Daqiiqadda firfircoonida walxaha - dhibaatooyinka iyo xalalka

1. Laba kubbadood oo ay isku xiran yihiin ul, sida ka muuqata sawirka hoose. Iska ilow cufka usha . Cufka kubbada P waa 600 garaam, cufka kubbada Q waa 400 garaam. Waa maxay daqiiqadda firfircoonida nidaamka ee ku saabsan AB?

La yaqaan:

dhidibka wareegga waa AB. Daqiiqadda firfircoonida walxaha - dhibaatooyinka iyo xalalka 1

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 Doonayo: Daqiiqada firfircoonida nidaamka

Xalka:

I = 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 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

2. Usha AB oo miisaankeedu yahay 2-kg ayaa ku wareegsanaa barta A, daqiiqadda firfircoonida usha waa 8 kg m ^2. Haddii lagu wareejiyo barta O (AO = OB), waa maxay daqiiqadda firfircoonida usha.

La yaqaan: Daqiiqadda firfircoonida walxaha - dhibaatooyinka iyo xalalka 2

Cufka usha AB (m) = 2 kg

Haddii lagu wareejiyo barta A si gacanka wareegga (r) = dhererka AB = r markaas daqiiqadda inertia (I) = 8 kg m ²

La rabo: Haddii lagu wareejiyo barta O si gacanka wareegga (r) = dhererka AO = dhererka OB = 1/2 r markaa waa maxay daqiiqadda firfircoonida usha.

Xalka:

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 sidaas darteed ½ r = 1 mitir, markaa daqiiqadda inertia:

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

3. Laba kubbadood oo ay isku xiran yihiin ul sida ku cad sawirka hoose. Iska ilow cufka ul. Waa maxay daqiiqadda firfircoonida nidaamka.

La yaqaan:

Cufka kubadda A (m)_A) = 200 garaam = 0.2 kg Daqiiqadda firfircoonida walxaha - dhibaatooyinka iyo xalalka 3

Cufka kubadda B (m _B ) = 400 garaam = 0.4 kg

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

Arag sidoo kale Noocyada dallacaadaha korontada - dhibaatooyinka iyo xalalka

Masaafada u dhaxaysa kubbadda B iyo dhidibka wareegga (r _B ) = 25 cm = 0.25 m

La Doonayo: Daqiiqada firfircoonida nidaamka

Xalka:

Daqiiqadda firfircoonida kubadda A:

I _A = (m _A )(r _A² ) = (0.2)(0) ² = 0

Daqiiqada firfircoonida kubadda B:

I _B = (m _B )(r _B² ) = (0.4)(0.25) ² = (0.4)(0.0625) = 0.025 kg m ²

Daqiiqada firfircoonida nidaamka:

I = I _A + I _B = 0 + 0.025 = 0.025 kg m ² = 25 x 10 ^-3 kg m ²

4. Afar walxood oo leh cufnaan kala duwan, oo lagu muujiyey jaantuska hoose. Go'aami daqiiqadda firfircoonida nidaamka ku saabsan xariiqda toosan P.

Solution

dhidibka wareegga waa xariiqda toosan ee P.

La yaqaan: Daqiiqadda firfircoonida walxaha - dhibaatooyinka iyo xalalka 4

Cufka walxaha A (m _A ) = m

Cufka walxaha B (m _B ) = 2m

Cufka walxaha C (m _C ) = 3m

Gudubka walxaha D (m _D ) = 4m

Masaafada u dhaxaysa walxaha A iyo dhidibka wareegga (r _A ) = b

Masaafada u dhaxaysa walxaha B iyo dhidibka wareegga (r _B ) = b

Masaafada u dhaxaysa walxaha C iyo dhidibka wareegga (r _C ) = 2b

Masaafada u dhaxaysa walxaha D iyo dhidibka wareegga (r _D ) = 2b

La Doonayo: Daqiiqada firfircoonida nidaamka ee ku saabsan xariiqda toosan ee P

Xalka:

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

I = mb ² + 2 mb ² + 12 mb ² + 16 mb ²

I = 31 mb ²

5. Afar walxood oo ay ku xiran yihiin ul. Iska ilow cufka ul. Go'aami daqiiqadda firfircoonida ku saabsan dhidibka wareegga iyada oo loo marayo walxaha m ₁ iyo m ₂ , sida ka muuqata sawirka hoose.

Known

Cufka walxaha 1 (m₁) = 1/4 kg Daqiiqadda firfircoonida walxaha - dhibaatooyinka iyo xalalka 5

Cufka walxaha 2 (m ₂ ) = 1/2 kg

Cufka walxaha 3 (m ₃ ) = 1/4 kg

Cufka walxaha 4 (m ₄ ) = 1/4 kg

Masaafada u dhaxaysa walxaha 1 iyo dhidibka wareegga (r ₁ ) = 0

Masaafada u dhaxaysa walxaha 2 iyo dhidibka wareegga (r ₂ ) = 0

Masaafada u dhaxaysa walxaha 3 iyo dhidibka wareegga (r ₃ ) = 10 cm = 10/100 m = 1/10 m

Masaafada u dhaxaysa walxaha 4 iyo dhidibka wareegga (r ₄ ) = 10 cm = 10/100 m = 1/10 m

