1. PHY 205 Ch1: Measurements and Vectors 1.Nature of Physics 2.Units (and standards) 3.Conversion of units 4.Dimensions of Physical Quantities 5.Significant Figures and Order of Magnitude 6.Vectors 7.General Properties of Vectors

2. PHY 205 Ch1: Measurements and Vectors S1. Nature of Physics (no exercise – replaces section 1 of book) A.Scientific Paradigm Abstract Realm: Theories, model s,… Reality: all phenomena in the Universe Theoretical Prediction Experimental Test

3. PHY 205 Ch1: Measurements and Vectors 1.Cont’d. Nature of Physics (no exercise – replaces section 1 of book) B.Physics: the science of fundamental processes Fundamental Science. Quantitative understanding of all processes involved Complex systems: Large number of processes involved. Fundamental Systems: Only a few processes at play Empirical Science (Based on observation, no quantitative “understanding” of the processes involved)

4. PHY 205 Ch1: Measurements and Vectors S2. Units and standards (added topic: standards) Measurements require material representation of concepts like distance, time etc. (ie physical quantities These material representations are called standards Example: bar with 2 scratches (obsolete now) for distance – called meter standard. Unit correspond to the number assigned to the standard e.g. 100 to meter standard gives cm 1 to standard gives the “ meter” unit. Systeme International of units: SI system Int. System (SI): m, s and kg. Fundamental (eg m ) or derived (eg N=kg m /s^2)

5. PHY 205 Ch1: Measurements and Vectors S3 Conversion of units So for example, to convert : 12 ft 2 Alternative scheme (not in book): just replace one unit by its value in terms of the new unit: 10 ft 3 = 10 (0.305 m) 3 = 0.0284 m 3 Unit prefixes: memorize the red ones in table 1-1 in book: centi, mille, micro, nano (pico), kilo, mega and giga

6. PHY 205 Ch1: Measurements and Vectors S4. Dimensions of Physical Quantities Dimensions L: length; T: mass: M Dimensions help check the validity of a result

7. PHY 205 Ch1: Measurements and Vectors S5. Significant figures and order of magnitude Number:Sig figs 10244 1024.036 0.0012414 0.00124105 102400Ambiguous so use sci. notation 1.024x10 5 4 1.02400x10 5 6 Learn rules Rules: X or / : quote result with nb of sig figs = smallest nb of sig figs but careful about exact numbers like 2 in 2  r: sig figs used in r or  are the only relevant ones And for + or - : answer has sig figs corresponding to number with fewest decimal places Examples:  r =2 x 3.14 x 2.1 =13.188 =13 15.332-0.16= 15.172 = 15.17 15.3-0.16=15.14 =15.1

8. PHY 205 Ch1: Measurements and Vectors S6/7. Vectors (slightly enhanced from book) Rectangular Coordinate systems: (1, 2 and 3 dimensions) The fact that we can erect a rectangular coordinate system in our universe is a hypothesis we make that has to be verified (and it is valid….most of the time)

9. PHY 205 Ch1: Measurements and Vectors S6/7. Vectors Definition of displacement: (1, 2 and 3 dim)

10. PHY 205 Ch1: Measurements and Vectors S6/7. Vectors Two representations of displacement (in 2 dimensions from now on): Component form: Graphical form (arrow with magnitude and direction):

11. PHY 205 Ch1: Measurements and Vectors S6/7. Vectors Properties of displacement: Addition Components arrows O x y

12. PHY 205 Ch1: Measurements and Vectors S6/7. Vectors Properties of displacement: Multiplication by number Components arrows O x y

13. PHY 205 Ch1: Measurements and Vectors S6/7. Vectors Properties of displacement: cont’d Subtraction Basis vectors

14. PHY 205 Ch1: Measurements and Vectors S6/7. Vectors Definition of vector: quantities that have all same properties as displacement Example velocity is displacement over time: