RE 11.e Mon. Review for Final (1-11) HW11: Pr s 39, 57, 64, 74, 78 Sat. 9 a.m. Final Exam (Ch. 1-11)

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1 Mon. Tue. We. ab i..4-.6, (.) ngula Momentum Pincile & Toque.7 -.9, (.) Motion With & Without Toque Rotation Coue Eval.0 Quantization, Quiz RE.c EP RE. RE.e Mon. Review fo inal (-) HW: P 9, 57, 64, 74, 78 Sat. 9 a.m. inal Exam (Ch. -)

2 Uing ngula Momentum The meaue of motion about a oint = = Magnitue Diection in Magnitue an Diection Oient Right han o finge cul fom the axi an with motion, then thum oint in iection of angula momentum.

3 If the Mae Don t ie in a Plane total B B C C D D C B C B D B D Jut looking at magnitue fo ball m T If all mae, itance, an ee ae the ame, m B b C. z D m in m in C D Given the ymmety, total 4m in zˆ but in total 4m zˆ I axi Geneally, it the moment of iia about the otational axi though total. z B. z C. z D. z zˆ

4 Rotational ngula Momentum an Rotational Enegy Recall now o K ot ot I I K ot I nalogou to K mv mv K m

5 Rotational ngula Momentum an Kiic Enegy Secial cae: igi boy Examle: babell in aoun a ivot at it cente at. The babell conit of two mall ball, each with ma 500 gam (0.5 kg), at the en of a vey low ma o of length 50 (0.5 m). The babell in clockwie with angula ee = 0 aian/. a) What i the moment of iia about? b) What i the iection of the angula velocity? c) What i the tanlational angula momentum? ) What i the otational angula momentum? e) What i the total angula momentum? f) What i the otational kiic enegy?

6 Uing ngula Momentum The meaue of motion about a oint Effect of a aial foce (like gavity o electic) un Eath Eath un un t t E E S S t v E E S E E E S E t S Eath un E = 0 E S t E Paallel Paallel E S contant Obit noncicula.y

7 Obit Non-cicula.y Same inteaction Relative to Diffeent Refeence Point Diffeent ngula Momenta C B Geneally, changing ngula Momenta B

8 ngula Momentum affect of a non-aial foce ole ball bll ball han ole oe t t b b v t b b b Paallel b b b t ball all. foce b b b t ball b Paallel oe b ball han ngula Momentum Pincile t ( about ) whee, ( about) ( about) Toque ( fom) analogou to Momentum Pincile t

9 ngula Momentum Pincile bll ole ole t ( about ) ( about) whee, ( about) Toque ( fom) ball ball han oe Quantifie motion about a oint analogou to Inteaction that change motion about a oint Momentum Pincile t Quantifie motion Inteaction that change motion

10 Examle: t t = 5, a aticle ha angula momentum <6, 8, -5> kg m / elative to location. contant toque <, -4, 8> N m elative to location act on the aticle. t t = 5., what i the angula momentum of the aticle elative to location? t o ave t o. f. i ave t. f. f. f 6,8, 6,8, 6,8, kg kg kg m m m / / /,, 4,8 4,8 Nm Nm ,.8,.6 Nm/ Nm kg m/ m. f 8.6,5.,.4 kg m /

11 Toque ( about) ( fom) Magnitue (yet anothe co ouct) in in in Making ene of the facto an co-ouct in ngle age angle, big effect Ditance age itance, big effect Small angle, mall effect Small itance, mall effect

6Nm (b) If the foce wee eenicula to but gave the ame toque a

12 in Examle: a) If = 4 m, = 8 N, an θ = 7, what i the magnitue of the toque about location, incluing unit? 4m 8N in 7 0.6Nm (b) If the foce wee eenicula to but gave the ame toque a in the eceing quetion, what woul it magnitue be? in 0.6Nm 4m 7.65N

13 yo-yo i in the x-y lane. You ull u on the ting with a foce of magnitue 0.6 N. What i the magnitue of the toque (about it cente) you exet on the yo-yo? = m, R= 0.05 m y z (z-axi oint out of age) x R a) N m b) 0.00 N m c) 0.0 N m ) 0.05 N m e) 0.6 N m f) cannot be etemine without knowing the length of the ting

14 y z (z-axi oint out of age) x Toque ( about) ( fom) Diection (yet anothe co ouct) Diection of toque: +z Oient Right han o finge tat in iection fom axi to oint of foce alication, then cul in iection of foce. The thum oint in iection of toque. Diection of toque: - z Diection of toque: no toque

