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Physics 218 Lecture 18

Physics 218 Lecture 18. Dr. David Toback. Checklist for Today. Things that were due Monday : Chapter 9 HW on WebCT Things that are due yesterday for Recitation Chapter 10 problems Things due Today: Read Chapters 12 & 13 Things due next Monday Chapter 10 in WebCT. The Schedule.

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Physics 218 Lecture 18

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  1. Physics 218Lecture 18 Dr. David Toback Physics 218, Lecture XVIII

  2. Checklist for Today • Things that were due Monday: • Chapter 9 HW on WebCT • Things that are due yesterday for Recitation • Chapter 10 problems • Things due Today: • Read Chapters 12 & 13 • Things due next Monday • Chapter 10 in WebCT Physics 218, Lecture XVIII

  3. The Schedule Rest of this Week: (3/24) • Lecture on Chaps 12 & 13 Next Week (3/31) • Mon: Chapter 10 & 11 due material in WebCT • Tues: Second lecture on Chaps 12 & 13 • Wed: Recitation on Chapters 12 & 13, Lab • Reading for Thurs: Chapters 14-16 • Thurs Lecture: Chap 14 Week after that (4/7) • Mon: Chapter 12 & 13 due material in WebCT • Tues: Second Lecture on Chap 14 • Wed: Recitation on Chap 14, Lab • Thurs Lecture: Chap 15, Part 1 Week of 4/14 • Monday: Chapter 14 due in WebCT • Tues: Exam 3 (Chaps 10-13) • Wed: Recitation on Chap 15, Lab • Thurs: Lecture on Chap 15, Part 2 Physics 218, Lecture XVIII

  4. Overview • Chapters 12-16 are about Rotational Motion • While we’ll do Exam 3 on Chapters 10-13, we’ll do the lectures on 12-16 in six combined lectures • Give extra time after the lectures to Study for the exam • The book does the math, I’ll focus on the understanding and making the issues more intuitive Physics 218, Lecture XVIII

  5. Rotational Motion • Start with Fixed Axis motion • The relationship betweenlinearandangularvariables • Rotating and translating at the same time • First kinematics, then dynamics • just like earlier this semester Physics 218, Lecture XVIII

  6. Physics 218, Lecture XVIII

  7. Overview: Rotational Motion • Take our results from “linear” physics and do the same for “angular” physics • We’ll discuss the analogue of • Position • Velocity • Acceleration • Force • Mass • Momentum • Energy Physics 218, Lecture XVIII

  8. Rotational Motion • Here we’re talking about stuff that goes around and around • Start by envisioning: A spinning object like a car tire Physics 218, Lecture XVIII

  9. Some Buzz Phrases • Fixed axis:I.e, an object spins in the same place… an ant on a spinning top goes around the same place over and over again Another example: Earth has a fixed axis, the sun • Rigid body:I.e, the objects don’t change as they rotate. Example: a bicycle wheel Examples of Non-rigid bodies? Physics 218, Lecture XVIII

  10. Overview: Rotational Motion • Take our results from“linear” physics and do the same for “angular” physics • Analogue of • Position ← • Velocity ← • Acceleration ← • Force • Mass • Momentum • Energy Start here! Chapters 1-3 Physics 218, Lecture XVIII

  11. Axis of Rotation: Definitions Pick a simple place to rotate around Call point O the “Axis of Rotation” Same as picking an origin Physics 218, Lecture XVIII

  12. An Important Relation: Distance If we are sitting at a radius R relative to our axis, and we rotate through an angle q, then we travel through a distance l Physics 218, Lecture XVIII

  13. Velocity and Acceleration Physics 218, Lecture XVIII

  14. Motion on a Wheel What is the linear speed of a point rotating around in a circle with angular speed w, and constant radius R? Physics 218, Lecture XVIII

  15. Examples Consider two points on a rotating wheel. One on the inside (P) and the other at the end (b): • Which has greater angular speed? • Which has greater linear speed? b R1 R2 Physics 218, Lecture XVIII

  16. Angular Velocity and Acceleration Are w and a vectors? w and aclearly have magnitude Do they have direction? Physics 218, Lecture XVIII

  17. Right-Hand Rule Yes! Define the direction to point along the axis of rotation Right-hand Rule This is true for Q, wand a Physics 218, Lecture XVIII

  18. Uniform Angular Acceleration Derive the angular equations of motion for constant angular acceleration Physics 218, Lecture XVIII

  19. Rotation and Translation Objects can both translate and rotate at the same time. They do both around their center of mass. Physics 218, Lecture XVIII

  20. Rolling without Slipping • In reality, car tires both rotate and translate • They are a good example of something which rolls (translates, moves forward, rotates) without slipping • Is there friction? What kind? Physics 218, Lecture XVIII

