Tusaalooyin su'aalo ah oo ku saabsan isku xirka giraangiraha

4 Tusaalooyin oo ku saabsan su'aalaha Isku xirka Giraangiraha

1. Laba taayir A iyo B waxaa isku xira xarig (fiiri sawirka). Haddii gacanka A uu laba jibaar ka badan yahay gacanka B, markaas waxa dhacaya waa...
A. vA = 2 vB
B. vA = 1/2 vB
C. vA = vB
D. ωA = ωB
E. ωA = 2 ωB
Dood
Waa la ogyahay in:
Radius-ka giraangiraha A (rA) = labanlaab radius-ka giraangiraha B (2 rB)
La weydiiyay:
- Xiriirka ka dhexeeya xawaaraha toosan ee giraangiraha A (vA) iyo xawaaraha toosan ee giraangiraha B (vB)
– Xiriirka ka dhexeeya xawaaraha xagasha ee giraangiraha A (ωA) iyo xawaaraha xagasha ee giraangiraha B (ωA).
Jawaab:
Giraangiraha A iyo B waxaa lagu xiraa cajalad si marka giraangiraha A uu wareego, giraangiraha B sidoo kale uu u wareego. Haddii 1 ilbiriqsi gudahood dusha sare ee giraangiraha A uu u dhaqaaqo 1 mitir, markaas dusha sare ee giraangiraha B sidoo kale uu u dhaqaaqo 1 mitir 1 ilbiriqsi gudahood. Markaa xawaaraha toosan ee giraangiraha A wuxuu la mid yahay xawaaraha toosan ee giraangiraha B (vA = vB).

Dhanka kale, haddii giraangiraha B uu dhammeeyo hal wareeg, giraangiraha A ma uusan dhammaystirin hal wareeg sababtoo ah wareegga giraangiraha B waa yar yahay halka wareegga giraangiraha A uu weyn yahay. Si kale haddii loo dhigo, xawaaraha xagasha giraangiraha A lama mid aha xawaaraha xagasha giraangiraha B. Waa maxay xiriirka ka dhexeeya xawaaraha xagasha giraangiraha A iyo xawaaraha xagasha giraangiraha B?

Xawaaraha giraangiraha A: vA = rA ωA = 2rB ωA
Xawaaraha giraangiraha B: vB = rB ωB
Xawaaraha giraangiraha A wuxuu la mid yahay xawaaraha giraangiraha B:
vA = vB
2rB ωA = rB ωB
2ωA = ωB
ωA = 1/2 ωB
Jawaabta saxda ah waa C.

2. Saddex taayir A, B iyo C ayaa isku xiran sida ku cad sawirka. Haddii raadka taayirada A, B iyo C ay yihiin 20 cm, 8 cm iyo 4 cm siday u kala horreeyaan, taayir B-na uu ku wareego xawaare xagal ah oo ah 10 rad.s.^-1, ka dibna giraangiraha C ayaa ku wareegaya xawaaraha xagal sida weyn…
A. 80 rad.s^-1
B. 50 rad.s^-1
C. 40 rad.s^-1
D. 20 rad.s^-1
E. 10 rad.s^-1
Dood
Waa la ogyahay in:
Gacanka taayirada A (rA) = 20 cm = 0,2 mitir
Gacanka giraangiraha B (rB) = 8 cm = 0,08 mitir
Gacanka taayirada C (rC) = 4 cm = 0,04 mitir
Xawaaraha xagasha ee giraangiraha B (ωB) = 10 rad/s
Su'aal: Xawaaraha xagasha ee giraangiraha C (ωC)
Jawaab:

Xawaaraha xagal iyo xawaaraha toosan ee giraangiraha giraangiraha A

Giraangiraha A iyo giraangiraha B way isku xiran yihiin, sidaas darteed way isku wareegaan. Haddii giraangiraha B uu wareeg ku wareego hal wareeg (360o), markaa inta lagu jiro isla waqtigaas, giraangiraha A sidoo kale wuxuu ku dhaqaaqaa wareeg hal wareeg (360o). Sababtoo ah way isku wareegaan, xawaaraha xagasha ee giraangiraha A (ωA) wuxuu la mid yahay xawaaraha xagasha ee giraangiraha B (ωB).
Xawaaraha xagasha ee giraangiraha A:
ωA = ωB = 10 raadiya/ilbiriqsi
Xawaaraha toosan ee giraangiraha A:
Cabbirka xawaaraha toosan ee geeska giraangiraha A waxaa lagu xisaabiyaa iyadoo la adeegsanayo qaacidada xiriirka ka dhexeeya xawaaraha toosan iyo xawaaraha xagasha, v = r ω.
vA = rA ωA = (0,2 m)(10 rad/s) = 2 m/s

Xawaaraha xagal iyo xawaaraha toosan ee cidhifka giraangiraha C

Wareegga giraangiraha A aad ayuu uga weyn yahay wareegga giraangiraha C. Marka giraangiraha C uu ku dhaqaaqo wareeg hal wareeg (360o), isla waqtigaas giraangiraha A weli ma dhammaystirin hal wareeg (360)^oSidaa 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 ama silsilad. Maadaama ay isku xiran yihiin, inta lagu jiro isla waqtigaas, masaafada ay ku socoto geeska giraangiraha A waa la mid tahay masaafada ay ku socoto geeska giraangiraha C. Markaa xawaaraha toosan ee geeska giraangiraha C (vC) waa la mid yahay xawaaraha toosan ee geeska giraangiraha A (vA).
Xawaaraha toosan ee giraangiraha C:
vC = vA = 2 m/s
Xawaaraha xagasha ee giraangiraha C:
vC = rC ωC
ωC = vC / rC = 2 / 0,04 = 50 radiyaan/ilbiriqsi = 50 radiyaan^-1.
Jawaabta saxda ah waa B.

