Tusaale ahaan daqiiqadda firfircoonida

25 Tusaalooyin Su'aalo ah oo ku saabsan Waqtiga Inertia

Daqiiqadda Inertia ee walxaha

1. Kubad miisaankeedu yahay 100 garaam ayaa lagu xiray xarig dhererkiisu yahay 30 cm sida sawirka ka muuqata. Daqiiqad firfircooni ah Kubadda ku saabsan dhidibka AB waa...
Dood
Waa la ogyahay in:
dhidibka wareegga waa AB
Cufka kubadda (m) = 100 garaam = 100/1000 = 0,1 kiilo garaam
Masaafada kubbadda laga bilaabo dhidibka wareegga (r) = 30 cm = 0,3 mitir
La weydiiyay: Daqiiqad firfircooni ah oo kubadda ah (I)
Jawaab:
Aniga = Mudane² = (0,1 kg)(0,3 m)²
I = (0,1 kg)(0,09 m²)
I = 0,009 kg m²

2. Cufka kubadda m₁ waa 100 garaam, cufnaanta kubbadduna waa m₂ Waa 200 garaam. Labada kubbadood waxaa isku xira silig dhererkiisu yahay 60 cm oo leh cufnaan aan la saadaalin karin. Dhidibka AB wuxuu ku yaal bartamaha siligga. Daqiiqadda firfircoonida labada kubbadood ee ku wareegsan dhidibka AB waa…
Dood
Waa la ogyahay in:
Cufka kubadda 1 (m₁) = 100 garaam = 100/1000 = 0,1 kiilo garaam
Masaafada kubadda 1 u jirta dhidibka wareegga (r)₁) = 30 cm = 30/100 = 0,3 mitir
Cufka kubadda 2 (m₂) = 200 garaam = 200/1000 = 0,2 kiilo garaam
Masaafada kubadda 2 u jirta dhidibka wareegga (r)₂) = 30 cm = 30/100 = 0,3 mitir
La weydiiyay: Daqiiqadda firfircoonida nidaamka laba kubbadood
Jawaab:
Aniga = m₁ r₁² +m₂ r₂²
I = (0,1 kg)(0,3 m)² + (0,2 kg)(0,3 m)²
I = (0,1 kg)(0,09 m²) + (0,2 kg) (0,09 m²)
I = 0,009 kg m² + 0,018 kg m²
I = 0,027 kg m²

3. Cufka kubadda m₁ waa 200 garaam, cufnaanta kubbadduna waa m₂ waa 100 garaam. Labada kubbadood waxaa isku xira silig dhererkiisu yahay 60 cm, cufkiisuna waa la iska indho tiraa. Dhidibka AB wuxuu ku yaal kubbadda m.₂Daqiiqadda firfircoonida nidaamka labada kubbadood ee ku wareegsan dhidibka AB waa…
Dood
Waa la ogyahay in:
Cufka kubadda 1 (m₁) = 200 garaam = 200/1000 = 0,2 kiilo garaam
Masaafada kubadda 1 u jirta dhidibka wareegga (r)₁) = 60 cm = 60/100 = 0,6 mitir
Cufka kubadda 2 (m₂) = 100 garaam = 100/1000 = 0,1 kiilo garaam
Masaafada kubadda 2 u jirta dhidibka wareegga (r)₂) = 0 mitir
La weydiiyay: Daqiiqadda firfircoonida nidaamka laba kubbadood
Jawaab:
Aniga = m₁ r₁² +m₂ r₂²
I = (0,2 kg)(0,6 m)² + (0,2 kg)(0)²
I = (0,2 kg)(0,36 m²) + 0
I = 0,072 kg m²

