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

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1 Fi Angula Momentum Quiz 10 R 11.a; HW10: 13*, 1, 30, 39 Mon , (.1) Rotational + Tanslational R 11.b Tues. P10 Mon , (.13) Angula Momentum & Toque Tues. Wed , (.11) Toque R 11.c P11 R 11.d ab Fi. 11 Rotation Couse vals Quantization, Quiz 11 R 11.e Mon. Review fo Final (1-11) HW11: Ch 11 P s 39, 57, 64, 74, 78 & Pactice xam

2 Intoducing Angula Momentum The measue of motion about a oint sun Magnitude sun ath towad aound sun ath sun ath sin aound Only aound comonent of momentum counts aound cos 90 sin sun sun ath sun ath sin aound sun ath sun ath sin

3 Using Angula Momentum The measue of motion about a oint Magnitude aound sin What is the magnitude of the angula momentum about location K, fo the object shown below? The magnitude of the object's momentum 7 kg m/s, the distance 0.6 m, and the angle 150

4 Using Angula Momentum The measue of motion about a oint Magnitude aound sin Detemine the magnitude of the tanslational angula momentum of the aticle at location O elative to each oint: A, B, C, D,, F, G, and H. F G H b 9m h 1m 50 kg m/s A w 11m D C B

5 ŷ. ẑ (ti of z-axis aow ointing at you) Using Angula Momentum The measue of motion about a oint Diection xˆ Distinguish with Right Hand Rule The one diection momentum and osition vectos neve oint is z Axis of otation But that s also tue fo Oient Right hand so finges cul with motion, then thum oints in conventional diection of angula momentum

6 ŷ. ẑ xˆ (ti of z-axis aow ointing at you) Using Angula Momentum The measue of motion about a oint Diection xamle 1 Distinguish with Right Hand Rule Oient Right hand so finges cul with motion, then thum oints in conventional diection of angula momentum What ae the diections of Angula Momentum fo aticle 1 about oint A and aticle about oint A a) b) c) d) 1 1 A

7 A comet obits the Sun, in the xy lane. Its momentum is shown by the ed aow. What is the diection of the comet's angula momentum about the Sun? y 1) +x ) x 3) +y 4) y 5) +z 6) z 7) towad the sun 8) away fom the sun x z (out of the age)

8 Using Angula Momentum The measue of motion about a oint Diection Distinguish with Right Hand Rule Detemine the diection of the tanslational angula momentum of the aticle at location O elative to each oint: A, B, C, D,, F, G, and H. ˆ ˆF ˆG ˆH b 9m h 1m 50 kg m/s ˆD ˆC w 11m ˆB ˆA

9 A ball falls staight down in the xy lane. Its momentum is shown by the ed aow. What is the diection of the ball's angula momentum about location A? y 1) +x ) x 3) +y 4) y 5) +z 6) z 7) zeo magnitude 10 kg m/s A 4m z (out of the age) x Given these values, what is the magnitude of the ball s angula momentum about A? 1) 10 kg m /s 3) 40 kg m /s 5) 0

10 ŷ Using Angula Momentum The measue of motion about a oint Magnitude and Diection Most Geneal xession ẑ. xˆ Coss Poduct ẑ Similaly fo osition and momentum in the y-z xˆ. and fo osition and momentum in the x-z ŷ 09_Coss-oduct.y

11 Using Angula Momentum The measue of motion about a oint Magnitude and Diection xamle: say you have a mass that, at some instant, has linea momentum 4,,0 kg m/ s and is A 5,3, 0 m fom some oint A. What is its angula momentum about this oint?

12 What is the diection of < 0, 0, 3> x < 0, 4, 0>? What is the diection of < 0, 4, 0> x < 0, 0, 3>? What is the diection of 1) +x ) x 3) +y 4) y 5) +z 6) z 7) zeo magnitude < 0, 0, 6> x < 0, 0, -3>?

13 If an object is taveling at a constant seed in a vetical cicle, how does the object's angula momentum change as the object goes fom the to of the cicle to the bottom of the cicle? 1. inceases. deceases 3. stays the same but the diection of changes 4. The diection and magnitude of emain the same

14 Using Angula Momentum The measue of motion about a oint ffect of a adial foce (like gavity o electic) sun F ath ath sun sun d dt d dt S S d dt v S S d dt F S ath sun 0 S d dt Paallel Paallel S constant Obit noncicula.y

15 Kele and Planetay Obits: Sweeing ou equal aea in equal time: If t 1 t, then A 1 A Some Geometic maniulation v t A A 1 t 1 h i h b v t v t v t Ab*h v th A v t sin A ½v t sin Some mathematical maniulation 1 t A mvsin m 1 m t sin 1 m t m t 1 Since is constant (and m is constant), A is the same fo the same time inteval

16 Relating negy, Radius and Angula Momentum in Cicula Obit Angula Momentum: Kinetic enegy: obit mv Kinetic and Gavitational Potential negy: Potential enegy: K U 1 mv G Mm obit m Gavitational Foce and Cicula motion: U ( & eendicula) K U v m K F net Mm G Mm U K G obit m mgmm ate in chate will aly same easoning to electic inteaction K K U U K 4m obit

17 Fi Angula Momentum Quiz 10 R 11.a; HW10: 13*, 1, 30, 39 Mon , (.1) Rotational + Tanslational R 11.b Tues. P10 Mon , (.13) Angula Momentum & Toque Tues. Wed , (.11) Toque R 11.c P11 R 11.d ab Fi. 11 Rotation Couse vals Quantization, Quiz 11 R 11.e Mon. Review fo Final (1-11) HW11: Ch 11 P s 39, 57, 64, 74, 78 & Pactice xam

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