Mechanics Lecture 19, Slide 1

Transcription

1 Mechanics Lecture 19, Slide 1

2 I do not like using capital omega because it reminds me of resistance..and E&M is pure EVIL!!!! Personally, I feel like lecture is moving too fast, could we slow it down a little? Also, the formula's are great but it would be great if a less mathematical and more conceptual way to understand Angular Momentum Vector and Precession could be taught. Thanks! It is incredibly hard to understand in what direction mass is acting on a gyroscope. Charlton Heston would have a hard time figuring the direction of Omega. I love this class and everything, but why is the third midterm right after the thanksgiving break? :(. I don't want to work over the thanksgiving break. It's time to, you know, give thanks. (And sleep a ton.) is the precession causing me not to fall on the bicycle while I am turning left or right? If precession occurs when the external torque is perpendicular to the L, then why do tops and even the earth precess around their axes Because there is a torque perp to L Dang. This stuff is getting really complicated. I'm pretty sure this is the earliest I will ever do an assignment. 2 days before it's due at 5:40 a.m. Personal Record achieved! Yay This is pretty weird stuff. Your Comments "the tide abides for, tarrieth for no man Yes it is Rube Today Not so! Thanks for going old-school Everything after this gets easier Could you please go over the ways to find the direction for angular momentum and precession? It is really confusing... (the right hand rule stuff!) Yes I will kinda Mechanics Lecture 20, Slide 2

3 I have posted the grade estimator on the Physics 211 webpage (for entertainment purposes only) Mechanics Lecture 20, Slide 3

4 Physics 211 Lecture 20 Today s Concepts: RHR recap A) Angular Momentum B) Precession Mechanics Lecture 20, Slide 4

5 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 5

6 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 6

7 In the slide about angular momentum and kinetic energy, where did the equation relating K, L, and I come from? It just popped up out of nowhere. K 1 = I 2 = 2 2 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 7

8 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 8

9 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 9

10 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 = 2 2 = 41 4 R R 2 i f Mechanics Lecture 20, Slide 10

11 Food for thought (not on any test) R R 2 i f We just used ext = 0 to find 2 = But = I So how do we get an without a? dl d( I) = = dt dt di = dt usually 0, but not now I d dt I Mechanics Lecture 20, Slide 11

12 Food for thought (not on any test) = EXT I di dt Now suppose EXT = 0: di I = 0 = dt di I dt So in this case we can have an without an external torque! Mechanics Lecture 20, Slide 12

13 I am not buying the spinning top and stool example. I don't think it would actually work. Prove it! Mechanics Lecture 20, Slide 13

14 You d have to keep spinning Mechanics Lecture 19, Slide 14

15 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 15

16 Precession Aerial View dl = L top d dl L (t) d L ( t dt) pivot dl dt EXT d = Ltop = L W dt top W W= ext L top This actually seems to make a fair amount of sense! But what do you have to do when the precession frequency gets too big? Mechanics Lecture 20, Slide 16

17 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 17

18 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 18

19 I feel silly, but why doesn't the top just fall straight down each time? Is there something about the spinning motion that can sustain it at an elevated angle even when only attached at a tiny pivot point? Here's what I kept thinking about as I went through the prelecture and it accurately describes my feelings. Mechanics Lecture 20, Slide 19

20 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 Mechanics Lecture 20, Slide 20

21 Clicker Question In which direction does point to begin with (use right hand rule)? L L L A B Mechanics Lecture 20, Slide 21

22 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) The torque caused by gravity is out of the page, so L has to change in the same direction. But, since L is in the opposite direction of the axel, precession has to make the disk go into the page.. B) The torque exerted by the gravity points out of the page Mechanics Lecture 20, Slide 22

23 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 23

24 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 24

25 CheckPoint 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 W= ext L top A) Torque increases, so precession frequency increases. B) Moment of inertia increases so precession frequency decreases C) Mass affects both torque and angular momentum equally so it cancels out. Mechanics Lecture 20, Slide 25

26 Clicker Question 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 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 26

27 Riding a Bike Practical Application: Keeps you from falling off your bike when you ride using no hands! 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 27

28 I = MR = 2 f d Mg L = I = W= M g d L Mechanics Lecture 20, Slide 28

29 L (using right hand rule) Mechanics Lecture 20, Slide 29