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. -)
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.
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
Rotational ngula Momentum an Rotational Enegy Recall now o K ot ot I I K ot I nalogou to K mv mv K m
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?
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
Obit Non-cicula.y Same inteaction Relative to Diffeent Refeence Point Diffeent ngula Momenta C B Geneally, changing ngula Momenta B
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
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
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, 5 5 5 kg kg kg m m m / / /,, 4,8 4,8 Nm Nm 5. -5 0..6,.8,.6 Nm/ Nm kg m/ m. f 8.6,5.,.4 kg m /
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
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
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? = 0.005 m, R= 0.05 m y z (z-axi oint out of age) x R a) 0.005 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
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
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? = 0.005 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
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
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.
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
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 75 0.5 5kg 0.m a t unit?
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 >
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 >
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?
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. -)