Last 6 lectures are easier

Transcription

1 Your Comments I love you. Seriously. I do. And you never post it. I felt really bad whilst completing the checkpoint for this. This stuff is way above my head and I struggled with the concept of precession. I hope there's some cool demos in lecture to help visualize what's going on... Cobalt labreport is taking more time than I expected. I'll catch up this weekend, I promise. ): I just want to take time to wish everyone a very nice day. Everything will be alright in the end as long as you try your best! It doesn't make much sense to me why moment of inertia of an object can decrease. I thought moment of inertia was characteristic of an object... I don't believe that flipping a spinning top over will cause you to rotate. Prove it! :) Though the material appears intimidating at first, this actually is making sense! Is torque always Mg for these problems? I'm confused about that and also about the "torque about the pivot." What does "about the pivot" really mean? The first half was good, but I need a lot more practice on precession...and what direction an object precesses in. I feel like this is relatively simple, but i know the homework problems will be difficult. To be honest, I didn't get to look at the prelectures because I've got a ton of work to do, but thank you for providing them online - they given me a nice general outline to refer back to whenever I need to review or study something again i just feel really confused and lost and i wish there were more direct resources to learn from. I dont really learn from the pre lecture. And the lecture is just a repeat of the prefecture but there is nothing concrete for me to reference and to figure out on my own since i feel like you just end up teaching everything to yourself in this class. We used to use Tipler & Mosca Physics for Scientists and Engineers Last 6 lectures are easier Mechanics Lecture 20, Slide 1

2 You had several quiz questions: Quizzes covers the previous weeks discussion material, or, when following an exam week, the last two weeks material. For example, this week's quiz will cover material from Discussion 8 and Discussion 9 (rotational kinematics, rotational dynamics, rotational energy). Next week's quiz will cover this week's discussion material (static equilibrium). Mechanics Lecture 20, Slide 2

3 Your grade so far Effort (500) Exams (500) Prelectures + Checkpoints + Lectures 100 Labs (9) 150 Quizzes (9) 100 Homework (26) 150 Hour exams (3 x 100 each) 300 Final Exam 200 Prelectures: 50 Preflight's: 25 Lecture participation: 25 You can miss up to 3 of each The lowest Quiz is dropped The lowest Homework is dropped To get lecture participation credit you need to vote on at least half of the questions in a lecture. (i.e. it is possible to get part of a bonus point but no participation point for a lecture) Bonus Points: You can earn up to 1 extra bonus point in every lecture (for a maximum of 25 bonus points for the semester) by getting the right answers to at least 5 of the clicker questions. At the end of the semester your bonus points are added to your effort scores (max 500) Your total score out of 1000 points determines your final grade. Its just a simple formula the computer calculates it. Your grade is determined entirely by the your performance on the components of the course as described above. There is no other extra credit possible. A+ (950), A (920), A- (900), B+ (880), B (860), B- (835), C+ (810), C (780), C- (750), D+ (720), D (690), D- (610), and F (<610). Most of you will get A s & B s in this class

4 I have posted the grade estimator on the Physics 211 webpage (for entertainment purposes only) Mechanics Lecture 20, Slide 4

5 You had many right hand rule questions When something spins Cross Product A BC B (thumb) C (fingers) A (out of palm) L I d dt Mechanics Lecture 20, Slide 5

6 Cross Product RF R R (out of palm) F F Mechanics Lecture 20, Slide 6

7 CheckPoint A disk is spinning with angular velocity on a pivoted horizontal axle as shown. Gravity acts down and the disk has a precession frequency W. If the mass of the disk were doubled but its radius and angular velocity were kept the same, the precession frequency would: A) Increase B) Decrease C) Stay the same Mechanics Lecture 20, Slide 7

8 Initial View x R y p L Mechanics Lecture 19, Slide 8

9 Final View But, we have to conserve angular momentum: a) L initial = I+mR 2 ; where I is the moment of inertia of the person and disk. b) L final = L initial = mvr = L ball ; when the person and disk stop, all of the angular momentum must belong to the ball. c) Now, here s where the train of thought derailed: Both of these angular momenta are positive, in the right-hand sense. C x d) The internal torque, which brought the disk to a top, however, does have a momentum (force) vector which points in the negative direction. A y p ball p R L B Mechanics Lecture 19, Slide 9

10 Physics 211 Lecture 20 Today s Concepts: A) Angular Momentum B) Precession Mechanics Lecture 20, Slide 10

11 Student on Stool There are no external torques acting on the student-stool system, so angular momentum will be conserved. Initially: L i I i i Finally: L f I f f f i I I i f i f I i I f L i L f Mechanics Lecture 20, Slide 11

12 Clicker Question A student sits on a freely turning stool and rotates with constant angular velocity 1. She pulls her arms in and her angular velocity increases to 2. In doing this her kinetic energy: A) Increases B) Decreases C) Stays the same i f I i I f L i L f Mechanics Lecture 20, Slide 12

