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# Introductory Physics - Physical Quantities, Units and Measurement

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Physical Quantities, Units and Measurement - An introduction for lower secondary science students

Physical Quantities, Units and Measurement - An introduction for lower secondary science students

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### Introductory Physics - Physical Quantities, Units and Measurement

1. 1. Introductory Physics Physical Quantities, Units and Measurement (Updated: 20150702)
2. 2. Statement of Copyright and Fair  Use The author of this PowerPoint believes that the  following presentation contains copyrighted materials  used under the Multimedia Guidelines and Fair Use  exemptions of U.S. Copyright law applicable to  educators and students. Further use is prohibited. If owners of images used in this presentation feel  otherwise, please contact the author and he will take  them down if other amicable resolutions cannot be  agreed upon. © Sutharsan John Isles 2
3. 3. Expected Prior Knowledge It is assumed that you know the following  sufficiently well. If you feel that you do not  know them sufficiently, please visit those topics  in your books before continuing further: Mathematical Symbols The Real Number System Fractions and Decimals Significant Figures Angles and Bearings Indices 3© Sutharsan John Isles
4. 4. 4 Terminology A feature a noticeable part of something http://simple.wiktionary.org/wiki/feature What do you notice about the two lines below? © Sutharsan John Isles
5. 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. 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. 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. 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
9. 9. 9 Terminology The following are subsets of physical  properties: Mechanical properties Electrical properties Thermal properties Optical properties © Sutharsan John Isles
10. 10. 10 Terminology A quantity something that can be quantified (given a  number to) A physical quantity a physical property that can be expressed in  numbers E.g. Length being quantified: 13 cm © Sutharsan John Isles
11. 11. 11 Units There are two common systems of units: SI units (Système International d’Unités) E.g. metre, kilogram, second The British engineering system (a.k.a.  imperial system of units) E.g. foot, pound, second © Sutharsan John Isles
12. 12. 12 Why SI Units? Two reasons: Facilitates international trade and  communications Facilitates exchange of scientific findings and  information © Sutharsan John Isles
13. 13. 13 Physical Quantities These may be divided into base quantities and derived quantities. Base quantities are expressed in base  units. Derived quantities are expressed in  derived units. There are seven base quantities and thus  seven base units. © Sutharsan John Isles
14. 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. 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. 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. 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. 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. 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. 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. 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
22. 22. 22 SI Derived Quantities & Units Derived units are defined as products of powers  of the base units. http://www.bipm.org/en/si/si_brochure/chapter1/1‐4.html There are derived units expressed only in terms  of base units. E.g. square metres [m2], metres per second [m/s],  etc. There are also derived units with special names,  usually names of scientists, and symbols for  their units. E.g. Newtons [N], Pascal [Pa], etc. © Sutharsan John Isles
23. 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
24. 24. Trivia Do you know the full names of scientists  after whom the following units were named? Newton Pascal Joule Watt Coulomb Volt Ohm 24© Sutharsan John Isles
25. 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. 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. 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. 28. Standard Form – Examples How do you express 80000 in standard form? Solution © Sutharsan John Isles 28 4 80000 8 10000 8 10 = × = ×
29. 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. 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. 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. 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
33. 33. 33 Scalar and Vector Quantities The formula for a vector quantity is designed  with the allowance for positive and negative  values and difference in meaning for each. Acceleration is a vector quantity. A negative acceleration is actually a deceleration. Negative values indicate “going in or doing the  opposite”. Can a scalar quantity have a negative value? © Sutharsan John Isles
34. 34. 34 Scalar and Vector Quantities Temperature is a scalar quantity. While temperatures may have negative values,  they do not represent a change in direction. A temperature reading at any point in time is a  static figure. © Sutharsan John Isles
35. 35. Precision and Accuracy The term precision refers to how consistently an  instrument measures something. Accuracy, on the other hand, refers to how  close the measured value is to the actual value. Thus, an instrument can be precise, but  inaccurate. E.g. A clock that is consistently one minute late at any  point in time. © Sutharsan John Isles 35
36. 36. Notes on Accuracy How accurate the reading is, is dependent  on the type of instrument being used. This  is referred to the degree of accuracy. It is important to keep in mind the  sensitivity and stability of the instrument  when measuring, especially in the case of  thermometers. These can affect accuracy  as well. © Sutharsan John Isles 36
37. 37. The Ruler Look at the ruler shown. What would you say is the degree of  accuracy of this instrument? © Sutharsan John Isles 37
38. 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. 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. 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. 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. 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. 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. 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. 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