15 yo-yo i in the x-y lane. You ull u on the ting with a foce of magnitue 0.6 N. What i the iection of the toque (about it cente) you exet on the yo-yo? = m, R= 0.05 m y z (z-axi oint out of age) x R ) +x ) x ) +y 4) y 5) +z 6) z 7) zeo magnitue

16 Clou of Dut Sta Multi-Paticle ngula Momentum Pincile: Clou of Dut about Sta... c... c t S t t S S S v. Paallel focu on one aticle itto fo the othe... t t t t c c t whee by eciocity t c

17 Multi-Paticle ngula Momentum Pincile: Clou of Dut about Sta t c t c t c... Sta... Clou of Dut o cental foce (electic, gavitation),etc. o, etc. c t.... all. aticle i i i 0 Note: toque een on each foce an it oint of alication.

18 Multi-Paticle ngula Momentum Pincile With Multi-Paticle ngula Momentum c... t whee c c tan i i Sta ot ot I fo igi object, etc. Clou of Dut

19 Multi-Paticle ngula Momentum Pincile With Multi-Paticle ngula Momentum Examle: oening a oo. You han ae full o you give the oo a quick uh with you foot nea the ege. Say you aly a 00 N foce fo 0.5 at 75. The oo 5kg an 0.m wie; what it ate of otation at the en of you uh? 00 N I oo.. f oo. f f foot I i I 0 oo.. i oo. t f w i f foot foot oo. oo. o of negligible aiu, about an en f I I? foot 0.m t t in oo. m w f 75 Sytem: oo ctive envionment: you foot, hinge (but alie at axi-no toque) oximation: negligible fictional toque at hinge xi: hinge Diection: toque & angula velocity ae both out of the boa (z) Reaonable? t m w w 4 foot m m in w w t foot in m w 00N in kg 0.m a t unit?

20 What the final angula ee of the mey-go-oun afte the ki jum on? y z (z-axi oint out of age) x Chil un an jum on laygoun mey-gooun. o the ytem of the chil + ik (excluing the axle an the Eath), which tatement i tue fom jut befoe to jut afte imact? K i total (macocoic) kiic enegy i total (linea) momentum i total angula momentum (about the axle) What i the initial angula momentum of the chil + ik about the axle? a. K,, an o not change b., an o not change c. oe not change. K an o not change e. K an o not change a) < 0, 0, 0 > b) < 0, Rmv, 0 > c) < 0, Rmv, 0 > ) < 0, 0, Rmv > e) < 0, 0, Rmv >

21 What the final angula ee of the mey-go-oun afte the ki jum on? y z (z-axi oint out of age) x The ik ha moment of iia I, an afte the colliion it i otating with angula ee. The otational angula momentum of the ik alone (not counting the chil) i fte the colliion, what i the ee (in m/) of the chil? fte the colliion, what i tanlational angula momentum of the chil about the axle? a. < 0, 0, 0 > b. < 0, I, 0 > c. < 0, I, 0 >. < 0, 0, I > e. < 0, 0, I > a. R b. c. R. /R e. R a. < 0, 0, 0 > b. < 0, Rm, 0 > c. < 0, Rm, 0 >. < 0, Rm( R), 0 > e. < 0, Rm( R), 0 >

22 What the final angula ee of the mey-go-oun afte the ki jum on? y z (z-axi oint out of age). f. i m. g.. f chil. f chil. i 0,0, I ik. 0,0, mr R 0,0, 0,0, I ik x. MR MR 0,0, mr 0,0, t mvr mvr Sytem: chil + mey-go-oun ctive envionment: none that change angula momentum oximation: negligible fictional toque at axel xi: xle 0,0, m M R 0,0, mvr m M R mvr mv m M v M R R m Reaonable?

24 Mon. Tue. We. ab i..4-.6, (.) ngula Momentum Pincile & Toque.7 -.9, (.) Motion With & Without Toque Rotation Coue Eval.0 Quantization, Quiz RE.c EP RE. RE.e Mon. Review fo inal (-) HW: P 9, 57, 64, 74, 78 Sat. 9 a.m. inal Exam (Ch. -)

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

Mon , (.12) Rotational + Translational RE 11.b Tues. Mon..-.3, (.) Rotational + Tanlational RE.b Tue. EP0 Mon..4-.6, (.3) Angula Momentum & Toque RE.c Tue. Wed..7 -.9, (.) Toque EP RE.d ab Fi. Rotation Coue Eval.0 Quantization, Quiz RE.e Mon. Review fo Final