Umfutho we-Angular

Umfutho we-Angular

Inani lokunyakaza kokujikeleza, okufana nobunzima (m) ekuhambeni okuqondile, yi- moment of inertia (I). Inani lokunyakaza kokujikeleza, okufana ne-velocity (v) ekuhambeni okuqondile, yi-angular velocity (ω). Ngakho-ke, into ejikelezayo inomfutho we-angular ongabalwa kusetshenziswa i-equation:

L = I ω

L = umfutho we-angular (kg m ² /s), I = umzuzu we-inertia (kg m ² ), ω = ijubane le-angular (rad/s)

Izinkinga zesampula zomfutho we-angular

Inkinga yesampula 1.

Inhlayiya enesisindo esingamagremu angu-0.5 ihamba ngendilinga enejubane elingaguquguquki elingu-2 rad/s. Thola umfutho we-angular wenhlayiya uma irediyasi yendlela yenhlayiya ingu-10 cm.

Isixazululo:

Isikhathi sokungabi namandla kwenhlayiya:

I = mr ² = (0.5 x 10 ^-3 kg)(1 x 10 ^-1 m) ² = (0.5 x 10 ^-3 kg)(1 x 10 ^-2 m ² ) = 0.5 x 10 ^-5 kg ​​​​m ²

Ijubane le-angular le-particle:

ω = 2 rad/s

Umfutho we-angular we-particle:

L = (0.5 x 10 ^-5 kg ​​​​m ² )(2 rad/s) = 1 x 10 ^-5 kg ​​​​m ² /s

Umthetho wokulondolozwa komfutho we-angular

Umthetho wokulondolozwa komfutho we-angular uthi uma umzuzu wamandla ophumela emzimbeni oqinile lapho ujikeleza ungu-zero, khona-ke umfutho we-angular womzimba oqinile lapho ujikeleza uhlala ungaguquki. Umthetho wokulondolozwa komfutho we-angular ungatholakala ngokwezibalo ngokushintsha isibalo somthetho wesibili kaNewton womfutho we-angular. Nasi isibalo somthetho wesibili kaNewton kumfutho we-angular:

Uma umzuzu wamandla ophumelayo ungu-zero, khona-ke isibalo esingenhla siyashintsha sibe:

I _t = umzuzu wokugcina we-inertia, I _o = umzuzu wokuqala we-inertia, ω _t = isivinini sokugcina se-angular, ω _o = isivinini sokuqala se-angular, L _t = umfutho wokugcina we-angular, L _o = umfutho wokuqala we-angular.

Izibonelo zezinkinga zomthetho wokulondolozwa komfutho we-angular

Inkinga yesampula 1.

Idiski yesilinda eqinile elinganayo iqala ukujikeleza ku-axis yayo ngesivinini sama-rad angu-4/s. Ubunzima kanye nerediyasi yediski kungu-1 kg kanye no-0.5 m. Uma ngenhla kwepuleti kubekwa indandatho enesisindo kanye nerediyasi engu-0.2 kg kanye no-0.1 m kanye nesikhungo sendandatho,

ngaphezu nje kwesikhungo sediski, khona-ke idiski nendandatho kuzojikeleza kanyekanye nesivinini se-angular sika…..

Isixazululo:

Isikhathi sokungabi namandla kwesilinda esiqinile: I = 1⁄2 mr ² = 1⁄2 (1 kg)(0.5 m) ² = (0.5)(0.25) = 0.125 kg m ²

Isikhathi sokungapheleli kwendandatho: I = mr ² = (0.2 kg)(0.1 m) ² = (0.2)(0.01) = 0.002 kg m ²

Umfutho wokuqala we-angular (L ₁ ) = Umfutho wokugcina we-angular (L ₂ )

I ₁ ω ₁ = I ₂ ω ₂

(0.125 kg m2 ⁾ (4 rad/s) = (0.125 kg m2 ⁺ 0.002 kg m2 ⁾ (ω ₂ )

(0.5) = (0.127)(ω ₂ )

