PHY 101 1nd Edition Lecture 2 Chapter 1 Introduction Outline I Fundamentals II SI Units III History of Length Mass and Time IV Unit Conversion Chapter 1 Introduction Continued II Dimensional Analysis III Coordinate Systems a Cartesian Coordinates b Polar Coordinates IV Trigonometry a Pythagorean Theorem Current Lecture Unit Conversion Ex Convert m s mph 1000m s 1000m s 1mile 1609 m 3600s 1hr 1000x3600mile 1609hr 2000mph 1 3 Dimensional Analysis Derived an equation F mv3 r Is this correct Use dimensional analysis to check if it s correct Dimension nature of physical quantity o Ex Dimension of length can be expressed in meters feet or furlongs o Doesn t depend on the size of the quantity Velocity L T v Acceleration a v t L T T L T 2 only quantities with the same dimensions can be added subtracted Ex Time Length o Kinematic energy E 1 2 mv2 All energy has the same dimensions 2 o Dimensions E 1 2 mv These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute m v2 v L T M L T 2 E M L2 T2 Ex Suppose you have the equation x at3 Is this dimensionally correct o Left side of equation x L o Right side of equation at3 a t3 L T2 T3 L T L this equation is dimensionally incorrect 1 7 Coordinate Systems Describing the position of an object A point on a line 1 coordinate A point on a plane 2 coordinates o Cartesian coordinate system rectangular coordinates Has an origin a reference point Has a set of axes Has a labeled point relative to the origin and axes o Usually x y coordinates Polar coordinate system o Has an origin o In terms of r distance from the origin and angle of line with respect to the reference line is measured COUNTERCLOCKWISE o Labeled r To convert between Cartesian and Polar coordinates you need to use trigonometry 1 8 Trigonometry Ratios of lengths of the sides of a right triangle o sin y x opposite hypotenuse o cos x r adjacent hypotenuse o tan y x opposite adjacent to find the inverse angle use o sin 1 y r o cos 1 x r o tan 1 y x To convert to radians o 180 radian 3 14 radian o make sure your calculator is in the correct MODE o SEE APPENDIX A Pythagorean Theorem o Relationship between the lengths of the sides of a right triangle X2 y2 r2 Ex If r 2m and y 1 m find x X2 r2 y2 2 2 1 2 4 1 3 take the square root of 3 to find x X 1 732 m Using the values given in the previous problem find sin 1 y r sin 1 1 2 30
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