4. Kubbad kasta waxay leedahay cuf dhan 100 garaam waxaana ku xiran silig miisaankiisu yar yahay. Dhererka siliggu waa 60 cm ballaciisuna waa 30 cm. Go'aami daqiiqadda firfircoonida nidaamka kubbadda ee ku saabsan dhidibka AB…
Dood
Waa la ogyahay in:
Cufka kubadda 1 (m₁) = m₂ = m₃ = m₄ = 100 garaam = 100/1000 = 0,1 kiilo garaam
Masaafada kubadda 1 u jirta dhidibka wareegga (r)₁) = 30 cm = 30/100 = 0,3 mitir
Masaafada kubadda 2 u jirta dhidibka wareegga (r)₂) = 30 cm = 30/100 = 0,3 mitir
Masaafada kubadda 3 u jirta dhidibka wareegga (r)₃) = 30 cm = 30/100 = 0,3 mitir
Masaafada kubadda 4 u jirta dhidibka wareegga (r)₄) = 30 cm = 30/100 = 0,3 mitir
La weydiiyay: Daqiiqadda firfircoonida nidaamka kubadda
Jawaab:
Aniga = m₁ r₁² +m₂ r₂² +m₃ r₃² +m₄ r₄²
I = (0,1 kg)(0,3 m)² + (0,1 kg)(0,3 m)² + (0,1 kg)(0,3 m)² + (0,1 kg)(0,3 m)²
I = (0,1 kg)(0,09 m²) + (0,1 kg) (0,09 m²) + (0,1 kg) (0,09 m²) + (0,1 kg) (0,09 m²)
I = 0,036 kg m²

5. Fiiri sawirka hoose. Afar walxood, mid walba oo leh cuf dhan 4m (masaafo r ka fog bartamaha), 3m (masaafo r ka fog bartamaha), 2m (masaafo 2r ka fog bartamaha), 2m (masaafo r ka fog bartamaha). Nidaamku wuxuu ku yaal diyaaradda xy. Haddii nidaamku uu ku wareego dhidibka x, markaa daqiiqadda inertia ee nidaamku waa…
A. 5 m r
B. 7 m r     
C. 5 m r²
D. 6 m r²
E. 7kii m r²

Dood:
Waa la garanayaa :
Waa la ogyahay in:
m₁ = 4m (masaafada r laga bilaabo bartamaha), m₂ = 3m (masaafada r laga bilaabo bartamaha), m₃ = 2m (masaafada 2r laga bilaabo bartamaha), m₄ = 2m (masaafada r laga bilaabo bartamaha)
La weydiiyay :
Daqiiqadda firfircoonida (I)?
Jawab :
Qaacidada daqiiqadda firfircoonida ee walaxda :
Aniga = Mudane²
Nidaamka waxaa lagu wareejiyaa dhidibka x si m uu u noqdo₂ iyo m₄ waxay ku taal dhidibka wareegga. Sababtoo ah waxay ku taal dhidibka wareegga, r₂ iyo r₄ waa eber.
I₁ = m₁ r₁² = 4mr²
I₂ = m₂ r₂² = 3m (0)² = 0
I₃ = m₃ r₃² = 2m (2r)² = 2m (4r)²) = 8mr²
I₄ = m₄ r₄² = 2m (0)² = 0
Daqiiqadda firfircoonida nidaamka :
I = aniga₁ + Aniga₂ + Aniga₃ + Aniga₄
I = 4mr² + 8mr²
I = 12mr²

6. Rod AB wuxuu leeyahay cufnaan dhan 3 kg marka la dhex wareego B, daqiiqaddiisa firfircoonidu waa 27 kg m²Haddii lagu wareejiyo C, daqiiqadda inertia waxay noqotaa…
A. 70 kg m²
B. 76 kg m²
C. 92 kg m²
D. 98 kg m²
E. 108 kg m²
Dood:

Waa la garanayaa :
m = 3 kg
I_B = 27 kg m²
La weydiiyay :
I_C ?
Jawab :
I_B = Mudane.²
27 kg m² = (3 kg)(r)²)
27 kg m² / 3 kg = r²
9 m² =r²
r = 3 m
Dhererka AB = dhererka AC = 3 mitir

Daqiiqadda Inertia Usha marka la dhex wareego C:
I_C = Mudane.²
I_C = (3 kg) (6m)²
I_C = (3 kg)(36 m)²) = 108 kg m²

7.