ω ₂ = 0.5 : 0.127

ω ₂ = 4 rad/s

Imibuzo nezimpendulo zomqondo

1. Kuyini umfutho we-angular?
   Impendulo: I-Angular momentum iyisilinganiso senani lokujikeleza into enalo, uma ucabangela ubunzima bayo nesimo sayo. Iwuhlobo lokujikeleza olufana ne-linear momentum.
2. Umfutho we-angular unqunywa kanjani ngokwezibalo?
   Impendulo: Umfutho we-angular (L) uchazwa ngokuthi $L=r\times p$, lapho $r$ iyivektha yesikhundla kusukela ku-axis yokujikeleza kuze kube seqophelweni lokusebenza, futhi $p$ umfutho oqondile.
3. Ingabe i-angular momentum iyi-scalar noma i-vector quantity?
   Impendulo: Umfutho we-angular uyinani le-vector.
4. Iyini iyunithi ye-angular momentum ohlelweni lwe-SI?
   Impendulo: Iyunithi yomfutho we-angular ohlelweni lwe-SI ingama-kilogram-meter ayisikwele ngomzuzwana (kg·m²/s).
5. I-angular momentum ilondolozwa kanjani?
   Impendulo: Esimisweni esivaliwe esingenazo izimpondo zangaphandle, umfutho ophelele we-angular uhlala ungaguquki.
6. Iyini isimiso sokulondolozwa komfutho we-angular?
   Impendulo: Isimiso sithi umfutho ophelele we-angular wesistimu evaliwe uhlala ungaguquki ngaphandle kokuthi kusetshenziswe i-torque yangaphandle.
7. Ukujika komskeyiti wesibalo kuhlobana kanjani nomfutho we-angular?
   Impendulo: Uma umuntu oskethayo edonsa izingalo nemilenze yakhe eduze komzimba wakhe ngesikhathi eshwibeka, wehlisa isikhathi sakhe sokungashukumi, okubangela ukuba ashwibeke ngokushesha. Lokhu kubonisa ukulondolozwa komfutho we-angular.
8. Buyini ubudlelwano phakathi kwe-torque kanye ne-angular momentum?
   Impendulo: I-Torque ($\tau$) izinga lokushintsha komfutho we-angular. Ngokwezibalo, τ=dI-L/isekhondi​.
9. Kungenzeka yini ukuthi into ibe nomfutho we-angular ngaphandle kwejubane le-angular?
   Impendulo: Cha, uma into inomfutho we-angular, inejubane le-angular. Ubukhulu kanye nesiqondiso somfutho we-angular kuncike kokubili kumzuzu we-inertia kanye nejubane le-angular.
10. Isikhathi sokungakhathali sithinta kanjani umfutho we-angular?
    Impendulo: Umfutho we-angular (L) uwumkhiqizo womzuzu we-inertia (I) kanye nejubane le-angular (ω). US $L=I\omega$, ukwanda kwesikhathi sokungaqhubeki kwejubane elithile le-angular kuzokwandisa umfutho we-angular.
11. Uyini umehluko phakathi kwe-spin kanye ne-orbital angular momentum ku-quantum mechanics?
    Impendulo: I-spin angular momentum iyimpahla engaphakathi yezinhlayiya, njengama-electron, futhi ayiveli ekuhambeni emkhathini. I-orbital angular momentum, ngakolunye uhlangothi, ivela ekuhambeni kwezinhlayiya ezizungeze iphuzu eliphakathi.
12. Iyiphi indima edlalwa yi-angular momentum ekwakhiweni kwezinhlelo zamaplanethi?
