Mon , (.12) Rotational + Translational RE 11.b Tues.

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1 Mon..-.3, (.) Rotational + Tanlational RE.b Tue. EP0 Mon..4-.6, (.3) Angula Momentum & Toque RE.c Tue. Wed , (.) Toque EP RE.d ab Fi. Rotation Coue Eval.0 Quantization, Quiz RE.e Mon. Review fo Final (-) HW: Ch P 39, 57, 64, 74, 78 & Pactice Exam

Oient Right hand o finge cul fom the axi and with

2 Uing Angula Momentum The meaue of motion about a oint Magnitude Diection in Magnitude and Diection Oient Right hand o finge cul fom the axi and with motion, then thum oint in diection of angula momentum.

3 What i the diection of < 0, 4, 0> x < 0, 0, 3>? ) +x ) x 3) +y 4) y 5) +z 6) z 7) zeo magnitude What i the diection of < 0, 0, 4> x < 0, 0, 3>?

4 If an object i taveling at a contant eed in a vetical cicle, how doe the object' angula momentum change a the object goe fom the to of the cicle to the bottom of the cicle?. inceae. deceae 3. tay the ame but the diection of change 4. The diection and magnitude of emain the ame

5 Uing Angula Momentum The meaue of motion about a oint Effect of a adial foce (like gavity o electic) un F Eath Eath un un d dt d dt E E S S d dt v E E S E E E S de dt F S Eath un E 0 E S d dt E Paallel Paallel E S contant Obit noncicula.y

6 Kele and Planetay Obit: Sweeing ou equal aea in equal time: If t t, then A A Some Geometic maniulation v t A A t h i h b v t v t v t Ab*h v th A v t in A ½v t in Some mathematical maniulation t A mvin m m t in m t m t Since i contant (and m i contant), A i the ame fo the ame time inteval

7 Relating Enegy, Radiu and Angula Momentum in Cicula Obit Angula Momentum: Kinetic enegy: obit mv Kinetic and Gavitational Potential Enegy: Potential enegy: K U mv G Mm obit m Gavitational Foce and Cicula motion: U ( & eendicula) E K U v m K F net Mm G Mm U K G obit m mgmm ate in chate we ll aly ame eaoning to electic inteaction while develoing Boh atom K K U U K 4m obit

9 c Multi-Paticle Angula Momentum: Cloud of Dut about Sta Sta 3 c. 3 Cloud of Dut c 3 c c c tot.. 3. c c tanlational. c otational. c

10 Multi-Paticle Angula Momentum: Cloud of Dut about Sta Sta c c c. 3 c tanlational. c otational. c Cloud of Dut _babell_ang_mom.y

11 09_babell_ang_mom.y c c 3 c tanlational. c otational. c Multi-Paticle Angula Momentum 3 3 Examle: the baton in about it own cente with and about the eon who holding it with It total angula momentum about the eon i Examle: the baton in about it own cente in the ooite diection, with and about the eon who holding it with It total angula momentum about the eon i

12 Rotational Angula Momentum ot. 3 3 Examle: ay we have two aticle m 0.kg, and v 3 v 3 v 3 v m 0.kg, and +

13 Focu on Rotational Angula Momentum ot. 3 3 While it deend on oition elative to cente of ma, aea to deend on total (not elative) momentum Fo v<<c, how that not the cae ot. mv mv 3 m3v3 Focuing on jut one aticle m m m m v v v 3 v. m v v m v m v Similaly fo all othe aticle, o m33 m m m3 v m v m m m33 Really only deend on m m3 oition and momentum m v m33 v elative 3 of cente of ma. ot. but o 0 m Sta m v m v m m v m v ot. ot. 3 3 v c. v 3 3 v v 3 v v v

14 Rotational Angula Momentum ot. 3 3 Fo v<<c ot. 3 3 ot. 3 Examle: ay we have two aticle m 0.kg, and mv mv 0.kg 3,0,0 m / v m m 0.kg 0.kg 0.kg 0,4,0 m / v 4, 3 v v 3,0 3 m / v 3 v 3 v v m 0.kg, and +