Laba kubbadood, oo loo arko inay yihiin walxo, ayaa ku xiran xarig silig ah sida ku cad sawirka. Haddii cufka kubbadaha P iyo Q ay yihiin 600 garaam iyo 400 garaam siday u kala horreeyaan, markaa daqiiqadda firfircoonida nidaamka labada kubbadood ee ku wareegsan dhidibka AB waa…

A. 0,008 kg.m²
B. 0,076 kg.m²
C. 0,124 kg.m²
D. 0,170 kg.m²
E. 0,760 kg.m²

Dood
Waa la garanayaa :
Cufka kubadda P (m)_P) = 600 garaam = 0,6 kg
Cufka kubadda Q (m)_Q) = 400 garaam = 0,4 kg
Masaafada kubadda P laga bilaabo dhidibka wareegga (r)_P) = 20 cm = 0,2 mitir
Masaafada kubadda Q u jirta dhidibka wareegga (r)_Q) = 50 cm = 0,5 mitir
La weydiiyay : Daqiiqad firfircooni ah (I) nidaamka marka loo eego dhidibka ama dhidibka wareegga AB
Jawab :

Qaacidada daqiiqadda firfircoonida ee walaxda :
Aniga = Mudane²
Sharaxaad: I = daqiiqadda firfircoonida, m = cufka walaxda, r = masaafada walaxda laga bilaabo dhidibka wareegga
Daqiiqad firfircoon oo kubadda ah P
I_P = (m_P)(r_P²) = (0,6)(0,2)² = (0,6)(0,04) = 0,024 kg m²
Daqiiqadda firfircoonida kubadda Q
I_Q = (m_Q)(r_Q²) = (0,4)(0,5)² = (0,4)(0,25) = 0,1 kg m²
Daqiiqadda firfircoonida nidaamka walxaha :
I = aniga_P + Aniga_Q = 0,024 + 0,1 = 0,124 kg m²
Jawaabta saxda ah waa C.

8.

Laba kubbadood oo ay silig isku xiran yihiin (cufnaanta siligga waa la iska indho tiray) ayaa loo habeeyay sida ku cad sawirka. Cabbirka daqiiqaddooda firfircooni waa…

A. 20 x 10^-3 kg.m²
B. 25 x 10^-3 kg.m²
C. 11 x 10^-2 kg.m²
D. 55 x 10^-2 kg.m²
E. 80 x 10^-2 kg.m²

Dood
Waa la garanayaa :
Cufka kubadda A (m)_A) = 200 garaam = 0,2 kg
Cufka kubadda B (m)_B) = 400 garaam = 0,4 kg
Masaafada u dhaxaysa kubadda A iyo dhidibka wareegga (r)_A= 0
Masaafada u dhaxaysa kubadda B iyo dhidibka wareegga (r)_B) = 25 cm = 0,25 mitir
La weydiiyay Daqiiqada firfircoonida (I) ee nidaamka
Jawab :
Daqiiqad firfircoon oo kubadda A ah
I_A = (m_A)(r_A²) = (0,2)(0)² = 0
Daqiiqadda firfircoonida kubadda B
I_B = (m_B)(r_B²) = (0,4)(0,25)² = (0,4)(0,0625) = 0,025 kg m²
Daqiiqadda firfircoonida nidaamka walxaha :
I = aniga_A + Aniga_B = 0 + 0,025 = 0,025 kg m² = 25x10^-3 kg m²
Jawaabta saxda ah waa B.

9.
Fiiri sawirka laba kubbadood oo ay silig isku xiran yihiin. Dhererka siliggu = 12 m, l₁ = 4 m oo cufka fiilada la iska indho tiro, markaas baaxadda daqiiqadda firfircoonida nidaamka waa…
A. 52,6 kg m²
B. 41,6 kg m²
C. 34,6 kg m²
D. 22,4 kg m²
E. 20,4 kg m²
Dood
Waa la garanayaa :
Cufka kubadda A (m)_A) = 0,2 kg
Cufka kubadda B (m)_B) = 0,6 kg
Masaafada u dhaxaysa kubadda A iyo dhidibka wareegga (r)_A) = 4 mitir
Masaafada u dhaxaysa kubadda B iyo dhidibka wareegga (r)_B) = 12 – 4 = 8 mitir
La weydiiyay Daqiiqada firfircoonida (I) ee nidaamka
Jawab :
Daqiiqad firfircoon oo kubadda A ah
I_A = (m_A)(r_A²) = (0,2)(4)² = (0,2)(16) = 3,2 kg m²
Daqiiqadda firfircoonida kubadda B
I_B = (m_B)(r_B²) = (0,6)(8)² = (0,6)(64) = 38,4 kg m²
Daqiiqadda firfircoonida nidaamka walxaha :
I = aniga_A + Aniga_B = 3,2 + 38,4 = 41,6 kg m²
Jawaabta saxda ah waa B.