    Impendulo: Njengoba ifu lama-molecule liwa ukuze lakhe izinkanyezi namaplanethi, ukulondolozwa komfutho we-angular kubangela ukuthi izinto zibe yi-disk ezungeze inkanyezi esanda kuzalwa, lapho amaplanethi angakheka khona.
13. I-gyroscope igcina kanjani ukuqondiswa kwayo esikhaleni?
    Impendulo: I-gyroscope ejikelezayo ine-angular momentum. Lapho i-torque yangaphandle izama ukushintsha ukuma kwayo, i-gyroscope iyaqhubeka, noma ishintsha i-axis yayo yokujikeleza, ngendlela eqondile ku-torque esetshenzisiwe ngenxa yokulondolozwa kwe-angular momentum.
14. Yini ebangela ukuguquka kwesimo endaweni ejikelezayo?
    Impendulo: Ukuguquka kwesimo endaweni ejikelezayo kubangelwa yi-torque ngenxa yamandla adonsela phansi asebenza esikhungweni sobukhulu besimo sendawo ephezulu, esiphambene nephuzu layo elijikelezayo. Le torque ibangela ushintsho endleleni yokunyakaza kwesimo sendawo ephezulu, okubangela ukuthi iqhubeke.
15. Kungani izinkanyezi zigoba ezicongweni zazo?
    Impendulo: Njengoba izinkanyezi zijikeleza, zizwa amandla e-centrifugal asunduza izinto ngaphandle. Lo mphumela unamandla kakhulu enkabazwe kunasezimpondweni, okuholela esimweni esigobile, noma esisicaba.
16. Umfutho we-angular uhlobene kanjani nomthetho wesibili kaKepler?
    Impendulo: Umthetho wesibili kaKepler uthi ingxenye yomugqa ehlanganisa iplanethi neLanga ikhukhula izindawo ezilinganayo ngezikhawu ezilinganayo zesikhathi. Lokhu kuwumphumela wokulondolozwa komfutho we-angular.
17. Kungani ikati lihlala lihlala ngezinyawo uma liwa?
    Impendulo: Amakati asebenzisa ukulondolozwa komfutho we-angular. Ngokusonta imizimba yawo nokushintsha izikhathi zawo zokungahlali kahle emoyeni, angazihlela kabusha ukuze ahlale phansi ngezinyawo zawo ngaphandle kokwephula imithetho yokulondolozwa kwemvelo.
18. Umzuzu wamagnetic uhlobene kanjani nomfutho we-angular kuma-electron?
    Impendulo: Umzuzu wamagnetic we-electron uvela ekujikelezeni kwawo kanye nomfutho we-orbital angular. Umzuzu wamagnetic ulingana nomfutho we-angular we-electron.
19. Kuyini i-angular momentum ngokwe-polar coordinates?
    Impendulo: Kuma-polar coordinates, i-angular momentum $L$ ngesisindo sephuzu singavezwa ngokuthi $L=mrv$, lapho $m$ yisisindo, $r$ ibanga eliyi-radial, futhi $v$ yijubane le-tangential.
20. Kwenzekani ngomfutho we-angular wesistimu evaliwe lapho izinto ezimbili zishayisana?
    Impendulo: Esimisweni esivaliwe lapho izinto ezimbili zishayisana khona, umfutho we-angular ophelele ngaphambi kokushayisana ulingana nomfutho we-angular ophelele ngemva kokushayisana, uma kuthathwa ukuthi akukho mandla angaphandle asebenzayo ohlelweni.

