Physics 218 Lecture 19 Dr David Toback Physics

Physics 218 Lecture 19 Dr. David Toback Physics 218, Lecture XIX 1

Checklist for Today • Things due Last Thursday: – Read Chapters 12 & 13 • Things that were due Monday: – Chapter 10 & 11 HW on Web. CT • 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 Web. CT Physics 218, Lecture XIX 2

The Schedule This Week (3/31) • Mon: Chapter 10 & 11 due material in Web. CT • 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 Web. CT • 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 Web. CT • Tues: Exam 3 (Chaps 10 -13) • Wed: Recitation on Chap 15, Lab • Thurs: Lecture on Chap 15, Part 2 Physics 218, Lecture XIX 3

Overview • Chapters 12 -16 are about Rotational Motion • While we’ll do Exam 3 on Chapters 1013, 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 4

Physics 218, Lecture XIX 5

Overview: Rotational Motion – Position – Velocity – Acceleration – Force – Mass – Momentum – Energy ← ← ← Start here! Physics 218, Lecture XIX Chapters 1 -3 • Take our results from “linear” physics and do the same for “angular” physics • Analogue of 6

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 7

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 8

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) = -w. R Velocity of bike (in ground frame) = w. R Physics 218, Lecture XIX 9

Bicycle comes to Rest A bicycle with initial linear velocity V 0 (at t 0=0) decelerates uniformly (without slipping) to rest over a distance d. For a wheel of radius R: a) What is the angular velocity at t 0=0? b) Total revolutions before it stops? c) Total angular distance traversed by the wheel? d) The angular acceleration? e) The total time until it stops? Physics 218, Lecture XIX 10

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 11

Uniform Circular Motion - Velocity • Velocity vector = |V| tangent to the circle • Is this ball accelerating? –Yes! why? Physics 218, Lecture XIX 12

Centripetal Acceleration • “Center Seeking” • Acceleration vector= V 2/R towards the center • Acceleration is perpendicular to the velocity Physics 218, Lecture XIX R 13

Circular Motion: Get the speed! Speed = distance/time Distance in 1 revolution divided by the time it takes to go around once Speed = 2 pr/T Note: The time to go around once is known as the Period, or T Physics 218, Lecture XIX 14

The Trick To Solving Problems Physics 218, Lecture XIX 15

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 Physics 218, Lecture XIX friction is required? 16

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 17

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 = Lsin. Q. 1. What is the velocity of the ball? 2. Calculate the period of the ball Physics 218, Lecture XIX 18

Exam 2 • Class average for the 2 nd 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 3 rd exam Physics 218, Lecture XIX 19

Should you Q-drop? • Many have asked “should I qdrop? ” – 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 20

Next Time • Wednesday Recitation: Recitation on Chapters 12 & 13 • Wednesday Lab: Elastic Collisions • Thursday: Lecture on Chapter 14 • Monday: Chapters 12 & 13 due in Web. CT Physics 218, Lecture XIX 21

Physics 218, Lecture XIX 22

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. a)What is the centripetal acceleration? b)What is the centripetal force? Physics 218, Lecture XIX 23

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 24

Show for constant acceleration that: Physics 218, Lecture XIX 25

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

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. 0 cm) • 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 27

Next Time • Read Chapter 10 – More on angular “Stuff” – Angular kinematics – Torque – Reading questions: Q 10. 7 & Q 10. 26 • HW 7 Due Monday (released this afternoon) • Exam 2 next Thursday on Chapters 47 Physics 218, Lecture XIX 28

More definitions • Frequency = Revolutions/sec w radians/sec /2 p f = w • Period = 1/freq = 1/f Physics 218, Lecture XIX 29

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 30