Relative and Circular Motion
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1 Relaie and Cicula Moion a) Relaie moion b) Cenipeal acceleaion Mechanics Lecue 3 Slide 1
2 Mechanics Lecue 3 Slide 2
3 Time on Video Pelecue Looks like mosly eeyone hee has iewed enie pelecue GOOD! Thank you o hose of you who did! Mechanics Lecue 3 Slide 3
4 Lecue Thoughs Mechanics Lecue 3 Slide 4
5 Wha is he speed of Mike elaie o he saion? A. -1 m/s B. 30 m/s C. 29 m/s D. 31 m/s 70% 30% 0% 0% Mechanics Lecue 3 Slide 5
6 Relaie Moion in 1 dimension Mechanics Lecue 3 Slide 6
7 Relaie Posiion and Refeence Fames Posiion of Mike in he gound fame is he eco sum of he posiion eco of Mike in he ain efeence fame and he posiion eco of he ain in he gound efeence fame. Mechanics Lecue 3 Slide 7
8 Relaie Moion and Refeence Fames Diffeeniae he posiion ecos o obain he elociy ecos Mechanics Lecue 3 Slide 8
9 Relaie Moion and Refeence Fames Mechanics Lecue 3 Slide 9
10 Relaie Moion and Refeence Fames Mechanics Lecue 3 Slide 10
11 Pelecue 3 Quesions 1 again A. B. C. D. -12m 0% 0% 0% 0% Mechanics Lecue 3 Slide 11
12 CheckPoin A gil sands on a moing sidewalk ha moes o he igh a 2 m/s elaie o he gound. A dog uns owad he gil in he opposie diecion along he sidewalk a a speed of 8 m/s elaie o he sidewalk. Wha is he speed of he dog elaie o he gound? dogbel 8 m/s belgound 2 m/s A) 6 m/s B) 8 m/s C) 10 m/s Mechanics Lecue 3 Slide 12
13 Wha is he speed of he dog elaie o he gound? dogbel 8 m/s belgound 2 m/s A) 6 m/s B) 8 m/s C) 10 m/s x dog gound dog bel bel gound ( 8 m/s) (2 m/s) 6 m/s Mechanics Lecue 3 Slide 13
14 CheckPoin A gil sands on a moing sidewalk ha moes o he igh a 2 m/s elaie o he gound. A dog uns owad he gil in he opposie diecion along he sidewalk a a speed of 8 m/s elaie o he sidewalk. Wha is he speed of he dog elaie o he gil? dogbel 8 m/s belgound 2 m/s A) 6 m/s B) 8 m/s C) 10 m/s 42% of you go his igh le s do his again Mechanics Lecue 3 Slide 14
15 Wha is he speed of he dog elaie o he gil? A. B. C. dogbel 8 m/s 0% 0% 0% belgound 2 m/s A) 6 m/s B) 8 m/s C) 10 m/s A) Because he gil is acually moing and he wo ecos ae opposie so ogehe hey make 6 m/s B) Because he gil is no moing elaie o he bel and he dog is going 8 m/s elaie o he bel he dog is also moing 8 m/s elaie o he gil.. C) The dog and gil ae unning owads each ohe so when you add he wo elociies ogehe i would be 82. Mechanics Lecue 3 Slide 15
16 Wha is he speed of he dog elaie o he gil? dogbel 8 m/s belgound 2 m/s A) 6 m/s B) 8 m/s C) 10 m/s B) Because he gil is no moing elaie o he bel and he dog is going 8 m/s elaie o he bel he dog is also moing 8 m/s elaie o he gil. Using he elociy fomula: dog gil dog bel bel gil 8 m/s 0 m/s 8 m/s Mechanics Lecue 3 Slide 16
17 Relaie Moion in 2 Dimensions Speed elaie o shoe Mechanics Lecue 3 Slide 17
18 Relaie Moion in 2 Dimensions Diecion w.. shoeline Mechanics Lecue 3 Slide 18
19 Relaie Moion in 2 Dimensions Caea!!!! The simple addiion of elociies as shown only woks fo speeds much less han he speed of ligh need special elaiiy a ~c. Mechanics Lecue 3 Slide 19
