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

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

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)

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)

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 = m 3 Unit prefixes: memorize the red ones in table 1-1 in book: centi, mille, micro, nano (pico), kilo, mega and giga

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

PHY 205 Ch1: Measurements and Vectors S5. Significant figures and order of magnitude Number:Sig figs Ambiguous so use sci. notation 1.024x x 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 = = = = =15.14 =15.1

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)

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

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):

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

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

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

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: