Physics 121 A&C Lecture 5: Relative & Circular Motion • GRAB a WORKSHEET as You Enter • Webassign Homework 2nd Assignment – (121 HW 2) Due Wednesday Oct 8th @ 11 pm. • Midterm Exam # 1 Thursday October 9th – – – – Kane Hall (Rooms & Seats Assigned) at 5:00 pm 55% Multiple Choice, 45% Hand Graded Lecture 68%, Tutorial 20%, Lab 12% Draw or Select Pictures or Graphs, Explain Reasoning, Crunch Numbers – Topics and Equation Sheet Will Be Posted Soon 1 Today’s SmartPhysics Results • PreLecture: – Graph of Blue Ball x vs t in Red Ball Frame: 46 - 41% – Can Swimmer in Fast Stream Reach Pt X : 45 - 48% • Checkpoint: – – – – Dog & Girl on Moving Walkway, vDGrnd: 94 - 90% Dog & Girl on Moving Walkway, vDGirl: 61 - 55% Rock on String Path After String Breaks: 78 - 76% Survey: 56% Need Review, 29% Never Done • Your Concerns: Relative Velocity, Centripetal Acceleration, 2-D Relative Motion 2 Relative Motion • All Motion is Relative to Some Reference Point or Reference Frame. – No Such Thing as Absolute Motion. – Notation:  rAB  v AB  a AB Components x AB v ABx • First Subscript Represents Object of Interest • Second Subscript Represents Reference Point • Note That We Assume (As Galileo Did): Time is the Same for All Observers. – Not Correct for Extremely Fast-Moving Objects • Einstein’s Relativity, Near Speed of Light, Phys 123 • PreLecture 3 Begins With 1-D Case, as Does Our Worksheet. 3 Worksheet: Car & Truck • Describe the Motion of Each Vehicle. • Draw Locations of Both Vehicles in the Truck Reference Frame. • Q1: Sketch Average Velocity Vectors for Car for Each Interval in the Truck Reference Frame. A. B. C. D. E. • Explain Motion of Car Relative to Truck • Q2: Draw Instantaneous Velocity of Car @ t = 2 A. B. C. D. E. F. Zero • Now a Short Lecture Before Page 2. 4 Analyzing Relative Motion • Compare Motion of an Object Seen by Observers in 2 Different Reference Frames – For Easy Cases, Perhaps Just Guess • Systematic Approach: Begin With Position: – Draw Object & Observers at a Single Instant – Label Symbols on Object & Observers (Ref. Pts.) – Draw Position Vectors for the Object From Each Observer & for One Observer From the Other. • These Vectors Always Make a Triangle. Flattened if 1‐D – Write the Vector Addition Equation for the Triangle • Note Order of Subscripts – Equations for v & a Have Same Form and Subscript Order 5 Worksheet: Boat in River • Draw Position Vectors for:  Boat / Start rBS  Boat / Log rBL  Log / Start rLS • Repeat at a Later Time, Boat Halfway Across.  rBL  rLS • Write Equation For Position Triangle  rBS Clicker Q3 & Q4 6 • Q3: Which of These is Valid for the Relative Positions of Boat, Log, and Start?    A. rBS  rLS  rBL    B. rBL  rLS  rBS    C. rLS  rBS  rBL    D. rBS  rSL  rBL E. None F. All 7 Which of These is Valid for the Relative Positions of Boat, Log, and Start?    rBS  rLS  rBL • Q4: Which Triangle Best Represents the Relative Velocities? A. B. C. D. E. None F. All Clicker Q5 8 Up the River • You May Now Analyze with Components OR Laws of Trigonometry. – For Components, Choose x- & y- Axes – Law of Sines – Law of Cosines sin  A sin  B sin C   A B C A2  B 2  C 2  2 BC cos  A 9 Relative & Circular Motion URLs The classic video from 1960, Frames of Reference. Sure it is old, but check out the 50 year old technology! 30 minutes of relative motion demos. This is a must see for every student of physics! It is a bit ahead of us, and discusses forces and the law of inertia, which we will get to next week: http://www.archive.org/details/frames_of_reference Circular motion video analysis, roller coaster & more (some errors): http://www.youtube.com/watch?v=-G7tjiMNVlc Circular motion described: http://en.wikipedia.org/wiki/Circular_motion Less intimidating (but still essentially complete) treatment of circular motion: http://www.physicsclassroom.com/Class/circles/ 10