20 Moing Sidewalk Quesion A man sas o walk along he doed line pained on a moing sidewalk owad a fie hydan ha is diecly acoss fom him. The widh of he walkway is 4 m and i is moing a 2 m/s elaie o he fie-hydan. If his walking speed is 1 m/s how fa away will he be fom he hydan when he eaches he ohe side? A. B. C. D. A) 2 m B) 4 m C) 6 m D) 8 m 90% 0% 10% 0% Mechanics Lecue 3 Slide 20
21 If he sidewalk wasn moing: Time o ge acoss: disance / speed 4m / 1m/s 4 s man sidewalk Mechanics Lecue 3 Slide 21
22 Jus he sidewalk: sidewalk hydan Mechanics Lecue 3 Slide 22
23 D D (speed of sidewalk) (ime o ge acoss) (2 m/s) (4 s) 8 m Mechanics Lecue 3 Slide 23
24 Combinaion of moions: Veco soluion man hydan man sidewalk man hydan sidewalk hydan man sidewalk 1ˆ i 0 ˆj 0ˆ i 2 ˆj 1ˆ i 2 ˆj sidewalk hydan man hydan man hydan man hydan man hydan ( 4 ) 2 coss coss ˆj ( ) 4ˆ i 0 ˆj 0 ( ) ( coss coss man hydan 0 ) 4ˆ i 0 ˆj iˆ 0ˆ i coss yj ˆ y 8m man hydan 0 4s man hydan man hydan ( 1ˆ i 2 ˆj ) coss coss 0ˆ i yj ˆ Mechanics Lecue 3 Slide 24
25 Mechanics Lecue 3 Slide 25
26 Swim Race A. B. C. Thee swimmes can swim equally fas elaie o he wae. They hae a ace o see who can swim acoss a ie in he leas ime. Relaie o he wae Beh swims pependicula o he flow Ann swims upseam a 30 degees and Caly swims downseam a 30 degees. Who ges acoss he ie fis? A) Ann B) Beh C) Caly Ann Beh Caly 60% y x 20% 20% 0% Mechanics Lecue 3 Slide 26
27 Look a jus wae & swimmes Time o ge acoss D / V y D A B 30 o 30 o C y x V ybeh V o V yann V o cos(30 o ) V ycaly V o cos(30 o ) Mechanics Lecue 3 Slide 27
28 Clicke Quesion Thee swimmes can swim equally fas elaie o he wae. They hae a ace o see who can swim acoss a ie in he leas ime. Relaie o he wae Beh swims pependicula o he flow Ann swims upseam a 30 degees and Caly swims downseam a 30 degees. Who ges acoss he ie second? A) Ann B) Caly C) Boh same Ann Caly y x Mechanics Lecue 3 Slide 28
29 Acceleaing (Non-Ineial) Fames of Refeence Acceleaing Fame of Refeence Confusing due o he fac ha he acceleaion can esul in wha appeas o be a push o pull. Mechanics Lecue 3 Slide 29
30 Acceleaed Fames of Refeence Acceleaing Fame of Refeence Acceleomee can deec change in elociy Mechanics Lecue 3 Slide 30
31 Ineial Fames of Refeence Ineial Fames of Refeence Non-acceleaing fames of efeence in a sae of consan ecilinea moion wih espec o one anohe. An acceleomee moing wih any of hem would deec zeo acceleaion. Mechanics Lecue 3 Slide 31
32 CheckPoin A gil wils a ock on he end of a sing aound in a hoizonal cicle aboe he head as shown fom aboe in he diagam. If he sing beaks a he insan shown which of he aows bes epesens he esuling pah of he ock? A B C D Afe he sing beaks he ock will hae no foce acing on i so i canno acceleae. Theefoe i will mainain is elociy a he ime of he beak in he sing which is dieced angen o he cicle. Top iew looking down Mechanics Lecue 3 Slide 32
33 Suey Mechanics Lecue 3 Slide 33
34 Roaing Refeence Fames Mechanics Lecue 3 Slide 34
