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Physics 111: Elementary Mechanics – Lecture 1 Carsten Denker NJIT Physics Department Center for Solar–Terrestrial Research Week 1 Information Chapter Measurement Units Conversion of Units Chapter 1 Sections 1-7 3 Sections 1-8 Adding and multiplying vectors Unit vectors September 5, 2005 Center for Solar-Terrestrial Research Objectives By to the end of Week 1 you should be able List the SI units List typical prefixes of units Convert from the English to the metric system Add/subtract two vectors Explain the commutative and associative law Distinguish between scalar and vector product Work with trigonometric functions September 5, 2005 Center for Solar-Terrestrial Research Measurements Use laws of physics to describe many different physical systems Small set of simple laws Common language is mathematics Test laws by experiments Select smallest set of standards and derive other standards International Bureau of Weights and Measures (Paris), National Bureau of Standards, etc. Système Internationale (SI), International System of Units, metric system, or mksA system September 5, 2005 Center for Solar-Terrestrial Research SI Units Length meter m Mass kilogram kg Time second s Electric Current ampere A Thermodynamic Temperature kelvin K Luminous Intensity candela cd Amount of Substance mole mol Why should we care about SI units? Mars Climate Orbiter: http://mars.jpl.nasa.gov/msp98/orbiter September 5, 2005 Center for Solar-Terrestrial Research Prefixes for SI Units 10x Prefix x=18 15 12 9 6 3 2 1 September 5, 2005 exa peta tera giga mega kilo hecto deca Symbol E P T G M k h da GeV MeV keV Center for Solar-Terrestrial Research Prefixes for SI Units 10x Prefix Symbol x=-1 deci centi milli micro nano pico femto atto d c m µ n p f a -2 -3 -6 -9 -12 -15 -18 September 5, 2005 cm mm µA nm pm fm Center for Solar-Terrestrial Research Units Language is mathematics Equations Diagrams/Visualization Quantities have dimensions Results have units Consistency September 5, 2005 Center for Solar-Terrestrial Research Precision Measurements Uncertainties Calculation Absolute Percent Result can not be better than data Use scientific notation to show significant figures Examples 3.14 + 0.5 = 3.6 123,400,000 = 1.234 x 108 0.003 = 3 x 10-3 September 5, 2005 Center for Solar-Terrestrial Research Vectors AB displacement from A to B BC displacement from B to C AC displacement from A to C or sum or resultant of displacements AB and BC Quantities that add like this are vectors Vectors have magnitude and direction September 5, 2005 Center for Solar-Terrestrial Research Adding Vector Geometrically Subtraction d a b a b Commutative Law Associative Law September 5, 2005 a b b a a b c a b c Center for Solar-Terrestrial Research Trigonometric Functions Please bring calculator to lecture and recitation! September 5, 2005 Center for Solar-Terrestrial Research Adding Vectors by Components Components ax a cos and ay a sin Magnitude and Angle a a a 2 x September 5, 2005 2 y and tan Center for Solar-Terrestrial Research ay ax Multiplying Vectors Scalar Product a b ab cos September 5, 2005 Vector Product a b c and c ab sin Center for Solar-Terrestrial Research Questions How much would a cup of coffee cost at the Cafeteria in (a) Italian Lira and (b) in Euros? How old are you in seconds? How long is your way to school in lightyears? How would the introduction of the metric system affect business and daily life in the US? September 5, 2005 Center for Solar-Terrestrial Research