Physics 218 Lecture 23

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1 Physics 218 Lecture 23 Dr. David Toback Physics 218, Lecture XXIII 1

2 Checklist for Today Things due Monday Chapter 14 in WebCT Things that were due yesterday Chapter 15 problems as Recitation Prep Things due next Monday Chapter 15 & 16 in WebCT Next week Chapter 18 reading Physics 218, Lecture XXIII 2

3 The Schedule This Week (4/14) Monday: Chapter 14 due in WebCT Tues: Exam 3 (Chaps 10-13) Wed: Recitation on Chap 15, Lab Thurs: Last lecture on Chaps Next Week (4/21) Monday: Chapter 15 & 16 due in WebCT Tues: Reading for Chapter 18 Lecture on Chapter 18 Wed: Recitation on Chapter 18 Thurs: Last lecture, Chapter 18 Week after that (4/28) No lectures or recitations Week after that (5/5) Final: Monday May 5 th, 1PM-3PM in this room Physics 218, Lecture XXIII 3

4 Overview Chapters are about Rotational Motion Concentrate on the relationship between linear and angular variables Do them in six combined lectures Last lecture today Angular Momentum and Energy The book does the math, I ll focus on the understanding and making the issues more intuitive Physics 218, Lecture XXIII 4

5 Physics 218, Lecture XXIII 5

6 Angular Quantities Position Angle θ Velocity Angular Velocity ω Acceleration Angular Acceleration α Force Torque τ Mass Moment of Inertia Ι Today we ll finish: Momentum Energy Physics 218, Lecture XXIII 6

7 Momentum Momentum vs. Angular Momentum: r r r p = mv L = I ω r Newton s Laws: F r r dp r = τ dt = r dl dt Physics 218, Lecture XXIII 7

8 Angular Momentum Definition Another definition: r r r L = r p Physics 218, Lecture XXIII 8

9 Angular Motion of a Particle Determine the angular momentum, L, of a particle, with mass m and speed v, moving in circular motion with radius r Physics 218, Lecture XXIII 9

10 Conservation of Angular Momentum if τ = 0 r τ = dl L r dt = Const By Newton s laws, the angular momentum of a body can change, but the angular momentum for a system cannot change Conservation of Angular Momentum Same as for linear momentum Physics 218, Lecture XXIII 10

11 This one you ve seen on TV Try this at home in a chair that rotates Get yourself spinning with your arms and legs stretched out, then pull them in Ice Skater r L = I ω r Physics 218, Lecture XXIII 11

12 Problem Solving For Conservation of Angular Momentum problems: BEFORE and AFTER Physics 218, Lecture XXIII 12

13 Conservation of Angular Momentum Before Physics 218, Lecture XXIII 13

14 Conservation of Angular Momentum After Physics 218, Lecture XXIII 14

15 Clutch Design As a car engineer, you model a car clutch as two plates, each with radius R, and masses M A and M B (I Plate = ½MR 2 ). Plate A spins with speed ω 1 and plate B is at rest. You close them so they spin together Find the final angular velocity of the system Physics 218, Lecture XXIII 15

16 Angular Quantities Position Angle θ Velocity Angular Velocity ω Acceleration Angular Acceleration α Force Torque τ Mass Moment of Inertia Ι Today we ll finish: Momentum Angular Momentum L Energy Physics 218, Lecture XXIII 16

17 Rotational Kinetic Energy KE trans = ½mv 2 KE rotate = ½Iω 2 Conservation of Energy must take rotational kinetic energy into account Physics 218, Lecture XXIII 17

18 Rotation and Translation Objects can both Rotate and Translate Need to add the two KE total = ½ mv 2 + ½Iω 2 Rolling without slipping is a special case where you can relate the two V = ωr Physics 218, Lecture XXIII 18

Rolling Down an Incline You take a solid ball of mass m and radius R and hold it at rest on a plane with height Z. You then let go and the ball rolls without slipping.

19 Rolling Down an Incline You take a solid ball of mass m and radius R and hold it at rest on a plane with height Z. You then let go and the ball rolls without slipping. What will be the speed of the ball at the bottom? What would be the speed if the ball didn t roll and there were no friction? Z Note: I sphere = 2/5MR 2 Physics 218, Lecture XXIII 19

20 A bullet strikes a cylinder A bullet of speed V and mass m strikes a solid cylinder of mass M and inertia I=½MR 2, at radius R and sticks. The cylinder is anchored at point 0 and is initially at rest. What is ω of the system after the collision? Is energy Conserved? Physics 218, Lecture XXIII 20

21 A rod of mass uniform density, mass m and length l pivots at a hinge. It has moment of inertia I=ml/3 and starts at rest at a right angle. You let it go: What is ω when it reaches the bottom? What is the velocity of the tip at the bottom? Rotating Rod Physics 218, Lecture XXIII 21

Less Spherical Heavy Pulley A heavy pulley, with radius R, starts at rest. We pull on an attached rope with constant force F T. It accelerates to final angular speed ω in time t.

22 Less Spherical Heavy Pulley A heavy pulley, with radius R, starts at rest. We pull on an attached rope with constant force F T. It accelerates to final angular speed ω in time t. A better estimate takes into account that there is friction in the system. This gives a torque (due to the axel) we ll call this τ fric. What is this better estimate of the moment of Inertia? R Physics 218, Lecture XXIII 22

23 Person on a Disk A person with mass m stands on the edge of a disk with radius R and moment ½MR 2. Neither is moving. The person then starts moving on the disk with speed V. Find the angular velocity of the disk Physics 218, Lecture XXIII 23

24 Same Problem: Forces Same problem but with Forces Physics 218, Lecture XXIII 24

25 Challenge Exam Announcement of this semester s 218 Challenge Exam: Monday April 28 th at 6:00PM Not required (just for fun) Does not (will not!!!) count as part of your final grade Test your skills against the best Aggies from all the Physics 218 sections (not just this lecture) on Physics 218 material Students who perform well will be recognized as Mechanics Scholars, and honored at a banquet in their honor. Other prizes, including cash. Handout information on my WebSite Physics 218, Lecture XXIII 25

26 Next Week Reading: Chapter 18 Harmonic Motion Last topic for the course Notes for the final: No more bonus points Exam is worth 200 points Problem 8 will consist of two items: 5 points for getting 100% on all your homework & WebCT quizzes 5 more points for getting 100 on the Mini-practice Exam final Physics 218, Lecture XXIII 26

Physics 218 Lecture 21

Physics 218 Lecture 21 Dr. David Toback Physics 218, Lecture XXI 1 Checklist for Today Things due Yesterday Chapters 12 & 13 in WebCT Things that are due for today Read Chapters 14-16 Things that are due