35 Roaing Refeence Fames Speed is consan. Diecion Changing Acceleaion Mechanics Lecue 3 Slide 35
36 Roaing Refeence Fames Mechanics Lecue 3 Slide 36
37 Roaing Refeence Fames Mechanics Lecue 3 Slide 37
38 Roaing Refeence Fames Mechanics Lecue 3 Slide 38
39 Cenipeal Acceleaion Consan speed in cicula pah Acceleaion dieced owad cene of cicle Wha is he magniude of acceleaion? Popoional o: 1. Speed 1. ime ae of change of angle o angula elociy Mechanics Lecue 3 Slide 39
40 Cenipeal Acceleaion Mechanics Lecue 3 Slide 40
41 Cenipeal Acceleaion Mechanics Lecue 3 Slide 41
42 Cenipeal Acceleaion Mechanics Lecue 3 Slide 42
43 ωr ω is he ae a which he angle θ changes: ω dθ d θ Once aound: x / 2πR / T ω θ / 2π / Τ Mechanics Lecue 3 Slide 43
44 ωr Anohe way o see i: dθ R dr dθ dθ R d Rω Mechanics Lecue 3 Slide 44
45 Cenipeal Acceleaion-Example Mechanics Lecue 3 Slide 45
46 Cenipeal Acceleaion due o Eah s oaion Mechanics Lecue 3 Slide 46
47 Mechanics Lecue 3 Slide 47
48 Rie Rescue N Dock Fame boa dock boa ie θ E ie dock Mechanics Lecue 3 Slide 48
49 Rie Rescue-Dock Fame j i j i j i j i dock dock dock dock dock ie dock ie boa ie ie 0.6 ˆ 2.5ˆ ) ( ˆ (0) (3.1)ˆ ˆ ) (24.8*sin )ˆ (24.8* cos 0 ˆ 0ˆ 0 0 θ θ N E dock î ĵ boa Dock Fame dock 0-2.5i0.6j ) ( mee dock ( ) ( ) j i j i j i j i j i j i mee boa mee mee boa boa dock boa boa boa mee mee dock dock mee dock ie boa boa ie boa 0 ˆ 0ˆ ) ( ˆ ) 24.8*sin ( )ˆ 24.8*cos ( 0.6 ˆ 2.5ˆ ) ( ) ( ˆ (0) (3.1)ˆ 0.6 ˆ 2.5ˆ ) ( ˆ ) 24.8*sin ( )ˆ 24.8*cos ( ) ( θ θ θ θ Mechanics Lecue 3 Slide 49
50 Rie Rescue-Dock Fame -2.5i0.6j ( ) dock 0 dock mee Dock Fame *cosθ *sinθ mee mee 0 cosθ 0 sinθ mee mee N ĵ î dock E boa mee mee 2 1 mee ( 2.5) ( 0.6) h Mechanics Lecue 3 Slide 50
51 mee dock dock h ( dock mee dock0 d d ( ( dock mee mee ( Rie Rescue-Dock Fame ) mee -2.5i0.6j ( ) ) 2.5ˆ i 0.6 ˆj ) dock ( ) ) dock 0 ((3.1)ˆ i (0) ˆj ) mee mee iˆ 0.6 ˆj 2 ( ) ( 0.6) mee 2 2 ( ) ( 0.6) 2.26km cosθ sinθ θ deg mee mee dock mee mee d ( ˆ i boa ie N ĵ Dock Fame dock mee î dock E (5.786) ˆj ) boa Mechanics Lecue 3 Slide 51
52 Rie Rescue- fame Child Fame boa dock N θ ĵ î E ie boa ie dock dock boa dock dock ie (24.8* cosθ )ˆ i (24.8*sinθ ) ˆj i ˆ ie dock (3.1)ˆ (0) j dock ( 3.1)ˆ i (0) ˆ j ( ) boa ie ( 24.8* cosθ )ˆ i ( 24.8*sinθ ) ( ) 0 dock 2.5ˆ i 0.6 ˆj 0ˆ i 0 ˆj 0 dock 0 dock 2.5i-0.6j ˆj ( dock mee ) Mechanics Lecue 3 Slide 52
53 Rie Rescue- fame ( ) ( ) ( ) ( ) h j i j i j i j i j i mee mee mee mee mee mee mee mee boa mee mee boa ie boa dock boa boa boa mee mee dock dock mee dock sin *sin cos *cos ˆ 0ˆ ) ( ˆ ) (24.8*sin )ˆ (24.8*cos 0.6 ˆ 2.5ˆ ) ( ) ( ˆ (0) 3.1)ˆ ( 0.6 ˆ 2.5ˆ ) ( θ θ θ θ θ θ N E dock î ĵ boa Child Fame dock 0 2.5i-0.6j ) ( mee dock θ Mechanics Lecue 3 Slide 53
54 dock mee dock d h ( ( dock mee mee ) ) ( mee dock 0 ( ) ) Rie Rescue dock mee iˆ 0.6 ˆj 2.5ˆ i 0.6 ˆj 2 ( ) ( 0.6) mee mee 2 ( 3.1)ˆ i (0) ˆj ) mee d 2 2 ( ) ( 0.6) 2.26km cosθ sinθ θ deg mee mee Mechanics Lecue 3 Slide 54
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