Daqiiqadda Inertia ee Jir Adag

10. Ul adag waxay leedahay cufnaan dhan 2 kg iyo dhererkeeduna yahay 2 mitir. Go'aami daqiiqadda firfircoonida usha haddii dhidibka wareegga uu ku yaal bartamaha usha!
Dood
Waa la ogyahay in:
Cufka usha adag (M) = 2 kg
Dhererka jirridda adag (L) = 2 mitir
La weydiiyay: Daqiiqad firfircooni ah
Jawaab:
Qaacidada daqiiqadda firfircoonida ul haddii dhidibka wareeggu uu ku yaal bartamaha ul:
I = (1/12) ML²
I = (1/12) (2 kg) (2 m)²
I = (1/12) (2 kg) (4 m)²)
I = (1/12)(8 kg m²)
I = 8/12 kg m²
I = 2/3 kg m²

11. Ul adag waxay leedahay cufnaan dhan 2 kg iyo dhererkeeduna yahay 2 mitir. Go'aami daqiiqadda firfircoonida usha haddii dhidibka wareegga uu ku yaal mid ka mid ah dhammaadka usha!
Dood
Waa la ogyahay in:
Cufka usha adag (M) = 2 kg
Dhererka jirridda adag (L) = 2 mitir
La weydiiyay: Daqiiqad firfircooni ah
Jawaab:
Qaacidada daqiiqadda firfircoonida ul haddii dhidibka wareegga uu ku yaal hal dhammaad oo usha ah:
I = (1/3) ML²
I = (1/3) (2 kg) (2 m)²
I = (1/3) (2 kg) (4 m)²)
I = (1/3)(8 kg m²)
I = 8/3 kg m²

12. Go'aami daqiiqadda firfircoonida saxan adag oo miisaankiisu yahay 10 kg iyo gacan 0,1 mitir, haddii dhidibka wareeggu uu ku yaal bartamaha saxanka, sida ka muuqata sawirka!
Dood
Waa la ogyahay in:
Cufka saxanka adag (M) = 10 kg
Gacanka saxanka adag (L) = 0,1 mitir
La weydiiyay: Daqiiqad firfircoon oo ah saxan adag
Jawaab:
Qaacidada loogu talagalay daqiiqadda firfircoonida usha haddii dhidibka wareegga uu ku yaal bartamaha saxanka:
I = (1/2) ML²
I = (1/2) (10 kg) (0,1 m)²
I = (1/2) (10 kg) (0,01 m)²)
I = (1/2)(0,1 kg m²)
I = 0,05 kg m²

13. Go'aami daqiiqadda firfircoonida kubbadda adag oo miisaankeedu yahay 20 kg iyo gacanka 0,1 mitir, haddii dhidibka wareegga uu ku yaal bartamaha kubadda, sida ku cad sawirka!
Dood
Waa la ogyahay in:
Cufka kubadda adag (M) = 20 kg
Gacanka kubbadda adag (L) = 0,1 mitir
La weydiiyay: Daqiiqad firfircooni ah
Jawaab:
Qaacidada daqiiqadda firfircoonida ul haddii dhidibka wareegga uu ku yaal bartamaha goob adag:
I = (2/5) ML²
I = (2/5)(20 kg)(0,1 m)²
I = (2/5)(20 kg)(0,01 m²)
I = (2/5)(0,2 kg m²)
I = 0,4/5 kg m²
I = 0,08 kg m²