  21. Derivation • The trick is to pick your reference frame correctly! • Think of the wheel as sitting still and the ground moving past it with speed V. Velocity of ground (in bike frame) = -wR => Velocity of bike (in ground frame) = wR Physics 218, Lecture XVIII

  22. Bicycle comes to Rest A bicycle with initial linear velocity V0(at t0=0) decelerates uniformly (without slipping) to rest over a distance d. For a wheel of radius R: • What is the angular velocity at t0=0? • Total revolutions before it stops? • Total angular distance traversed by the wheel? • The angular acceleration? • The total time until it stops? Physics 218, Lecture XVIII

  23. Show Show for constant acceleration that: Physics 218, Lecture XVIII

  24. Uniform Circular Motion • Fancy words for moving in a circle with constant speed • We see this around us all the time • Moon around the earth • Earth around the sun • Merry-go-rounds • Constant w and Constant R Physics 218, Lecture XVIII

  25. Uniform Circular Motion - Velocity • Velocity vector = |V| tangent to the circle • Is this ball accelerating? • Yes! why? Physics 218, Lecture XVIII

  26. Centripetal Acceleration • “Center Seeking” • Acceleration vector= V2/Rtowards the center • Acceleration is perpendicular to the velocity R Physics 218, Lecture XVIII

  27. Circular Motion: Get the speed! Speed = distance/time Distance in 1 revolution divided by the time it takes to go around once Speed = 2pr/T Note: The time to go around once is known as the Period, or T Physics 218, Lecture XVIII

  28. Ball on a String A ball at the end of a string is revolving uniformly in a horizontal circle (ignore gravity) of radius R. The ball makes N revolutions in a time t. What is the centripetal acceleration? Physics 218, Lecture XVIII

  29. The Trick To Solving Problems Physics 218, Lecture XVIII

  30. Banking Angle You are a driver on the NASCAR circuit. Your car has m and is traveling with a speed V around a curve with Radius R What angle, Q, should the road be banked so that no friction is required? Physics 218, Lecture XVIII

  31. Skidding on a Curve A car of mass m rounds a curve on a flat road of radius R at a speed V. What coefficient of friction is required so there is no skidding? Kinetic or static friction? Physics 218, Lecture XVIII

  32. Conical Pendulum • A small ball of mass m is suspended by a cord of length L and revolves in a circle with a radius given by r = LsinQ. • What is the velocity of the ball? • Calculate the period of the ball Physics 218, Lecture XVIII

  33. Exam 2 • Class average for the 2nd exam (including the 5 points) was 80.1% • Average for first two exams is a 78.7% • Straight scale for curve for now • Many have asked “should I q-drop?” • Talk to your advisor and read my FAQ! • Generic advice: Drop if you can’t keep up with the homework by yourself Physics 218, Lecture XVIII

  34. Next Week • Monday: Chapter 10 & 11 due material in WebCT • Tuesday: Second lecture on Chaps 12 & 13 • Wednesday Recitation: Recitation on Chapters 12 & 13 • Wednesday Lab: Elastic Collisions Physics 218, Lecture XVIII

  35. End of Lecture Notes Physics 218, Lecture XVIII

  36. Circular Motion Example A ball of mass m is at the end of a string and is revolving uniformly in a horizontal circle (ignore gravity) of radius R. The ball makes N revolutions in a time t. • What is the centripetal acceleration? • What is the centripetal force? Physics 218, Lecture XVIII

  37. Next Time • Exam 2 is Thursday! • Bonus Points for getting a 100 on the mini-practice exam BEFORE the in-class exam Next week: • Chapter 8HW due Monday morning • Lecture next Thursday will cover Chapters 9 and 10: • Reading questions due: Q10.7 & Q10.26 Physics 218, Lecture XVIII

  38. Computer Hard Drive A computer hard drive typically rotates at 5400 rev/minute Find the: • Angular Velocity in rad/sec • Linear Velocity on the rim (R=3.0cm) • Linear Acceleration It takes 3.6 sec to go from rest to 5400 rev/min, with constant angular acceleration. • What is the angular acceleration? Physics 218, Lecture XVIII

  39. Next Time • Read Chapter 10 • More on angular “Stuff” • Angular kinematics • Torque • Reading questions: Q10.7 & Q10.26 • HW7 Due Monday (released this afternoon) • Exam 2 next Thursday on Chapters 4-7 Physics 218, Lecture XVIII

  40. More definitions • Frequency = Revolutions/sec w radians/sec f = w /2p • Period = 1/freq = 1/f Physics 218, Lecture XVIII

  41. Motion on a Wheel cont… A point on a circle, with constant radius R, is rotating with some speed w and an angular acceleration a. What is the linear acceleration? Physics 218, Lecture XVIII

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