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UB PHY 101 - Dimentional Analysis

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PHY 101 1nd Edition Lecture 2 Chapter 1: Introduction OutlineI. FundamentalsII. SI UnitsIII. History of Length, Mass and TimeIV. Unit ConversionChapter 1: Introduction ContinuedII. Dimensional AnalysisIII. Coordinate Systemsa. Cartesian Coordinatesb. Polar CoordinatesIV. Trigonometrya. Pythagorean TheoremCurrent Lecture- Unit Conversion- Ex. Convert m/s  mph1000m/s= 1000m/s(1mile/1609 m)(3600s/1hr)=(1000x3600mile)/ 1609hr= 2000mph1.3 Dimensional Analysis- Derived an equation  F=(mv3)/r- Is this correct? Use dimensional analysis to check if it’s correct- Dimension: nature of physical quantityo Ex. Dimension of length can be expressed in meters, feet or furlongso Doesn’t depend on the size of the quantity- Velocity = L/T =[v]- Acceleration = [a] = [v]/[t] = (L/T)/T = L/T2- ***only quantities with the same dimensions can be added/subtracted- Ex. Time + Lengtho Kinematic energy = E=(1/2)mv2 **All energy has the same dimensions**o Dimensions: [E] = [(1/2)mv2]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)2E= M(L2/T2)- Ex. Suppose you have the equation x=at3. Is this dimensionally correct?o Left side of equation: [x] = Lo Right side of equation: [at3]= [a][t3]=[L/T2][T3]=L*T ≠ L  this equation is dimensionally incorrect1.7 Coordinate Systems- Describing the position of an object- A point on a line = 1 coordinate- A point on a plane = 2 coordinateso 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 axeso Usually (x,y) coordinates- Polar coordinate systemo Has an origino In terms of r (distance from the origin) and Θ (angle of line with respect to the reference line Θ is measured COUNTERCLOCKWISE!!o Labeled ( r, Θ)- To convert between Cartesian and Polar coordinates you need to use trigonometry1.8 Trigonometry- Ratios of lengths of the sides of a right triangleo sin Θ = y/x = opposite/hypotenuseo cos Θ = x/r = adjacent/ hypotenuseo tan Θ = y/x = opposite/ adjacent- to find the inverse/angle use:o Θ = sin-1(y/r)o Θ = cos-1 (x/r)o Θ = tan-1 (y/x)- To convert to radians:o 180° = Π radian = 3.14 radiano ** make sure your calculator is in the correct MODEo **SEE APPENDIX A**- Pythagorean Theoremo Relationship between the lengths of the sides of a right triangleX2 + 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 Θ.Θ = sin-1 (y/r) = sin-1(1/2) =


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UB PHY 101 - Dimentional Analysis

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