Arag sidoo kale Tamarta laga soo saaro falgalka isku-dhafka - dhibaatooyinka iyo xalalka

La Doonayo: Daqiiqada firfircoonida

Xalka:

I = m ₁ r ₁² + m ₂ r ₂² + m ₃ r ₃² + m ₄ r ₄²

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}

Waa maxay daqiiqadda firfircoonida ee walaxda?
- Jawaab: Hal walax oo cuf ah $m$ meel fog $r$ laga bilaabo dhidib wareeg ah, daqiiqadda firfircoonida $I$ ayaa la bixiyaa $I = m \times r^{2}$ .
Maxaa daqiiqadda inertia badanaa loogu yeeraa "qaab-dhismeedka wareegga" ee cufka?
- Jawaab: Sida cufku u yahay cabbir u ah iska caabbinta shay ee isbeddellada ku yimaada dhaqdhaqaaqa turjumaadda (sababtoo ah sharciga labaad ee Newton), daqiiqadda firfircoonidu waa cabbir u ah iska caabbinta shay ee isbeddellada ku yimaada dhaqdhaqaaqa wareegga.
Sidee bay isbeddelka masaafada walax ka timaadda dhidibka wareegga u saameeyaan daqiiqadda firfircoonida?
- Jawaab: Daqiiqada inertia waxay u dhigantaa labajibbaaranaha masaafada u dhaxaysa dhidibka wareegga. Haddii aad labanlaabto masaafada, daqiiqada inertia waxay kordhi doontaa afar dhibcood.
Waa maxay sababta labajibbaaran ee masaafada (r) u yahay²) loo isticmaalay qaacidada daqiiqadda firfircoonida halkii laga isticmaali lahaa masaafada oo keliya?
- Jawaab: Labajibbaaranaha masaafada waxaa loo isticmaalaa sababta oo ah sida tamarta dhaqdhaqaaqa wareegga u shaqeyso. Dhaqdhaqaaqa wareegga, walax kasta oo ka mid ah shay ayaa gacan ka geysata tamarta dhaqdhaqaaqa wareegga iyadoo lagu saleynayo cufkeeda iyo masaafada ay ka fog tahay dhidibka oo laba jibbaaran.
Sidee ayuu isu beddelaa daqiiqadda firfircoonida ee walax haddii cufkeedu saddex jibaarmo iyadoo la ilaalinayo masaafada joogtada ah ee dhidibka?
- Jawaab: Haddii cufku saddex jibaarmo oo masaafada la ilaaliyo, daqiiqadda inertia sidoo kale way saddex jibaarmi doontaa sababtoo ah waxay si toos ah ugu dhigantaa cufnaanta.
Walax ma yeelan kartaa daqiiqad aan firfircoonayn oo eber ah? Haddii ay sidaas tahay, xaaladdee?
- JawaabHaa, walaxdu waxay yeelan doontaa daqiiqad eber ah haddii ay si toos ah ugu taal dhidibka wareegga, taasoo ka dhigaysa masaafada $r$ laga bilaabo dhidibka waxay la mid tahay eber.
Maxay walxaha kala duwan ee isku cufnaanta iyo cabbirka leh u leeyihiin daqiiqado kala duwan oo firfircooni ah marka ay ku wareegayaan faasas kala duwan?
- Jawaab: Qaybinta cufka ku wareegsan dhidibka wareegga ayaa go'aamisa daqiiqadda inertia. Xitaa haddii laba shay ay leeyihiin cuf iyo cabbir isku mid ah, qaybintooda cufnaanta marka loo eego dhidibka wareegga way kala duwanaan kartaa, taasoo horseedaysa daqiiqado kala duwan oo inertia ah.
Daqiiqadda firfircoonida ma tahay tiro scalar ah ama tiro vector ah?
- Jawaab: Daqiiqada inertia waa tiro scalar ah. Si kastaba ha ahaatee, jirro adag oo leh qaabab adag iyo dhidibyo badan oo wareeg ah, waxaa lagu matalaa tensor.
Haddii laba qaybood, mid walbana uu miisaankiisu yahay $m$ , waxay ku yaalliin masaafooyin $r_{1}$ iyo $r_{2}$ laga bilaabo dhidibka wareegga, waa maxay daqiiqadda isku dhafan ee inertia?
- Jawaab: Daqiiqada inertia waa wax lagu daro walxaha kala duwan. Sidaa darteed, daqiiqada isku dhafan ee inertia $I = m \times r_{12} + m \times r_{22}$ .
Sidee ayuu daqiiqadda firfircoonida ula xiriiraa ilaalinta dhaqdhaqaaqa xagasha?
- JawaabDhaqdhaqaaq xagal ah $L$ waa natiijada daqiiqadda firfircoonida $I$ iyo xawaaraha xagal $ω$ , oo lagu matalay isla'egta $L = I \times ω$ Haddii aysan jirin wax dhaqdhaqaaq dibadeed ah oo ku saabsan nidaamka, dhaqdhaqaaqa xagasha ayaa sii ahaan doona mid joogto ah. Taas macnaheedu waa haddii daqiiqadda firfircoonida ay isbeddesho (sida qof iskeytka jiidaya gacmahooda), xawaaraha xagasha waa inuu la qabsadaa si badeecaddu u ahaato mid joogto ah.