Introductory Physics - Physical Quantities, Units and Measurement
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This document provides an introduction to physical quantities, units, and measurement in physics. It begins with definitions of key terminology like physical property, scalar and vector quantities, and standard form notation. It then discusses the International System of Units (SI) including the seven base units, common prefixes, and how to convert between multiples and submultiples of units. The document also covers derived SI units and examples of converting between derived units. It emphasizes the importance of understanding whether a quantity is scalar or vector.
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Introductory Physics - Physical Quantities, Units and Measurement
- 5. 5 Terminology A characteristic a typical feature of something http://simple.wiktionary.org/wiki/characteristic Compare the vehicles below. What is characteristic of both vehicles? A limousine An ordinary car © Sutharsan John Isles
- 6. 6 Terminology A property something that gives an object its characteristics Observe a piece of rubber band. What do you notice when it is pulled and released? What could you say is characteristic of objects made with the same type of material? Ultimately, what can you say is a property of rubber? Note: Rubber is not the only elastic material. (Spandex used in stretch jeans, is another example.) © Sutharsan John Isles
- 7. 7 Terminology Consider the following: You can feel the effects of a force (throwing you off) as you stand at the edge on a merry‐go‐round while it is spinning. You can see that one line is longer than the other. Physical something that is real in the sense that it can be seen, felt, etc. (i.e. not imaginary) and can thus be described in terms of what you observe or perceive http://en.wikipedia.org/wiki/Physical_property © Sutharsan John Isles
- 8. 8 Terminology A physical property a measurable (or perceived) property of something observable without having to change the composition or identity of that thing Examples of physical properties include the following: Length Mass Colour Smell Temperature Solubility Resistivity Conductivity © Sutharsan John Isles
- 14. 14 SI Base Quantities & Units Quantity Symbol Unit Abbreviation Length l metre m Mass m kilogram kg Time t seconds s Electric current I ampere A Thermodynamic temperature T kelvin K Amount of substance n mole mol Luminous intensity Iv candela cd http://www.bipm.org/en/si/si_brochure/chapter2/2‐1/ © Sutharsan John Isles
- 15. 15 Common SI Prefixes for Units Prefix Symbol Value Decimal Equivalent Scale (Short) peta P 1015 1 000 000 000 000 000 quadrillion tera T 1012 1 000 000 000 000 trillion giga G 109 1 000 000 000 billion mega M 106 1 000 000 million kilo k 103 1 000 thousand deci d 10-1 0.1 tenth centi c 10-2 0.01 hundredth milli m 10-3 0.001 thousandth micro μ 10-6 0.000 001 millionth nano n 10-9 0.000 000 001 billionth http://en.wikipedia.org/wiki/Long_and_short_scales © Sutharsan John Isles
- 16. 16 Multiples & Submultiples of SI Units – The Metre Multiples Submultiples Value Symbol Name Value Symbol Name 103 m km kilometre 10-1 m dm decimetre 106 m Mm megametre 10-2 m cm centimetre 109 m Gm gigametre 10-3 m mm millimetre 1012 m Tm terametre 10-6 m μm micrometre 1015 m Pm petametre 10-9 m nm nanometre http://en.wikipedia.org/wiki/Metre © Sutharsan John Isles
- 17. Conversion between multiples and submultiples of a base unit How do you convert from kilometres to metres? E.g. Convert 3 km to metres Solution 17 3 3 3 1000 1 3000 km m m = × × = × × = kilo metre © Sutharsan John Isles
- 18. Conversion between multiples & submultiples of a base unit How do you convert from metres to kilometres? E.g. Convert 70 m to kilometres Solution Begin with Recognise that ∴ 18 1 1000km m= 1 1 1000 m km= 1 70 70 1000 0.07 m km km = × = © Sutharsan John Isles
- 19. Conversion between multiples & submultiples of a base unit How do you convert from millimetres to metres? E.g. Convert 45 mm to metres Solution 19 1 45 45 metre 1000 1 45 1 1000 45 1000 0.045 mm m m m = × × = × × = = © Sutharsan John Isles
- 20. Conversion between multiples & submultiples of a base unit How do you convert from millimetres to centimetres? E.g. Convert 13 mm to centimetres Solution 20 1 13 13 metre 1000 1 1 13 1 100 10 1 13 10 1.3 mm m cm cm = × × = × × × = × = © Sutharsan John Isles
- 21. Conversion between multiples & submultiples of a base unit How do you convert from centimetres to millimetres? E.g. Convert 11.5 cm to millimetres Solution 21 1 11.5 11.5 metre 100 10 11.5 1 1000 1 115 1 1000 115 cm m m mm = × × = × × = × × = © Sutharsan John Isles
- 23. 23 SI Derived Quantities & Units Name Symbol Derivation Unit area A m × m m2 volume V m2 × m m3 speed, velocity v m ÷ s m/s acceleration a m/s ÷ s m/s2 density ρ kg ÷ m3 kg/m3 force F kg × m/s2 kg m/s2 = N pressure P N ÷ m2 N/m2 = Pa energy, work E, W N × m N m = J power P J ÷ s J/s = W electrical charge Q A × s A s = C electric potential difference V W ÷ A W/A = V electrical resistance R V ÷ A V/A = Ω moment of force (torque) τ (or M) N × m N m Note highlighted: Essence of derivation in each case is different. © Sutharsan John Isles