3. Nidaam giraangireed oo leh radi RA = 2 cm; RB = 4 cm iyo RC = 10 cm ayaa isku xiran sida ku cad sawirka. Giraangiraha B wuxuu ku wareegaa 60 wareeg daqiiqaddii, sidaa darteed xawaaraha toosan ee giraangiraha C waa…

A. 8π cm.s^-1
B. 12 cm.s.^-1
C. 12π cm.s^-1
D. 24 cm.s.^-1
E. 24π cm.s^-1
Dood
Waa la ogyahay in:
Gacanka giraangiraha A (rA) = 2 cm
Radius-ka giraangiraha B (rB) = 4 cm
Gacanka taayirada C (rC) = 10 cm
Xawaaraha xagasha ee giraangiraha B (ωB) = 60 wareeg/daqiiqo = 60 wareeg/60 ilbiriqsi = 1 wareeg/ilbiriqsi = 1(2π radian)/ilbiriqsi = 2π rad/s
Su'aal: Xawaaraha toosan ee giraangiraha C (vC)
Jawaab:
Xawaaraha toosan ee giraangiraha B
Xawaaraha toosan ee geeska giraangiraha B:
vB = rB ωB = (4 cm)(2π rad/s) = 8π cm/s
Xawaaraha toosan ee giraangiraha A
Giraangiraha A iyo giraangiraha B waxaa ku xiran xarig sidaa darteed xawaaraha toosan ee cidhifka giraangiraha A (vA) waa isku mid xawaaraha toosan ee cidhifka giraangiraha B (vB).
vA = vB = 8π cm/s
Xawaaraha toosan ee giraangiraha C
Giraangiraha C iyo giraangiraha A waxaa ku xiran xarig sidaa darteed xawaaraha toosan ee cidhifka giraangiraha C (vC) waa isku mid xawaaraha toosan ee cidhifka giraangiraha A (vA).
vC = vA = vB = 8π cm/s
Jawaabta saxda ah waa A.

4. Ka fiirso xiriirka giraangiraha soo socda! Radi giraangiraha RA = 25 cm, RB = 15 cm, RC = 40 cm, giraangiraha C-na wuxuu ku wareegaa xawaare wareeg ah oo ah 60 wareeg daqiiqaddii. Xawaaraha xagasha ee giraangiraha A waa…
A. 2,5π rad.s^-1
B. 3π rad.s^-1
C. 3,2π rad.s^-1
D. 3,5π rad.s^-1
E. 3,8π rad.s^-1
Dood
Waa la ogyahay in:
Gacanka taayirada A (rA) = 25 cm = 0,25 mitir
Gacanka giraangiraha B (rB) = 15 cm = 0,15 mitir
Gacanka taayirada C (rC) = 40 cm = 0,4 mitir
Xawaaraha xagasha ee giraangiraha C (ωC) = 60 wareeg/daqiiqo = 60 wareeg/60 ilbiriqsi = 1 wareeg/ilbiriqsi = 1(2π radian)/ilbiriqsi = 2π rad/s
Su'aal: Xawaaraha xagasha ee giraangiraha A (ωA)
Jawaab:
Xawaaraha toosan ee giraangiraha C:
vC = rC ωC = (0,4 m)(2π rad/s) = 0,8π m/s
Xawaaraha toosan ee giraangiraha B
Giraangiraha C iyo giraangiraha B waxaa ku xiran xarig sidaa darteed xawaaraha toosan ee cidhifka giraangiraha C (vC) waa isku mid xawaaraha toosan ee cidhifka giraangiraha B (vB).
vB = vC = 0,8π m/s
Xawaaraha xagal iyo xawaaraha toosan ee giraangiraha giraangiraha A
Giraangiraha A iyo giraangiraha B way isku xiran yihiin sida ka muuqata sawirka kore, sidaa darteed xawaaraha xagasha ee giraangiraha A lama mid aha xawaaraha xagasha ee giraangiraha B. Tani waa sababta oo ah wareegga giraangiraha A ayaa ka weyn kan giraangiraha B. Inta lagu jiro isla waqtigaas, marka giraangiraha A uu ku dhaqaaqay goobaabin hal wareeg (360)^o), giraangiraha B weli ma gaarin hal wareeg (360^oSi kastaba ha ahaatee, inta lagu jiro isla waqtigaas, masaafada uu maro cidhifka giraangiraha A waa la mid ah masaafada uu maro cidhifka giraangiraha B. Markaa xawaaraha toosan ee cidhifka giraangiraha A (vA) waa la mid ah xawaaraha toosan ee cidhifka giraangiraha B (vB).
Xawaaraha toosan ee giraangiraha A
vA = vB = vC = 0,8π m/s
Xawaaraha xagasha ee giraangiraha A
vA = rA ωA
ωA = vA / rA = 0,8π / 0,25 = 3,2π rad/s
Jawaabta saxda ah waa C.