15 Rotational Angula Momentum ot. 3 3 Fo v<<c ot. 3 3 ot. 3 m v Secial cae: igid body Paticle velocitie mut be eendicula to thei oition vecto (othewie they d be moving in and out) m v all aticle tavel thei cicle in the ame eiod, T m m m m ot. 3 3 m Moment of Inetia (again) T v v I all. aticle i m i i all. aticle i m i i 3 3 v 3 ot. v I

16 Angula Seed Refehe The Eath otate on it axi once evey 4 hou. What i it angula eed? Radiu: 6.4e6 m Ma: 6e4 kg ) / (4*60*60) ) * 6.4e6 / (4*60*60) 3) (6e4) * * 6.4e6 / (4*60*60) 4) (6e5) * (6.4e6) * / (4*60*60)

17 Moment of Inetia Refehe A diatomic molecule uch a molecula nitogen (N ) conit of two atom each of ma M, whoe nuclei ae a ditance d aat. What i the moment of inetia of the molecule about it cente of ma? a) Md b) Md c) ½ Md d) ¼ Md e) 4 Md d

18 Rotational Angula Momentum Secial cae: igid body Examle: A babell in aound a ivot at it cente at A. The babell conit of two mall ball, each with ma 500 gam (0.5 kg), at the end of a vey low ma od of length 50 (0.5 m). The babell in clockwie with angula eed 0 adian/. a) What i the moment of inetia about A? b) What i the diection of the angula velocity? c) What i the tanlational angula momentum? d) What i the otational angula momentum? e) What i the total angula momentum?

19 Rotational Angula Momentum Secial cae: igid body Examle: Next the cente of the babell (of length 50, two 0.5kg mae) i mounted on the end of a low ma igid od of length b m. The aaatu i tated in uch a way that although the od otate clockwie with angula eed 90 adian/, the babell maintain it vetical oientation. a) What i the moment of inetia about B? b) What i the diection of the angula velocity? c) What i the tanlational angula momentum? d) What i the otational angula momentum? e) What i the total angula momentum?

20 If the Mae Don t ie in a Plane total A A B B C C D D A C B A C B D A B D Jut looking at magnitude fo ball A A A A A A Am A T If all mae, ditance, and eed ae the ame, m A B b A A C. z A A D A m in m in A A C D Given the ymmety, total 4m in zˆ but in total 4m zˆ I axi Geneally, it the moment of inetia about the otational axi though total A. z B. z C. z D. z zˆ

21 Rotational Angula Momentum and Rotational Enegy Recall now o K ot ot I I K ot I Analogou to K mv mv K m

22 Rotational Angula Momentum and Kinetic Enegy Secial cae: igid body Examle: A babell in aound a ivot at it cente at A. The babell conit of two mall ball, each with ma 500 gam (0.5 kg), at the end of a vey low ma od of length 50 (0.5 m). The babell in clockwie with angula eed 0 adian/. a) What i the moment of inetia about A? b) What i the diection of the angula velocity? c) What i the tanlational angula momentum? d) What i the otational angula momentum? e) What i the total angula momentum? f) What i the otational kinetic enegy?

23 Mon..-.3, (.) Rotational + Tanlational RE.b Tue. EP0 Mon..4-.6, (.3) Angula Momentum & Toque RE.c Tue. Wed , (.) Toque EP RE.d ab Fi. Rotation Coue Eval.0 Quantization, Quiz RE.e Mon. Review fo Final (-) HW: Ch P 39, 57, 64, 74, 78 & Pactice Exam

Fri Angular Momentum Quiz 10 RE 11.a; HW10: 13*, 21, 30, 39 Mon , (.12) Rotational + Translational RE 11.b Tues.

Fri Angular Momentum Quiz 10 RE 11.a; HW10: 13*, 21, 30, 39 Mon , (.12) Rotational + Translational RE 11.b Tues. Fi. 11.1 Angula Momentum Quiz 10 R 11.a; HW10: 13*, 1, 30, 39 Mon. 11.-.3, (.1) Rotational + Tanslational R 11.b Tues. P10 Mon. 11.4-.6, (.13) Angula Momentum & Toque Tues. Wed. 11.7 -.9, (.11) Toque R