Lect19 - Physics 211 Lecture 19 Today's Concepts Angular...

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Unformatted text preview: Physics 211 Lecture 19 Today's Concepts: Angular Momentum The Prelecture is now available is (as of 4am this morning) Physics 211 Lecture 19, Slide 1 Physics I missed having a prelecture. missed All of it, considering there was no prelecture. would have been nice to have a prelecture this time around. this Kind of everything... and also about the exam...possibly being really nice and Kind making it really easy?? Why was there no prelecture? Why I don't even know what to put here. don't All of it since we had no prelecture All i guess everything cuz of the absence of prelecture guess of Rotation sucks :( And a prelecture would have helped so much with this! Rotation would ..ugh and can the prelecture be posted asap?? i need the notes to learn! ..ugh be Everything was really hard to understand without the prelecture Everything Im a little sad there was no preflight for this, but It would make my day to see Im little my you do a backflip in lecture! in Um..I have found that these preflights are undoubtedly much harder to do are Um..I have without a prelecture! Nothing really, just maybe get that prelecture up! up! Nothing Nothing, But I would like to add that I have yet to pull an all nighter to to understand this stuff until tonight. I don't know what's going on at all since there was no prelecture. don't I feel like I’m missing something without the prelecture. feel all due to the lack of prelecture all why there was no prelecture? why Go over everything in class to clarify the topic since there is no prelecture. Go is conservation of angular momentum equivalent to conservation of is translational momentum? Everything.. there was no prelecture.. Everything.. I don't know...? Whatever was on the prelecture? And how to do the last two don't problems. just overall review since there's no prelecture just anything that would have been in the prelecture anything all of this since we didnt get a prelecture all get Dont really know yet with no pre-lecture Dont really Everything. This preflight was hard without a prelecture. Everything. Wow, I miss prelectures. You guys have done a really good job keeping up with Wow, making them though. Where is my prelecture? =( Where Acute prelecture withdrawal remedies. withdrawal Acute Dude there was no prelecture Dude why couldn't the prelecture be put up just without animation? i am mildly be why frustrated right now about this I have to say that you guys have been doing great with the prelectures. I really have hope you don't get too much heat for not having this one up on time. People have to realize that you have lives too. we need the prelecture we I don't have a lot of pre-knowledge about angular momentum and without the prelecture, I feel as though I'm lost. I feel kind of bad for not actually giving a serious response to this question, but this feel you should rename this the "Witty Comment Box", because that's what everyone uses it for. Ironically, this was also a witty comment (or was it?) Har, har, har, I'm a pirate. Har Q: What is the name of the first electricity detective? A: Sherlock Ohms Q: During last lecture I was losing hope of ever getting my degree and physics During minor, because torque and I don't seem to get along. However, the video of Bruce made me so happy that I now have the will to go on. Thanks. everything, please play some red hot chili peppers music, everything, I'm terrible at physics, but I really like it. Thanks for putting me into that I'm dilemma. Can you let us see the prelectures after they close? I can't see them and I think Can after they would be great to study from Um...I wanna join Physics Van! Can I still do that? join You need to play hoedown throwdown as the last song before you begin the You as 10 o'clock lecture. Libby Cervantes said she will get up and do the dance to it in front of the class if you call her down 11-11, It's My Birthday!! Angular Momentum Angular We have shown that for a system of particles FEXT dp = dt Momentum is conserved if FE X T = 0 What is the rotational version of this?? The rotational analogue of force F is torque τ = r × F Define the rotational analogue of momentum p to be angular momentum: L=r×p Physics 211 Lecture 19, Slide 5 Angular Momentum Lets consider the rate of change of L: dL d = (r × p) dt dt d dp ⎞ ⎛ dr ⎞⎛ (r × p) = ⎜ × p ⎟ + ⎜ r × ⎟ dt dt ⎠ ⎝ dt ⎠⎝ = ( v × mv ) =0 So dL dp =r× dt dt (so what...?) Physics 211 Lecture 19, Slide 6 Physics Angular Momentum Angular dL dp =r× dt dt Recall that FEXT dp = dt dL = r × FEXT dt τEXT Which gives us: τ EXT dL = dt dp = !! dt