14. Go'aami daqiiqadda firfircoonida kubbadda khafiifka ah ee godka ah oo miisaankeedu yahay 0,5 kg iyo gacanka 0,1 mitir, haddii dhidibka wareegga uu ku yaal bartamaha kubadda, sida ku cad sawirka!
Dood
Waa la ogyahay in:
Cufka kubbad khafiif ah (M) = 0,5 kg
Gacanka wareegsan ee khafiifka ah (L) = 0,1 mitir
La weydiiyay: Daqiiqadda qaacidada inertia
Jawaab:
Qaacidada daqiiqadda firfircoonida ul haddii dhidibka wareegga uu ku yaal bartamaha kubbadda khafiifka ah:
I = (2/3) ML²
I = (2/3) (0,5 kg) (0,1 m)²
I = (2/3) (0,5 kg) (0,01 m)²)
I = (2/3)(0,005 kg m²)
I = 0,01/3 kg m²

15. Saxan adag oo leydi ah wuxuu leeyahay cufnaan dhan 2 kg, dhererkiisuna waa 0,5 mitir iyo ballaciisuna waa 0,2 mitir. Go'aami daqiiqadda firfircoonida saxanka adag haddii dhidibka wareeggu uu ku yaal bartamaha saxanka, sida ka muuqata sawirka!
Dood
Waa la ogyahay in:
Cufka saxan adag oo leydi ah (M) = 2 kg
Dhererka saxanka (a) = 0,5 mitir
Ballaca saxanka (b) = 0,2 mitir
La weydiiyay: Daqiiqadda qaacidada inertia
Jawaab:
Qaacidada daqiiqadda firfircoonida saxan adag oo leydi ah haddii dhidibka wareeggu uu ku yaal bartamaha saxanka adag:
I = (1/12) M (a)² + b²)
I = (1/12)(2)(0,52 + 0,22)
I = (2/12)(0,25 + 0,04)
I = (1/6)(0,29)
I = 0,29/6 kg m²

16. Waa kan hadal ku saabsan arrimaha dhaqdhaqaaqa wareegga.

(1) Xawaaraha xagasha

(2) Meesha uu ku yaal dhidibka wareegga

(3) Qaabka shayga

(4) Cufka shay

Waxyaabaha saameeya baaxadda daqiiqadda firfircoonida waa...

A. (1), (2), (3) iyo (4)

B. (1), (2) iyo (3)

C. (1), (3) iyo (4)

D. (2), (3) iyo (4)

E. (2) iyo (4) oo keliya

Dood

Daqiiqadda qaacidada inertia:

Aniga = Σm r²

Sharaxaad: m = cufka shayga, r = masaafada u jirta dhidibka wareegga.

Iyada oo lagu saleynayo qaacidadan, waxaa lagu soo gabagabeynayaa in daqiiqadda inertia ay saameyn ku leedahay booska dhidibka wareegga (2) iyo cufka shayga (4).

Jawaabta saxda ah waa E.

17. Laba kubbadood, oo loo arko inay yihiin walxo, ayaa ku xiran xarig silig ah sida ku cad sawirka. Haddii cufka kubbadaha P iyo Q ay yihiin 600 garaam iyo 400 garaam siday u kala horreeyaan, markaa daqiiqadda firfircoonida nidaamka labada kubbadood ee ku wareegsan dhidibka AB waa…

A. 0,008 kg m²

B. 0,076 kg m²

C. 0,124 kg m²

D. 0,170 kg m²

E. 0,760 kg m²

Dood

Waa la ogyahay in :

dhidibka wareegga waa AB.

m_p = 600 garaam = 0,6 kg, m_q = 400 garaam = 0,4 kg

r _p = 20 cm = 0,2 m, r _q = 50 cm = 0,5 m

La weydiiyay : Daqiiqadda firfircoonida nidaamka?

Jawaab :

I = m _p r _p ² + m _q r _q ²

I = (0,6 kg)(0,2 m) ² + (0,4 kg)(0,5 m) ²

I = (0,6 kg)(0,04 m ² ) + (0,4 kg)(0,25 m ² )

I = 0,024 kg m ² + 0,1 kg m ²

I = 0,124 kg m ²

Jawaabta saxda ah waa C.