Izinkinga Nezixazululo

1. Inkinga: Isisindo sephuzu m = 2 kg sihamba ngesivinini v = 3 m/s embuthanweni we-radius r = 4 m. Bala umfutho wayo we-angular mayelana nesikhungo sembuthano.

Isixazululo: $L=m\times r\times v$ =2×4×3=24 kg.m ² /s

2. Inkinga: Imbulunga eqinile enobunzima obungu-3 kg kanye nerediyasi engu-0.5 m ijikeleza ububanzi bayo ngejubane eliyi-angular ω = 2 rad/s. Iyini i-angular momentum yayo?

Isixazululo: Kwisiyingi esiqinile, I = 2/5 m r ²

$L=I\times \omega$

L=2/5×3×(0.5) ² ×2=0.6 kg.m ² /s

3. Inkinga: Isisindo sephuzu elingama-3 kg sihamba ngesivinini esingama-4 m/s emgqeni oqondile. Uyini umfutho waso oqondile cishe ngephuzu elingamamitha ama-5 ukusuka emgqeni waso wokunyakaza?

Isixazululo:

$L=m\times v\times r$

L=3×4×5=60 kg.m ² /s

4. Inkinga: Idiski enobunzima obungu-5 kg ​​kanye nerediyasi engu-3 m ijikeleza ngesivinini se-angular esingu-2 rad/s. Bala umfutho wayo we-angular.

Isixazululo: Ngediski, I = 1/2 ​m r ²

$L=I\times \omega$

L=1/2×5×3 ² ×2=45 kg.m ² /s

5. Inkinga: Induku enobude obungu-4 m kanye nesisindo esingu-2 kg ijikeleza cishe kolunye uhlangothi ngejubane eliyi-angle elingu-3 rad/s. Thola umfutho wayo we-angle.

Isixazululo: Ngenduku cishe kolunye uhlangothi, I = 1/3 ​ml l ²

$L=I\times \omega$

L=1/3×2×4 ² ×3=96 kg.m ² /s

6. Inkinga: Luyini ushintsho ku-angular momentum uma umzimba ojikelezayo uphinda kabili ijubane lawo le-angular?

Isixazululo: Ubudlelwano phakathi kwe-angular momentum (L) kanye ne-angular velocity (ω) bungu- $L=I\times \omega$ . Uma i-ω iphindwe kabili, i-angular momentum nayo izophindeka kabili.

7. Inkinga: Uma irediyasi yendlela eyindilinga yenhlayiya ehambayo iphinda kabili ngenkathi igcina ijubane lingaguquguquki, i-angular momentum ishintsha ngasiphi isici?

Isixazululo: Umfutho we-Angular, $L=m\times r\times v$ . Uma u-r ephindwe kabili, u-L naye uzophindeka kabili.

8. Inkinga: Ingane enesisindo esingama-30 kg imi onqenqemeni lwe-merry-go-round ephumule. Irediyasi ye-merry-go-round ingu-2 m. Uma ingane iqala ukugijima ngesivinini esingu-2m/s maqondana nomhlabathi onqenqemeni, thola umfutho we-angular wengane maqondana nesikhungo.

Isixazululo: $L=m\times r\times v$ =30×2×2=120 kg.m ² /s

9. Inkinga: Isilinda esinobunzima obungu-6 kg kanye nerediyasi engu-2 m ijikeleza nxazonke kwe-axis yayo ephakathi ngejubane le-angular elingu-5 rad/s. Bala umfutho wayo we-angular.

Isixazululo: Ngesilinda, I = 1/2 m r ²

$L=I\times \omega$ =1/2×6×2 ² ×5=120 kg.m ² /s

10. Inkinga: Uzoba yini umfutho omusha we-angular womzimba uma umzuzu wawo we-inertia wehliswa ngesigamu futhi ijubane lawo le-angular liphindwe kathathu?

Isixazululo: Njengoba $u-L=I\times \omega$ , uma $ngincishisiwe$ phakathi kanti $u-\omega$ uphindwe kathathu, $u-L$ omusha uzoba ngu -1/2×3=1.5 × owokuqala.

11. Inkinga: I-hoop enobunzima obungu-2kg kanye ne-radius engu-1m ijikeleza ngesivinini se-angular esingu-4 rad/s. Bala umfutho wayo we-angular.

Isixazululo: Ngesiyingi, I = m r ²

$L=I\times \omega$

L=2×1 ² ×4=8 kg.m ² /s

12. Inkinga: Ifeni inama-blade anobude obungu-0.5m kanye nesisindo esiphelele esingu-1kg. Uma ijikeleza ngesivinini se-angle esingu-10 rad/s, thola umfutho wayo we-angle.

Isixazululo: Uma sicabanga ukuthi ama-fan blades afana nezinduku ezijikelezayo cishe kolunye uhlangothi, I = 1/3 ​ml l ²

$L=I\times \omega$ =1/3×1×0.5 ² ×10=0.833 kg.m ² /s

13. Inkinga: Bala umfutho we-angular womhlaba nge-axis yawo ngenxa yokujikeleza kwawo. Njengoba kunikezwe: Isisindo somhlaba =5.972×10 ²⁴ kg , Irediyasi $r=6371\text{km}$ , ω = 7.27 × 1 0 ⁻⁵ rad/s.

