Physics 218 Lecture 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

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/R towards 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 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 Exam 2 next Thursday on Chapters 4-7 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

w radians/sec  f = w /2p More definitions Frequency = Revolutions/sec 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