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UT Arlington PHYS 1443 - Lecture Notes

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PHYS 1443 Lecture #2AnnouncementsUncertaintiesSignificant FiguresSlide 5Dimension and Dimensional AnalysisSlide 7ExamplesSome FundamentalsSome More FundamentalsDisplacement, Velocity and SpeedCoordinate SystemsDifference between Speed and VelocityWednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat1PHYS 1443 Lecture #2Wednesday, Aug. 25, 2004Venkat1. Dimensional Analysis2. Fundamentals3. One Dimensional Motion•Displacement•Velocity and Speed•Acceleration•Motion under constant accelerationWednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat2Announcements•Homework #2 is due 1pm, Wednesday, September 1st 2004•Reading assignment is–Appendix A–Appendix B•Quiz on September 1st will cover both appendicesWednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat3Uncertainties•Physical measurements have limited precision, however good it is, due to:–Number of measurements –Quality of instruments (meter stick vs micro-meter)–Experience of the person doing measurements–Etc–In many cases, uncertainties are more important and difficult to estimate than the central (or mean) valuesStat.{{Syst.Wednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat4Significant Figures•Significant figures denote the precision of the measured values–Significant figures: non-zero numbers or zeros that are not place-holders•34 has two significant digits, 34.2 has 3, 0.001 has one because the 0’s before 1 are place holders, 34.100 has 5, because the 0’s after 1 indicates that the numbers in these digits are indeed 0’s.•When there are many 0’s, use scientific notation: –31400000=3.14x107–0.00012=1.2x10-4Wednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat5Significant Figures•Operational rules:–Addition or subtraction: Keep the smallest number of decimal place in the result, independent of the number of significant digits: 12.001+ 3.1= ???–Multiplication or Division: Keep the smallest significant figures in the result: 12.001 x 3.1 = ???, because the smallest significant figures is ?.Wednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat6Dimension and Dimensional Analysis•An extremely useful concept in solving physical problems•Good to write physical laws in mathematical expressions•No matter what units are used the base quantities are the same–Length (distance) is length whether meter or inch is used to express the size: Usually denoted as [L]–The same is true for Mass ([M])and Time ([T])–One can say “Dimension of Length, Mass or Time”–Dimensions are used as algebraic quantities: Can perform algebraic operations, addition, subtraction, multiplication or divisionWednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat7Dimension and Dimensional Analysis•One can use dimensions only to check the validity of one’s expression: Dimensional analysis–Eg: Speed [v] = [L]/[T]=[L][T-1]•Distance (L) traveled by a car running at the speed V in time T•L = V*T = [L/T]*[T]=[L]•More general expression of dimensional analysis is using exponents: eg. [v]=[LnTm] =[L]{T-1] where n = 1 and m = -1Wednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat8Examples•Show that the expression [v] = [at] is dimensionally correct•Speed: [v] =L/T•Acceleration: [a] =L/T2•Thus, [at] = (L/T2)xT=LT(-2+1) =LT-1 =L/T= [v]2m 2mmnvkra DimensionlessconstantLengthSpeed mmnmnTLTLLTL21rvvkra221r va1n  12nmn•Suppose the acceleration a of a circularly moving particle with speed v and radius r is proportional to rn and vm. What are n andm?Wednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat9Some Fundamentals•Kinematics: Description of Motion without understanding the cause of the motion•Dynamics: Description of motion accompanied with understanding the cause of the motion•Vector and Scalar quantities:–Scalar: Physical quantities that require magnitude but no direction •Speed, length, mass, height, volume, area, magnitude of a vector quantity, etc–Vector: Physical quantities that require both magnitude and direction•Velocity, Acceleration, Force, Momentum•It does not make sense to say “I ran with velocity of 10miles/hour.”•Objects can be treated as point-like if their sizes are smaller than the scale in the problem–Earth can be treated as a point like object (or a particle)in celestial problems•Simplification of the problem (The first step in setting up to solve a problem…)–Any other examples?Wednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat10Some More Fundamentals•Motions:Can be described as long as the position is known at any time (or position is expressed as a function of time)–Translation: Linear motion along a line–Rotation: Circular or elliptical motion–Vibration: Oscillation•Dimensions–0 dimension: A point–1 dimension: Linear drag of a point, resulting in a line  Motion in one-dimension is a motion on a line–2 dimension: Linear drag of a line resulting in a surface–3 dimension: Perpendicular Linear drag of a surface, resulting in a stereo objectWednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat11Displacement, Velocity and SpeedOne dimensional displacement is defined as: Displacement is the difference between initial and final potions of motion and is a vector quantity. How is this different than distance?ixxxfAverage velocity is defined as: Displacement per unit time in the period throughout the motiontxttxxviixffAverage speed is defined as: Spent Time TotalTraveled Distance TotalvCan someone tell me what the difference between speed and velocity is?Wednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat12Coordinate Systems•Makes it easy to express locations or positions•Two commonly used systems, depending on convenience–Cartesian (Rectangular) Coordinate System•Coordinates are expressed in (x,y)–Polar Coordinate System •Coordinates are expressed in (r)•Vectors become a lot easier to express and computeO (0,0)(x1,y1)=(r)r1x =How are Cartesian and Polar coordinates related?r =y1x1+x+y1y =cosr qsinr qtanq =( )2 21 1x y+11yxWednesday, Aug. 25, 2004 PHYS 1443, Fall 2004Venkat13Difference between Speed and Velocity•Let’s take a simple one dimensional translation that has many steps:Let’s call this line as X-axisLet’s have a couple of motions in a total time interval of 20 sec.+10m+15m-15m-5m -10m+5mTotal Displacement:0iifxxxxx iTotal Distance


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UT Arlington PHYS 1443 - Lecture Notes

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