Isixazululo: Uma sicabanga ukuthi umhlaba uyindilinga eqinile, I = 2/5 m r ²

$L=I\times \omega$ =2/5×5.972×10 ²⁴ ×(6371×10 ³ ) ² ×7.27×10 ⁻⁵

L ≈ 7.07 × 1 0 ³³ kg.m ² / s

14. Inkinga: Ingane iya enkabeni yesikhulumi esijikelezayo. Ingabe umfutho we-angular uyakhula, uyancipha noma uhlala unjalo?

Isixazululo: Umfutho we-angular uyalondolozwa. Njengoba ingane iqhubekela enkabeni, umzuzu we-inertia uyancipha. Ukuze kulondolozwe umfutho we-angular, ijubane le-angular liyakhula. Ngakho-ke, umfutho we-angular uhlala ufana.

15. Inkinga: Uma amandla e-kinetic omzimba ojikelezayo ephindwe kabili, i-angular momentum yawo ishintsha ngasiphi isici?

Isixazululo: Amandla e-Kinetic K = 1/2 ​I ω ² kanye ne-Angular momentum $L=I\omega$ . Uma amandla e-kinetic ephindwe kabili futhi $u-I$ ehlala engaguquki, u-ω ² uphindwe kabili. Lokhu kusho ukuthi $u-\omega$ ukhushulwa nge-factor ka -√ 2 ​.$Ngakho-ke,\; u-L$ ukhushulwa nge-factor ka -√ 2 ​.

16. Inkinga: Isondo lebhayisikili eliyi-radius engu-0.3 m linomphetho onesisindo esingu-1.5 kg. Uma lijikeleza ngesivinini esiyi-angle esingu-5 rad/s, thola umfutho walo we-angle.

Isixazululo: Uma sibheka umugqa njengongqimba, I = m r ²

$L=I\times \omega$ =1.5×0.32×5=6.75 kg.m ² /s

L = 1.5 × 0. 3 2 × 5 = 6.75 kg.m ² / s

17. Inkinga: Umuntu oshwiba eqhweni udonsa izingalo zakhe ngaphakathi ngenkathi ejikeleza. Kwenzekani ngomfutho wakhe ojikelezayo?

Isixazululo: Umfutho we-engile womskeyitha uyalondolozwa. Ngokudonsa izingalo zakhe, wehlisa umzuzu wakhe wokungakhathali, ngaleyo ndlela ujikeleza ngokushesha (isivinini esikhulu se-engile) ukuze alondoloze umfutho wakhe we-engile.

18. Inkinga: Isondo elijikelezayo linomzuzu wokungangeni okungu-0.2 kg.m. ² kg.m. ² futhi lijikeleza ngejubane eliyi-angle elingu-10 rad/s. Thola umfutho walo oyi-angle.

Isixazululo:

$L=I\times \omega$ =0.2×10=2 kg.m ² /s

L = 0.2 × 10 = 2 kg.m ² / s

19. Inkinga: Uhlelo lune-torque yangaphandle engu-zero esebenza kulo. Ungathini ngomfutho walo we-angular?

Isixazululo: Uma i-torque yangaphandle ehlanzekile ingu-zero, khona-ke ngokokulondolozwa komfutho we-angular, umfutho we-angular ophelele wesistimu uhlala ungaguquki.

20. Inkinga: Isisindo sephuzu m = 5 kg sihamba ngesivinini v = 3 m/s siqonde ngqo emgqeni osihlanganisa nephuzu P. Uma ibanga elisuka ephuzu P lingu-4 m, thola umfutho walo we-angular mayelana nephuzu P.

Isixazululo:

$L=m\times r\times v$ =5×4×3=60 kg.m ² /s

L = 5 × 4 × 3 = 60 kg.m ² / s