11 Tusaalooyin ah Dhibaatooyinka Dhaqdhaqaaqa Wareega ee Isku Midka ah
1. Walaxdu waxay ku socotaa goobaabin iyadoo xawaare xagal joogto ah oo ah 10 rad/s. Go'aami (a) xawaaraha xagal ee walaxda 10 ilbiriqsi ka dib (b) xagasha ay walaxda hoos u dhigtay 10 ilbiriqsi ka dib.
Dood
(a) xawaare xagal ah 10 ilbiriqsi ka dib
Walaxdu waxay ku socotaa goobaabin isku mid ah = walaxdu waxay ku socotaa xawaare xagal oo joogto ah. Markaa xawaaraha xagasha ka dib 10 ilbiriqsi wuxuu ahaanayaa 10 radian/ilbiriqsi.
(b) xagasha xiran 10 ilbiriqsi ka dib
Xawaaraha xagal ee joogtada ah ee 10 radians/ilbiriqsi wuxuu la macno yahay in 1 ilbiriqsi kasta, walaxdu ay wareegto xagal 10 radians ah. 2 ilbiriqsi ka dib, walaxdu waxay wareegtay xagal 2 x 10 = 20 radians ah. 10 ilbiriqsi ka dib, walaxdu waxay wareegtay xagal 10 x 10 radians ah = 100 radians ah.
2. Barta ku taal cidhifka dhululubada waxay ku socotaa goobaabin xawaare joogto ah oo ah 10 m/s. Gacanka dhululubada = 1 mitir. Go'aami (a) xawaaraha cidhifka dhululubada 5 ilbiriqsi ka dib (b) masaafada uu ku safray cidhifka dhululubada 5 ilbiriqsi ka dib (c) dardargelinta dhexe ee dhibcaha 0,5 mitir iyo 1 mitir u jira dhidibka wareegga.
Dood
(A) xawaaraha dhibic ku taal geeska dhululubada ka dib 5 ilbiriqsi
Dhululubadu waxay ku socotaa goobaabin xawaare joogto ah, sidaas darteed 5 ilbiriqsi ka dib, xawaaraha cidhifka dhululubadu wuxuu ahaanayaa 10 mitir/ilbiriqsi.
(B) Masaafada lagu safray dhibic ku taal geeska dhululubada ka dib 5 ilbiriqsi
Iyada oo aan lahayn qaacido
Xawaaraha 10 mitir/ilbiriqsi wuxuu la macno yahay in 1 ilbiriqsi kasta, barta ku taal geeska dhululubada ay dhaqaaqdo 10 mitir. 1 ilbiriqsi ka dib, barta ku taal geeska dhululubada waxay dhaqaaqdaa 10 mitir. 2 ilbiriqsi ka dib, barta ku taal geeska dhululubada waxay dhaqaaqdaa 20 mitir. 5 ilbiriqsi ka dib, barta ku taal geeska dhululubada waxay dhaqaaqdaa goobo 50 mitir ah.
Isticmaalka qaacidada :
v = s/t
s = vt = (10)(5) = 50 mitir
(C) dardargelinta bartamaha dhexe (a)s)
Xawaaraha dhexe ee dhibic 0,5 mitir u jirta dhidibka waa:
as =v2 / r = 102 / 0,5 = 100 / 0,5 = 200 m/s2
Xawaaraha dhexe ee dhibic 1 mitir u jirta dhidibka waa:
as =v2 / r = 102 / 0,5 = 100 / 1 = 100 m/s2
3. Jadwal wareeg ah oo leh gacan 2 mitir ah ayaa ku socda xawaare xagal joogto ah oo ah 60 rpm. Go'aami (a) xawaaraha xagal ee miiska wareeggu 2 ilbiriqsi ka dib (b) xagasha uu ku xiran yahay miiska wareeggu 1 daqiiqo ka dib (b) xawaaraha tangential, dardargelinta dhexe iyo masaafada uu ku safray hal dhibic 1 mitir laga bilaabo dhidibka wareegga (c) xawaaraha tangential, dardargelinta dhexe iyo masaafada uu ku safray hal dhibic oo ku taal geeska miiska wareeggu.
