Fi. 11.1 Angula Momentum Quiz 10 RE 11.a; HW10: 13*, 21, 30, 35, 39 Mon. 11.2-.3, (.12) Rotational + Tanslational RE 11.b Tues. EP10 Mon. 11.4-.6, (.13) Angula Momentum & Toque Tues. Wed. 11.7 -.9, (.11) Toque RE 11.c EP11 RE 11.d Lab Fi. L11 Rotation Couse Evals 11.10 Quantization, Quiz 11 RE 11.e Mon. Review fo Final (1-11) HW11: Ch 11 P s 39, 57, 64, 74, 78 & Pactice Exam
towad aound q suneath Intoducing Angula Momentum The measue of motion about a oint sun Magnitude L aound suneath suneath sinq Only aound comonent of momentum counts aound 90 q sinq cos q suneath sun sun Eath L sinq aound suneath suneath sin q
Using Angula Momentum The measue of motion about a oint Magnitude L aound sinq 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 q = 150
Using Angula Momentum The measue of motion about a oint Magnitude L aound sinq Detemine the magnitude of the tanslational angula momentum of the aticle at location O elative to each oint: A, B, C, D, E, F, G, and H. L F L G L H b= 9m h = 12m L E L D = 50 kg m/s L A L C L B w= 11m
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
ŷ. ẑ xˆ (ti of z-axis aow ointing at you) Using Angula Momentum The measue of motion about a oint Diection Examle Distinguish with Right Hand Rule Oient Right hand so finges cul with motion, then thum oints in conventional diection of angula momentum
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 2) x 3) +y 4) y 5) +z 6) z 7) towad the sun 8) away fom the sun x z (out of the age)
ŷ. ẑ xˆ (ti of z-axis aow ointing at you) Using Angula Momentum The measue of motion about a oint Diection Examle 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 2 about oint A a) L 1 =+z L 2 =+z b) L 1 = z L 2 =+z c) L 1 =+z L 2 = z d) L 1 = z L 2 = z 1 1 A 2 2
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, E, F, G, and H. LˆF LˆG LˆH b= 9m h = 12m LˆE LˆD = 50 kg m/s LˆA LˆC w= 11m LˆB
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 2) 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 2 /s 3) 40 kg m 2 /s 5) 0
L= x y z y ẑ ŷ x. x Using Angula Momentum The measue of motion about a oint Magnitude and Diection L=( y x x y )z y L= y x z xˆ Most Geneal Exession L= ( z y y z ), ( x z z x ), ( y x x y )z L= Coss Poduct ẑ y Similaly fo osition and momentum in the y-z L=( z y y z )x z L= y z x xˆ. y z L= z y x and fo osition and momentum in the x-z ŷ L=( x z z x )y 09_Coss-oduct.y
L= Using Angula Momentum The measue of motion about a oint Magnitude and Diection = ( z y y z ), ( x z z x ), ( y x x y ) Examle: say you have a mass that, at some instant, has linea momentum 4,2,0 kgm/ s and is A 5,3, 0 m fom some oint A. What is its angula momentum about this oint?
L= = ( z y y z ), ( x z z x ), ( y x x y ) ŷ What is the diection of < 0, 0, 3> x < 0, 4, 0>? What is the diection of < 0, 4, 0> x < 0, 0, 3>? 1) +x 2) x ẑ xˆ 3) +y (ti of z-axis aow ointing at you) 4) y 5) +z 6) z 7) zeo magnitude. What is the diection of < 0, 0, 6> x < 0, 0, -3>?
Fi. 11.1 Angula Momentum Quiz 10 RE 11.a; HW10: 13*, 21, 30, 39 Mon. 11.2-.3, (.12) Rotational + Tanslational RE 11.b Tues. EP10 Mon. 11.4-.6, (.13) Angula Momentum & Toque Tues. Wed. 11.7 -.9, (.11) Toque RE 11.c EP11 RE 11.d Lab Fi. L11 Rotation Couse Evals 11.10 Quantization, Quiz 11 RE 11.e Mon. Review fo Final (1-11) HW11: Ch 11 P s 39, 57, 64, 74, 78 & Pactice Exam