18. Daqiiqadda firfircoonida shay ku wareegaya meel go'an waxaa saameeya...

A. cufka shayga

B. mugga shayga

C. cufnaanta shayga

D. dardargelinta xagal-wareegga

E. xawaaraha xagasha bilowga ah

Dood

Daqiiqadda qaacidada inertia:

Aniga = ∑mr²

Sharaxaad: I = daqiiqadda inertia, m = cufnaanta, r = masaafada u jirta dhidibka wareegga

Jawaabta saxda ah waa A.

19. Rod AB oo leh cufnaan dhan 2 kg ayaa lagu wareejiyaa barta A, daqiiqadda firfircooniduna waa 8 kg m²Marka lagu wareejiyo barta dhexe ee O (AO = OB), daqiiqadda inertia waxay noqotaa...

A. 2 kg m²

B. 4 kg m²

C. 8 kg m²

D. 12 kg m²

E. 16 kg m²

Dood

Waa la ogyahay in:

Cufka usha AB (m) = 2 kg

Haddii lagu wareejiyo barta A si gacanka wareegga (r) = masaafada AB = r markaa daqiiqadda inertia (I) = 8 kg m²

La weydiiyay: Haddii lagu wareejiyo barta O si gacanka wareegga (r) = masaafada AO = masaafada OB = 1/2 r markaa daqiiqadda inertia waxay noqotaa (I) = ……

Jawaab:

Aniga = Mudane ²

8 kg m ² = (2 kg) r ²

8 m ² = (2) r ²

r ² = 8 m ^2/2

r ² = 4 m ²

r = 2 mitir

Haddii lagu wareejiyo barta O si 1/2 r = 1 mitir, markaa daqiiqadda inertia waxay noqonaysaa:

I = mr ² = (2 kg)(1 m ) ² = (2 kg)(1 m ² ) = 2 kg m ²

Jawaabta saxda ah waa A.

20. Laba kubbadood, oo loo arko inay yihiin walxo, ayaa ku xiran xarig silig ah sida ku cad sawirka. Haddii cufka kubbadaha P iyo Q ay yihiin 600 garaam iyo 400 garaam siday u kala horreeyaan, markaa daqiiqadda firfircoonida nidaamka labada kubbadood ee ku wareegsan dhidibka AB waa…

A. 0,008 kg.m²

B. 0,076 kg.m²

C. 0,124 kg.m²

D. 0,170 kg.m²

E. 0,760 kg.m²

Dood

Waa la ogyahay in :

Cufka kubadda P (m)_P) = 600 garaam = 0,6 kg

Cufka kubadda Q (m)_Q) = 400 garaam = 0,4 kg

Masaafada kubadda P laga bilaabo dhidibka wareegga (r)_P) = 20 cm = 0,2 mitir

Masaafada kubadda Q u jirta dhidibka wareegga (r)_Q) = 50 cm = 0,5 mitir

La weydiiyay Daqiiqada inertia (I) ee nidaamka ku saabsan dhidibka ama dhidibka wareegga AB

Jawab :
Qaacidada daqiiqadda firfircoonida ee walaxda :

Aniga = Mudane ²

Sharaxaad: I = daqiiqadda firfircoonida, m = cufka walaxda, r = masaafada walaxda laga bilaabo dhidibka wareegga

Daqiiqad firfircoon oo kubadda ah P

I_P = (m_P)(r_P²) = (0,6)(0,2)² = (0,6)(0,04) = 0,024 kg m²

Daqiiqadda firfircoonida kubadda Q

I_Q = (m_Q)(r_Q²) = (0,4)(0,5)² = (0,4)(0,25) = 0,1 kg m²

Daqiiqadda firfircoonida nidaamka walxaha :

I = aniga_P + Aniga_Q = 0,024 + 0,1 = 0,124 kg m²

Jawaabta saxda ah waa C.