Dood
Waa la garanayaa :
Jawab :
(A) Xawaaraha xagasha ( ) 2 ilbiriqsi kadib
Xawaaraha xagasha waa mid joogto ah sidaa darteed 2 ilbiriqsi ka dib xawaaraha xagasha ee miiska rogrogmada wuxuu ahaanayaa 6,28 radian/ilbiriqsi
(B) geeska ( ) oo ay ku wareegsan yihiin miis wareeg ah 1 daqiiqo ka dib
Xawaaraha xagal ahaan ee 1 wareeg/ilbiriqsi macnaheedu waa in ilbiriqsi kasta uu sameeyo hal wareeg. 60 ilbiriqsi ka dib, miiska wareeggu wuxuu sameeyay 60 wareeg. Ama, si kale haddii loo dhigo,
Xawaaraha xagal ee 6,28 radians/ilbiriqsi macnaheedu waa in ilbiriqsi kasta oo rogan-ku uu wareego xagal dhan 6,28 radians. 60 ilbiriqsi ka dib, rogan-ku wuxuu wareegay xagal dhan 376,8 radians.
4. Taayir gaari ayaa had iyo jeer sameeya 120 wareeg 60 ilbiriqsi kasta. Waa maxay xawaaraha xagasha ee taayirku? Ku sheeg: (a) wareegyada daqiiqaddii (rpm) ama wareegyada daqiiqaddii (b) darajo ilbiriqsikiiba (o/s) (c) raadiyaan ilbiriqsikiiba (rad/s)
Dood
(A) Xawaaraha xagal ee giraangiraha ee cutubyada wareegyada daqiiqaddii (rpm)
120 wareeg / 60 ilbiriqsi = 120 wareeg / 1 daqiiqo = 120 wareeg / daqiiqo = 120 wareeg
(B) Xawaaraha xagasha ee giraangiraha darajo / ilbiriqsi (o/ s)
1 wareeg = 360o, 120 wareeg = 43200o
Markaa 120 wareeg / 60 ilbiriqsi = (120)(360)o) / 60 ilbiriqsi = 43200o / 60 ilbiriqsi = 720o/ilbiriqsi
(C) Xawaaraha xagal ee giraangiraha ee raadiyaanka/ilbiriqsi (rad/s)
1 wareeg = 6,28 radiyaan
Markaa 120 wareeg / 60 ilbiriqsi = (120)(6,28) raadiyaan / 60 ilbiriqsi = 753,6 raadiyaan / 60 ilbiriqsi = 12,56 raadiyaan/ilbiriqsi
5. Marmar ayaa lagu wareejiyaa baaquli wareegsan oo dhexroorkiisu yahay 1 m. Haddii marmarku ku wareego geeska baaquli xawaare xagal joogto ah oo ah 50 rpm, markaa xawaaraha toosan iyo dardargelinta dhexe ee marmarka waa….
A. 50 ms-1 iyo 2500 ms-2
B. 5π ms-1 iyo 25π2 ms-2
C. 5π/3 ms-1 iyo 25π2/18 ms-2
D. 5π/6 ms-1 iyo 25π2/18 ms-2
E. 5π/12 ms-1 iyo 25π2/36 ms-2
Dood
Waa la ogyahay in:
Dhexroorka goobaabin (D) = 1 mitir
Gacanka goobada (r) = 0,5 mitir
Xawaaraha xagasha (ω) = 50 rpm = 50 wareeg / 1 daqiiqo
1 kacaan = 2π radian
50 wareeg = 50 (2π radian) = 100π radian
1 daqiiqo = 60 ilbiriqsi
Xawaaraha xagasha (ω) = 100π radiyaan / 60 ilbiriqsi = (10π/6) radiyaan/ilbiriqsi
Su'aal: Xawaaraha toosan (v) iyo dardargelinta bartamaha (a)s)
Jawaab:
Xawaaraha toosan (v):
v = r ω = (0,5) (10π/6) = 5π/6 m/s
Dardargelinta bartamaha dhexe (a)s):
as =v2/r = (5π/6)2 : 0,5 = 25π2/36: 0,5 = (25π2/36)(1/0,5)
as = (25π)2/18) m/s2
Jawaabta saxda ah waa D.
