (SI) 1 is the globally accepted standard for measurement. It ensures that scientists and engineers around the world can communicate their findings accurately and consistently. Here are some key reasons why SI units are crucial: 1. Consistency: SI units provide a consistent framework for measurements, which is essential for comparing results from different experiments and studies. 2. Accuracy: Using standardized units reduces the risk of errors and misunderstandings in scientific communication. 3. Global Collaboration: SI units facilitate international collaboration in science, engineering, and industry, as everyone uses the same measurement system. 4. Education and Training: Teaching and learning are simplified when a single, coherent system of units is used. Case Study: Mars Climate Orbiter2 In 1999, NASA’s Mars Climate Orbiter mission failed because of a mix -up between metric and imperial units. The spacecraft was lost because one team used imperial units (pounds) while another used metric units (newtons) for a crucial calculation. This incid ent highlights the importance of using a standardized system of units to avoid costly mistakes. Self-study resources A SLS lesson on Physical Quantities and SI units https://for.edu.sg/01si 1 The International System of Units (SI) provides definitions of units of measurement that are widely accepted in science and technology. The International Bureau of Weights and Measures (BIPM) located in Sèvres near Paris, France has the task of ensuring world -wide uniformity of measurements and their traceability to the SI. A*STAR’s National Metrology Centre (NMC) is the national measurement institute of Singapore and it establishes and maintains measurement standards at the highest level of accuracy locally. 2 Read more about the importance of indicating physical units in the found in Page 38 below

National Junior College Science Department | Physics 4 1.1.2 Physical Qu