21. Laba kubbadood oo ay silig isku xiran yihiin (cufnaanta siligga waa la iska indho tiray) ayaa loo habeeyay sida ku cad sawirka. Cabbirka daqiiqaddooda firfircooni waa…

A. 20 x 10^-3 kg.m²

B. 25 x 10^-3 kg.m²

C. 11 x 10^-2 kg.m²

D. 55 x 10^-2 kg.m²

E. 80 x 10^-2 kg.m²

Dood

Waa la ogyahay in :

Cufka kubadda A (m)_A) = 200 garaam = 0,2 kg

Cufka kubadda B (m)_B) = 400 garaam = 0,4 kg

Masaafada u dhaxaysa kubadda A iyo dhidibka wareegga (r)_A= 0

Masaafada u dhaxaysa kubadda B iyo dhidibka wareegga (r)_B) = 25 cm = 0,25 mitir

La weydiiyay Daqiiqada firfircoonida (I) ee nidaamka

Jawaab :

Daqiiqad firfircoon oo kubadda A ah

I _A = (m _A )(r _A ² ) = (0,2)(0) ² = 0

Daqiiqadda firfircoonida kubadda B

I _B = (m _B )(r _B ² ) = (0,4)(0,25) ² = (0,4)(0,0625) = 0,025 kg m ²

Daqiiqadda firfircoonida nidaamka walxaha :

I = aniga_A + Aniga_B = 0 + 0,025 = 0,025 kg m² = 25x10^-3 kg m²

Jawaabta saxda ah waa B.

22. Afar walxood oo cufnaan kala duwan leh ayaa ku yaal isla hal meel, sida ka muuqata sawirka. Daqiiqadda inertia ee nidaamka oo leh dhidib toosan p waa…

A. 17 mb²

B. 22 mb²

C. 27 mb²

D. 31 mb²

E. 33 mb²

Dood

Dhidibka wareegga = xariiqda toosan p

Waa la ogyahay in:

Cufka walxaha A (m)_A) = m

Cufka walxaha B (m)_B) = 2m

Cufka walxaha C (m)_C) = 3m

Cufka walxaha D (m)_D) = 4m

Masaafada walxaha A laga bilaabo dhidibka wareegga (r)_A) = b

Masaafada walxaha B laga bilaabo dhidibka wareegga (r)_B) = b

Masaafada walxaha C laga bilaabo dhidibka wareegga (r)_C) = 2b

Masaafada walxaha D laga bilaabo dhidibka wareegga (r)_D) = 2b

La weydiiyay: Daqiiqadda firfircoonida nidaamka oo leh dhidib toosan p

Jawaab:

Aniga = m_A r_A² +m_B r_B² +m_C r_C² +m_D r_D²

I = (m) (b) ² + (2m) (b) ² + (3m) (2b) ² + (4m) (2b) ²

I = mb² + 2 mb² + (3m) (4b)²) + (4m) (4b)²)

I = mb ² + 2 mb ² + 12 mb ² + 16 mb ²

I = 31 mb ²

Jawaabta saxda ah waa D.

23. Fiiri sawirka soo socda!

Afar qaybood ayaa ku xiran ul cufnaan aan la taaban karin. Daqiiqadda inertia ee nidaamka ku wareegsan dhidibka waa iyada oo loo marayo m₁ iyo m₂ waa…

A. 1/200 kg.m²

B. 1/300 kg.m²

C. 1/400 kg.m²

D. 1/600 kg.m²

E. 1/800 kg.m²

Dood

Waa la ogyahay in:

Cufka walxaha 1 (m₁) = 1/4 kg

Cufka walxaha 2 (m₂) = 1/2 kg

Cufka walxaha 3 (m₃) = 1/4 kg

Cufka walxaha 4 (m₄) = 1/4 kg

Masaafada walxaha 1 u jirta dhidibka wareegga (r)₁= 0

Masaafada walxaha 2 u jirta dhidibka wareegga (r)₂= 0

Masaafada walxaha 3 u jirta dhidibka wareegga (r)₃) = 10 cm = 10/100 mitir = 1/10 mitir

Masaafada walxaha 4 u jirta dhidibka wareegga (r)₄) = 10 cm = 10/100 mitir = 1/10 mitir

La weydiiyay: Daqiiqadda firfircoonida nidaamka

Jawaab:

Aniga = m₁ r₁² +m₂ r₂² +m₃ r₃² +m₄ r₄²

I = (1/4)(0) ² + (1/2)(0) ² + (1/4)(1/10) ² + (1/4)(1/10) ²

I = 0 + 0 + (1/4)(1/100) + (1/4)(1/100)

I = 1/400 + 1/400

I = 2/400

I = 1/200 kg ^{m 2}

Jawaabta saxda ah waa A.

