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Physics 218 Lecture 19. Dr. David Toback. Checklist for Today. Things due Last Thursday: Read Chapters 12 & 13 Things that were due Monday : Chapter 10 & 11 HW on WebCT Things that are due tomorrow for Recitation Chapter 12&13 problems Read Lab hand out on webpage Things due next Monday

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## Physics 218 Lecture 19

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**Physics 218Lecture 19**Dr. David Toback Physics 218, Lecture XIX**Checklist for Today**• Things due Last Thursday: • Read Chapters 12 & 13 • Things that were due Monday: • Chapter 10 & 11 HW on WebCT • Things that are due tomorrow for Recitation • Chapter 12&13 problems • Read Lab hand out on webpage • Things due next Monday • Chapter 12 & 13 in WebCT Physics 218, Lecture XIX**The Schedule**This 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 Next week (4/7) • Mon: Chapter 12 & 13 material due in WebCT • Tues: Second Lecture on Chap 14 • Wed: Recitation on Chap 14, Lab • Thurs Lecture: Chap 15, Part 1 Week after that (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 XIX**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 XIX**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 XIX**Rotation and Translation**Objects can both translate and rotate at the same time. They do both around their center of mass. Physics 218, Lecture XIX**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 XIX**Derivation**The trick is to pick 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 XIX**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 XIX**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 XIX**Uniform Circular Motion - Velocity**• Velocity vector = |V| tangent to the circle • Is this ball accelerating? • Yes! why? Physics 218, Lecture XIX**Centripetal Acceleration**• “Center Seeking” • Acceleration vector= V2/Rtowards the center • Acceleration is perpendicular to the velocity R Physics 218, Lecture XIX**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 XIX**The Trick To Solving Problems**Physics 218, Lecture XIX**Banking Angle**You are a driver on the NASCAR circuit. Your car has mass 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 XIX**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 XIX**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 XIX**Exam 2**• Class average for the 2nd exam (including the 5 points) was 65% • Average for first two exams is a 69% • Note for students who didn’t take the mini-practice exam: • Exam 2 Average=51%!!! High score=75 • Two exam average = 60%, almost 20 points below those who took it • Planning on only a small curve for now, will decide after the 3rd exam Physics 218, Lecture XIX**Should you Q-drop?**• 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 XIX**Next Time**• Wednesday Recitation: Recitation on Chapters 12 & 13 • Wednesday Lab: Elastic Collisions • Thursday: Lecture on Chapter 14 • Monday: Chapters 12 & 13 due in WebCT Physics 218, Lecture XIX**End of Lecture Notes**Physics 218, Lecture XIX**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 XIX**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 XIX**Show**Show for constant acceleration that: Physics 218, Lecture XIX**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 XIX**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 XIX**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 XIX**More definitions**• Frequency = Revolutions/sec w radians/sec f = w /2p • Period = 1/freq = 1/f Physics 218, Lecture XIX**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 XIX

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