6. Shay wuxuu ku socdaa goobaabin leh gacan 50 cm ah. Haddii shaygu uu ku wareego 120 rpm, markaas waqtiga wareegga iyo xawaaraha shaygu waa siday u kala horreeyaan….
A. 0,5 s iyo 2π ms-1
B. 0,5 s iyo 0,2π ms-1
C. 0,5 s iyo π ms-1
D. 2 s iyo 5π ms-1
E. 2 s iyo 10π ms-1
Dood
Waa la ogyahay in:
Gacanka (r) = 50 cm = 0,5 mitir
Xawaaraha xagasha (ω) = 120 rpm = 120 wareeg / 1 daqiiqo = 120 wareeg / 60 daqiiqo = 2 wareeg / 1 ilbiriqsi
1 kacaan = 2π radian
Xawaaraha xagasha (ω) = 2 (2π radians) / 1 ilbiriqsi = 4π radians/ilbiriqsi
Su'aal: Waqtiga wareegga (T) iyo xawaaraha toosan (v)
Jawaab:
Waqtiga ama muddada wareegga (T):
Xiliga waa waqtiga ay shay ku qaadato inuu dhammeeyo hal wareeg.
Shay wuxuu sameeyaa 2 wareeg 1 ilbiriqsikiiba = shay wuxuu sameeyaa 1 wareeg 0,5 ilbiriqsikiiba. Markaa waqtiga ama muddada wareegga waa 0,5 ilbiriqsi.
Xawaaraha walaxda (v):
v = r ω = (0,5 mitir)(4π radians/ilbiriqsi) = 2π mitir/ilbiriqsi
Jawaabta saxda ah waa A.
Baro agabka ku saabsan dhaqdhaqaaqa wareegga iyo dhaqdhaqaaqa wareegga caadiga ah si aad si fiican u fahamto doodda su'aashan.
7. Giraangiraha leh gacan 10 cm ah ayaa si isku mid ah u wareegaya, isagoo dhammaystiraya 180 wareeg daqiiqaddii. Xawaaraha toosan ee barta ku taal geeska giraangiraha waa…
Dood
Waa la ogyahay in:
La weydiiyay:
Xawaaraha toosan (v)?
Jawaab:
Barta ku taal cidhifka giraangiraha waxay 0,1 mitir u jirtaa bartamaha giraangiraha.
Jawaabta saxda ah waa A.
8. Shay ayaa ku socda xawaare joogto ah v oo ku socda waddo wareegsan oo leh gacan R oo leh dardargelin dhexe (as) Si dardargelinta dhexe ay saddex jibaar u noqoto tii asalka ahayd markaas...
A. v waxaa la sameeyaa 4 jeer halka R-na la sameeyo 2 jeer mar kale.
B. v waxaa la sameeyaa 2 jeer R-na waxaa la sameeyaa 4 jeer mar kale
C. v waxaa la sameeyaa 3 jeer R-na waxaa la sameeyaa 3 jeer mar kale.
D. v ayaa harsan R-na waa la labanlaabayaa mar kale
E. v ayaa mar kale la labanlaabay R-na wuu sii jirayaa
Dood
Jawaabta saxda ah waa C.
9. Giraangiraha A, B iyo C way isku xiran yihiin sida ku cad sawirka. Haddii giraangiraha giraangiraha A, B iyo C ay yihiin 10 cm, 4 cm iyo 2 cm siday u kala horreeyaan, giraangiraha B-na uu ku wareego xawaare xagal ah oo ah 5 rad.s.-1 ka dibna giraangiraha C wuxuu ku wareegayaa xawaare xagal ah….