Physics 211 Lecture 19, Slide 7 Analogue of FEXT What does it mean? What τ EXT dL = dt where L = r × p and τ ext = r × FEXT In the absence of external torques τ EXT dL = =0 dt Total angular momentum is conserved Physics 211 Lecture 19, Slide 8 Physics Example – disk dropped on disk disk ω = ω0 ω =ωf ω=0 Linitial 1 = MR 2ω0 + 0 2 ω =ωf = L final 1 1 2 = MR ω f + MR 2ω f 2 2 1 MR 2ω0 = MR 2ω f 2 1 ω f = ω0 2 Physics 211 Lecture 19, Slide 9 What about Kinetic Energy? What ω = ω0 ω =ωf ω=0 K before ω =ωf L2 = 2 I before K= 12L Iω = 2 2I 2 same x2 K after L2 = 2 I after Physics 211 Lecture 19, Slide 10 In both cases shown below a solid disk of mass M, radius R, and initial angular velocity ω0 is dropped onto an initially is stationary second disk having the same radius. In Case 2 the mass of the bottom disk is twice as big as in Case 1. If there are no external torques acting on either system, in which case is the final kinetic energy of the system biggest? Preflight A) Case 1 B) Case 2 C) Same M ω = ω0 M ω = ω0 M ω =0 Case 1 2M ω =0 Case 2 Physics 211 Lecture 19, Slide 11 Same initial L Preflight … in which case is the final kinetic energy of the system biggest? in A) Case 1 B) Case 2 C) Same L K= 2I M M M Case 1 2M 2M Case 2 Physics 211 Lecture 19, Slide 12 2 Same final L point particle moving in a straight line point L = R× p axis R1 θ1 R2 p θ2 R3 p θ3 D p L1 = R1 × p = R1 p sin(θ1 ) = pD L2 = R2 × p = R2 p sin(θ 2 ) = pD L3 = R3 × p = R3 p sin(θ 3 ) = pD Physics 211 Lecture 19, Slide 13 L = R× p axis L = mvD = pD D p Direction given by right hand rule (out of the page in this case) (out Physics 211 Lecture 19, Slide 14 Playground Example Playground Before After M Top View ω R m v LBefore = mvR LBefore = LAfter LAfter 1 = Iω = ( MR 2 + mR 2 )ω 2 Disk Kid v 1 ω= R (1 + M 2m ) Physics 211 Lecture 19, Slide 15 Preflight The magnitude of the angular momentum of a freely rotating The disk around its center is L. You toss a heavy block onto the disk along the direction shown. Friction acts between the disk and the block so that eventually the block is at rest on the disk and rotates with it. What is the magnitude of the final angular momentum of the disk-block system: A) > L B) < L C) = L Top View Top Instead of a block, imagine it’s a kid hopping onto a merry go round Physics 211 Lecture 19, Slide 16 Preflight Preflight The magnitude of the angular momentum of a freely rotating disk around its center is L. You toss a heavy block onto the disk along the direction shown. Friction acts between the disk and the block so that eventually the block is at rest on the disk and rotates with it. What is the magnitude of the final angular momentum of the disk-block system: A) > L B) < L C) = L Top View Instead of a block, imagine it’s a kid hopping onto a merry go round Physics 211 Lecture 19, Slide 17 Example: Throwing ball from stool Example: A student sits on a stool which is free to rotate. The moment of inertia of the student plus the stool is I. She throws a heavy ball of mass M with speed v such that its velocity vector passes a distance d from the axis of rotation. What is the angular speed ωF of the student-stool system after she throws the ball? M ωF I top view: initial I final final d v Physics 211 Lecture 19, Slide 18 Physics Conserve angular momentum (since there are no external torques acting on the student-stool system): Li = 0 Lf = 0 = IωF - Mvd Mvd ωF = I M ωF I top view: initial I final final d v Physics 211 Lecture 19, Slide 19 Physics Act A student is riding on the outside edge of a merry-go-round rotating about a frictionless pivot. She holds a heavy ball at rest in her hand. If she releases the ball, the angular velocity of the merry-go-round will: A) increase B) decrease C) stay the same ω2 ω1 Physics 211 Lecture 19, Slide 20 Physics 211 Lecture 19, Slide 21 Physics m Things to watch: L=2R ω = 2π f m M ω0 ωf Lbefore = I disk ω0 Lafter = ( I disk + I rod )ω f Physics 211 Lecture 19, Slide 22 Physics M I diskα disk = − I rod α rod ωf τ disk = −τ rod α disk (Newton's 3rd law) law) I rod =− α rod I disk Physics 211 Lecture 19, Slide 23 Physics Same as (a) – L is still conserved Physics 211 Lecture 19, Slide 24 Physics L K= 2I 2 K initial L2 = 2 I disk K final L2 = 2 ( I disk + I rod ) W fric = ΔK Shortcut: 1 1 2 I rod = ML2 = M ( 2 R ) 12 12 1 = MR 2 3 2⎛1 ⎞ = ⎜ MR 2 ⎟ 3⎝2 ⎠ 2 I rod = I disk In this case 3 Physics 211 Lecture 19, Slide 25 Physics ...
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This note was uploaded on 09/22/2011 for the course PHYSICS 211 taught by Professor Selig during the Fall '10 term at University of Illinois, Urbana Champaign.

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