24. Laba kubbadood oo loo arko inay yihiin walxo ayaa isku xira xarig silig ah sida ku cad sawirka. Haddii cufka kubbadaha P iyo Q ay yihiin 600 garaam iyo 400 garaam siday u kala horreeyaan, markaa daqiiqadda firfircoonida nidaamka labada kubbadood ee ku wareegsan dhidibka AB waa…

A. 0,008 kg m²
B. 0,076 kg m²
C. 0,124 kg m²
D. 0,170 kg m²
E. 0,760 kg m²

Dood
Waa la garanayaa :
dhidibka wareegga waa AB.
m_p = 600 garaam = 0,6 kg, m_q = 400 garaam = 0,4 kg
r_p = 20 cm = 0,2 m, r_q = 50 cm = 0,5 m
La weydiiyay : Daqiiqadda firfircoonida nidaamka?
Jawab :
Aniga = m_p r_p² +m_q r_q²
I = (0,6 kg)(0,2 m)² + (0,4 kg)(0,5 m)²
I = (0,6 kg)(0,04 m²) + (0,4 kg) (0,25 m²)
I = 0,024 kg m² + 0,1 kg m²
I = 0,124 kg m²
Jawaabta saxda ah waa C.

25. Laba shay oo adag, dhululubo iyo wareeg, ayaa ku yaal meel siman. Labada shayba waxaa jiidaya xoog isku mid ah, iyadoo barta taabashada ay ku taal bartamaha, waxayna leeyihiin xawaare bilow ah oo isku mid ah. Kee baa sax ah weedhaha soo socda?

(1) Haddii raadka labada shay ay isku mid yihiin oo sagxadduna siman tahay, markaa xawaaraha labada shay had iyo jeer waa isku mid.

(2) Haddii gacanka kubbadu uu weyn yahay oo dhulku uu qallafsan yahay, markaa xawaaraha labada shay had iyo jeer wuu isku mid noqon doonaa.

(3) Haddii raadka uusan isku mid ahayn oo sagxadduna ay simbiriirixan tahay, markaa xawaaraha ugu dambeeya ee labada shay wuxuu noqon doonaa mid isku mid ah ilaa inta xawaaraha bilowga ahi uu kala duwan yahay.

(4) Haddii raadka uusan isku mid ahayn oo dhulku simbiriirixan yahay, xawaaraha labada shay had iyo jeer wuu kala duwanaan doonaa.

Dood

Daqiiqadda firfircoonida dhululubo adag = 1/2 mR²

Daqiiqadda firfircoonida kubbadda adag = 2/5 mR²

Ka soo qaad in cufnaanta labada shay ay isku mid yihiin oo raadka labada shay ay isku mid yihiin, markaa daqiiqadda inertia ee dhululubada ayaa ka weyn (1/2) halka daqiiqadda inertia ee wareega adag uu ka yar yahay (2/5). Sidaas darteed, xawaaraha wareega ayaa ka weyn sababtoo ah daqiiqaddiisa inertia ayaa ka yar.

Haddii gacanka kubbadda uu weyn yahay, daqiiqadda firfircoonida kubbadda cagta ayaa kordheysa waxayna la mid noqon kartaa daqiiqadda firfircoonida dhululubada. Sidaa darteed, xawaaraha kubbadda cagta iyo dhululubada ayaa isku mid noqon kara.

Weedha saxda ah (2)

 

Isha su'aasha:

Su'aalaha Imtixaanka Qaranka ee Fiisigiska ee Dugsiga Sare/Dugsiga Sare ee Xirfadda