A. 80 rad.s-1
B. 55 rad.s-1
C. 40 rad.s-1
D. 25 rad.s-1
E. 10 rad.s-1
Dood
Waa la ogyahay in:
Jawaab:
Xiriirka ka dhexeeya giraangiraha A iyo giraangiraha B
Giraangiraha A iyo B way isku xiran yihiin, sidaas darteed way isku wareegaan. Maadaama ay isla wareegaan, xawaaraha xagasha ee giraangiraha A = xawaaraha xagasha ee giraangiraha B.
Xiriirka ka dhexeeya giraangiraha A iyo giraangiraha C
Wareegga giraangiraha A aad ayuu uga weyn yahay wareegga giraangiraha C. Haddii giraangiraha C uu qaatay xagal 360 aho ama samee hal wareeg, isla waqtigaas, giraangiraha A ma gaarin 360o ama hal wareeg. Sidaa darteed, xawaaraha xagasha ee giraangiraha A lama mid aha xawaaraha xagasha ee giraangiraha C.
Si kastaba ha ahaatee, giraangiraha A iyo C waxaa isku xira xarig. Sababtoo ah waxaa isku xira xarig, inta lagu jiro isla waqtigaas, masaafada uu maro cidhifka giraangiraha A = masaafada uu maro cidhifka giraangiraha C. Markaa xawaaraha toosan ee giraangiraha A = xawaaraha toosan ee giraangiraha B.
Gunaanad:
Jawaabta saxda ah waa D.
10. Shay lehdhaqdhaqaaq wareeg ah oo siman oo leh gacan 6 mitir ah. Haddii 2 daqiiqo gudahood shaygu sameeyo 16 wareeg, markaa xawaaraha toosan shaygu waa….
A. 0,8 p ms-1
B. 1,0 p ms-1
C. 1,2 p ms-1
D. 1,4 p ms-1
E. 1,6 p ms-1
Dood
Waa la ogyahay in:
Gacanka (r) = 6 mitir
Xawaaraha xagasha (ω) = 16 wareeg / 2 daqiiqo = 8 wareeg / daqiiqo = 8 wareeg / 60 ilbiriqsi = 0,13 wareeg / ilbiriqsi.
Waxaa la weydiiyay: xawaaraha toosan (v)?
Jawaab:
Qaacidada xiriirka ka dhexeeya xawaaraha toosan (v) iyo xawaaraha xagal (ω):
v = r ω = (6 mitir)(0,13 wareeg/ilbiriqsi) = 0,8 wareeg mitir/ilbiriqsi
Jawaabta saxda ah waa A.
Haddii lagu muujiyo raadiyaan:
1 kacaan = 2π radians = 2(3,14) = 6,28 radians
Xawaaraha xagasha = 8 (6,28) radians / 60 ilbiriqsi = 50,24 radians / 60 ilbiriqsi = 0,84 radians/ilbiriqsi
v = r ω = (6 mitir)(0,84 radiyaan/ilbiriqsi) = 5,04 radiyaan/ilbiriqsi
11. Barafeeye taageere oo leh gacan 20/π cm ah ayaa 4 jeer ku wareegi kara 1 ilbiriqsi gudahood. Xawaaraha toosan ee caaradda barafeeyuhu waa…
A. 3,2 ms-1
B. 1,6 ms-1
C. 1,3 ms-1
D. 1,0 ms-1
E. 0,8 ms-1
Dood
Waa la ogyahay in:
Gacanka (r) = 20/π m = 20 / 3,14 cm = 6,4 cm = 0,064 mitir
Xawaaraha xagasha (ω) = 4 wareeg / 1 ilbiriqsi = 4 wareeg/ilbiriqsi
1 kacaan = (2)(3,14) raadiyaan = 6,28 raadiyaan
Xawaaraha xagasha (ω) = (4)(6,28) raadiyaan/ilbiriqsi = 25,12 raadiyaan/ilbiriqsi
Su'aal: Xawaaraha toosan (v) ee caaradda mashiinka?
Jawaab:
v = r ω = (0,064 mitir) (25,12 raadiyaan/ilbiriqsi) = 1,6 mitir/ilbiriqsi
Jawaabta saxda ah waa B.