13 K 1 I L 2I (using L I) L is conserved: I f < I i K f > K i K increases! i f I i I f L i L f Mechanics Lecture 20, Slide 13

14 Since the student has to force her arms to move toward her body, she must be doing positive work! The work/kinetic energy theorem states that this will increase the kinetic energy of the system! i f I i I f L i L f Mechanics Lecture 20, Slide 14

15 Clicker Question A puck slides in a circular path on a horizontal frictionless table. It is held at a constant radius by a string threaded through a frictionless hole at the center of the table. If you pull on the string such that the radius decreases by a factor of 2, by what factor does the angular velocity of the puck increase? A) 2 B) 4 C) 8 i f Mechanics Lecture 20, Slide 15

16 Clicker Question Since the string is pulled through a hole at the center 2 of rotation, there is no torque: Angular 2 momentum is conserved. R L1 I11 mr 1 L2 I22 m mr 1 m R R R 2 i f Mechanics Lecture 20, Slide 16

17 i need to see the right hand rule for this done in person. also, does this only apply to tops? what other real life example is there? and can we do the person sitting on a stool holding a large top demo in class? I'd like to see that done in person as well. i think that would help me understand. Mechanics Lecture 20, Slide 19

18 You d have to keep spinning Mechanics Lecture 19, Slide 20

19 Precession The magnitude of the torque about the pivot is Mgd. The direction of this torque at the instant shown is out of the page (using the right hand rule). ext dl dt The change in angular momentum at the instant shown must also be out of the page! Mechanics Lecture 20, Slide 21

20 Precession Aerial View dl L top d dl L (t) d L ( t dt) pivot dl dt EXT L top d dt W L top W W ext L top I'm confused with the idea that "valid if tau is small compared to L", could you explain that? Mechanics Lecture 20, Slide 22

21 Precession ext dl dt W ext L top In this example: ext Mgd L top I W Mgd I Direction: The tip of L moves in the direction of. Mechanics Lecture 20, Slide 23

22 CheckPoint A disk is spinning with angular velocity on a pivoted horizontal axle as shown. Gravity acts down. In which direction does precession cause the disk to move? A) Into the page B) Out of the page C) Up D) Down Mechanics Lecture 20, Slide 24

23 Precession is weird as hell and confuses me more than anything else I've seen in this class. This was completely awful. I don't understand how you figure out in what direction the precession will make the object rotate. This was completely awful. I don't understand how you figure out in what direction the precession will make the object rotate. Here's what I kept thinking about as I went through the prelecture and it accurately describes my feelings. Mechanics Lecture 20, Slide 25

24 Clicker Question The torque on the gyroscope is out of the page. In which direction must the angular momentum L change? A) Out of the page B) Into the page ext dl dt But is the direction of the torque due to the object's weight always pointing in the counter clockwise direction in the aerial view? Mechanics Lecture 20, Slide 26

25 Clicker Question In which direction does point to begin with (use right hand rule)? L L L A B Mechanics Lecture 20, Slide 27

26 CheckPoint In which direction does precession cause the disk to move? A) Into the page B) Out of the page C) Up D) Down L A) in this case, w is pointing towards the pivot, so L is also towards the pivot and the precision frequency is in the opposite direction than it would be if L is pointing away from the pivot. B) Using the right hand rule: fingers point to the CM from the pivot, curl down in the direction of weight, and thus the torque from the weight points out of the screen. Mechanics Lecture 20, Slide 28

27 Clicker Question A disk is spinning with angular velocity on a pivoted horizontal axle as shown. If the mass of the disk were doubled but its radius and angular velocity were kept the same: A) The angular momentum of the disk doubles B) The torque about the pivot doubles C) Both A and B L I Mechanics Lecture 20, Slide 29

28 If the mass of the disk were doubled but its radius and angular velocity were kept the same, the precession frequency would A) Increase B) Decrease C) Stay the same CheckPoint W ext L top Mgd I Mechanics Lecture 20, Slide 30

29 CheckPoint If the radius of the disk were doubled but its mass and angular velocity were kept the same, the precession frequency would A) Increase B) Decrease C) Stay the same W ext L top Mgd I Mechanics Lecture 20, Slide 31

30 Riding a Bike Please go over how precession and gyroscopes work. Also, please explain why bicycles do not fall over when in motion, since the answer seems to be related to these concepts. Riding straight ( 0) Lean Left ( out of page) Lean Right ( into page) Wheel steers straight Wheel steers left Wheel steers right (see 2:30) Mechanics Lecture 20, Slide 32

31 I MR 2 f d Mg L I W M g d L Mechanics Lecture 20, Slide 33

32 L (using right hand rule) Mechanics Lecture 20, Slide 34