- 25. Conversion between multiples & submultiples of derived units How do you convert from squared centimetres to squared metres? E.g. Convert 8 cm2 to squared metres Solution 25 2 2 2 8 1 8 1 1 1 1 8 1 100 100 1 8 1 10000 0.0008 cm cm cm m m m m = × = × × × × × = × × = © Sutharsan John Isles
- 26. 26 Standard Form Also called the scientific notation, it is a way of representing numbers that are too large or too small. It is generally denoted as A × 10n, where 1 ≤ A < 10 and A c R and n is an integer. Depending on the requirement, A can be in any number of significant figures. © Sutharsan John Isles
- 27. Standard Form – Examples How do you express 0.0008 in standard form? Solution © Sutharsan John Isles 27 4 4 8 0.0008 10000 8 10 8 10− = = = ×
- 28. Standard Form – Examples How do you express 80000 in standard form? Solution © Sutharsan John Isles 28 4 80000 8 10000 8 10 = × = ×
- 29. Standard Form – Examples One of the best estimates to a number called the Avogadro’s Number is 602,214,141,070,409,084,099,072. If only the first 4 digits of this number were significant, how would you express this number in standard form? Solution © Sutharsan John Isles 29 23 602214141070409084099072 602200000000000000000000 6.022 10 ≈ = × http://www.americanscientist.org/issues/pub/an-exact-value-for-avogadros-number
- 30. 30 Scalar and Vector Quantities A scalar quantity has magnitude only and is completely described by a certain number with appropriate units. E.g. The distance is 7 m. Other examples of scalar quantities include mass, time and temperature. © Sutharsan John Isles
- 31. 31 Scalar and Vector Quantities A vector quantity has both a magnitude and a direction and can be represented by a straight line in a particular direction. E.g. The displacement is 5 m in the direction 045°. Other examples of vector quantities include velocity, force and momentum. © Sutharsan John Isles
- 32. 32 Scalar and Vector Quantities Why is it useful to understand which quantity is a vector and which quantity is a scalar? Consider the following formula where v is the final velocity, u is the initial velocity, a is the acceleration and t is the time for which the vehicle accelerated: v = u + at Solve for a when v = 10 m/s, u = 0 m/s and t = 2 s. Solve for a when u = 10 m/s, v = 0 m/s and t = 2 s. What do you observe about the answers? © Sutharsan John Isles
- 38. The Modern Vernier Callipers © Sutharsan John Isles 38 Image source: http://www.mitutoyo.co.jp/eng/useful/catalog/pdf/202.pdf Can you name the parts of this instrument?
- 39. The Modern Vernier Callipers © Sutharsan John Isles 39 Image source: http://www.mitutoyo.co.jp/eng/useful/catalog/pdf/202.pdf Inside jaws Outside jaws Screw clamp Vernier scale Main scale Depth probe
- 40. The Modern Vernier Callipers Invented by Pierre Vernier. The word “vernier” is now used to refer to certain movable parts of measuring instruments. Measures to an accuracy of 0.01 cm or 0.1 mm © Sutharsan John Isles 40
- 41. The Micrometer Screw Gauge © Sutharsan John Isles 41 Image source: http://www.mitutoyo.co.jp/eng/useful/catalog/pdf/50.pdf Do you think you can name the parts of this instrument?
- 42. The Micrometer Screw Gauge © Sutharsan John Isles 42 Rotating scale Thimble Ratchet Sleeve (with main scale) Frame Anvil Spindle Lock Image source: http://www.mitutoyo.co.jp/eng/useful/catalog/pdf/50.pdf
- 43. The Micrometer Screw Gauge The first micrometric screw was invented by William Gascoigne and the modern day MSG is a result of a series of adaptations by other inventors. Measures to an accuracy of 0.001 cm or 0.01 mm © Sutharsan John Isles 43
- 44. Comparing Accuracies Note: While the word “accuracy” has been used, it should be noted that no measurement can be said to be 100% accurate and there would always be a certain level of uncertainty. Device Accuracy Ruler 1 mm Vernier Calipers 0.1 mm Micrometer Screw Gauge 0.01 mm © Sutharsan John Isles 44
- 45. 45 Acknowledgement Created by: Sutharsan John Isles Mathematica fonts by Wolfram Research, Inc. References http://www.wikipedia.org http://www.bipm.org/en/home/ Giancoli, D.C. (2005). Physics: Principles with applications. Upper Saddle River, NJ: Pearson Education, Inc. Duncan, T. (2000). Advanced physics. London, UK: Hodder Murray. Chang, R. (1994). Chemistry. Hightstown, NJ: McGraw‐Hill, Inc. Hughes, E. (1888). Hughes electrical and electronic technology (10th ed.). Harlow, England: Pearson Education Limited Poh, L.Y. (2007). Effective guide to ‘O’ Level Physics (2nd ed.). Singapore: Pearson Education South Asia Pte Ltd. Billstein, R., Libeskind, S. & Lott, J.W. (2001). A problem solving approach to mathematics for elementary school teachers. (7th ed.). Reading, MA: Addison Wesley Longman © Sutharsan John Isles