Angular liwiro

Angular liwiro

Kuchuluka kwa kayendedwe kozungulira, komwe kuli kofanana ndi kulemera (m) mu kayendedwe kolunjika, ndi mphindi ya inertia (I). Kuchuluka kwa kayendedwe kozungulira, komwe kuli kofanana ndi liwiro (v) mu kayendedwe kolunjika, ndi liwiro la angular (ω). Chifukwa chake, chinthu chozungulira chili ndi mphamvu ya angular yomwe ingawerengedwe pogwiritsa ntchito equation:

L = Ine ω

L = angular momentum (kg m ² /s), I = mphindi ya inertia (kg m ² ), ω = angular velocity (rad/s)

Zitsanzo za mavuto a angular momentum

Chitsanzo cha vuto 1.

Tinthu tolemera magalamu 0.5 timayenda mozungulira ndi liwiro lokhazikika la 2 rad/s. Dziwani mphamvu ya angular ya tinthu ngati utali wa njira ya tinthu ndi 10 cm.

yankho;

Nthawi ya inertia ya tinthu:

Ine = 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

Liwiro la angular la tinthu tating'onoting'ono:

ω = 2 rad/s

Mphamvu ya angular ya tinthu tating'onoting'ono:

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

Lamulo losunga mphamvu ya angular

Lamulo losunga mphamvu ya angular momentum limati ngati mphamvu yomwe imabwera chifukwa cha thupi lolimba ikazungulira ndi zero, ndiye kuti mphamvu ya angular ya thupi lolimba ikazungulira nthawi zonse imakhala yokhazikika. Lamulo losunga mphamvu ya angular momentum likhoza kupezedwa mwa masamu posintha equation ya lamulo lachiwiri la Newton la angular momentum. Nayi equation ya lamulo lachiwiri la Newton pa mphamvu ya angular:

Ngati mphamvu yomwe yabwera pambuyo pake ndi zero, ndiye kuti equation yomwe ili pamwambapa imasintha kukhala:

I _t = mphindi yomaliza ya inertia, I _o = mphindi yoyambirira ya inertia, ω _t = liwiro lomaliza la angular, ω _o = liwiro loyambirira la angular, L _t = mphamvu yomaliza ya angular, L _o = mphamvu yoyambirira ya angular.

Zitsanzo za mavuto a lamulo losunga mphamvu ya angular

Chitsanzo cha vuto 1.

Disiki yolimba ya silinda yofanana imazungulira poyamba pa mzere wake ndi liwiro la 4 rad/s. Kulemera ndi utali wa diski ndi 1 kg ndi 0.5 m. Ngati pamwamba pa mbaleyo pali mphete yokhala ndi utali ndi utali wa 0.2 kg ndi 0.1 m ndi pakati pa mpheteyo,

pamwamba pang'ono pakati pa diski, ndiye kuti diski ndi mphete zidzazungulira limodzi ndi liwiro la angular la…..

yankho;

Nthawi ya kulephera kwa silinda yolimba: I = 1⁄2 mr ² = 1⁄2 (1 kg)(0.5 m) ² = (0.5)(0.25) = 0.125 kg m ²

Nthawi ya kulephera kwa mphete: I = mr ² = (0.2 kg)(0.1 m) ² = (0.2)(0.01) = 0.002 kg m ²

Mphamvu yoyambirira ya angular (L ₁ ) = Mphamvu yomaliza ya angular (L ₂ )

I ₁ ω ₁ = I ₂ ω ₂

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

(0.5) = (0.127)(ω ₂ )

ω ₂ = 0.5 : 0.127

ω ₂ = 4 rad/s

Mafunso ndi mayankho a malingaliro

1. Kodi mphamvu ya angular ndi chiyani?
   Yankho: Mphamvu ya angular ndi muyeso wa kuchuluka kwa kuzungulira kwa chinthu, poganizira kulemera kwake ndi mawonekedwe ake. Ndi njira yozungulira ya mphamvu yolunjika.
2. Kodi mphamvu ya angular imatsimikiziridwa bwanji mwa masamu?
   Yankho: Mphamvu ya angular (L) imatanthauzidwa kuti $L=r\times p$, kumene $r$ ndi vekitala ya malo kuchokera ku mzere wozungulira mpaka pogwiritsira ntchito, ndipo $p$ ndi mphamvu yolunjika.
3. Kodi angular momentum ndi scalar kapena ventricle?
   Yankho: Mphamvu ya angular ndi kuchuluka kwa vekitala.
4. Kodi gawo la angular momentum mu dongosolo la SI ndi chiyani?
   Yankho: Gawo la angular momentum mu dongosolo la SI ndi kilogram-mita sikweya pa sekondi (kg·m²/ s).
5. Kodi mphamvu ya angular imasungidwa bwanji?
   Yankho: Mu dongosolo lotsekedwa lopanda ma torque akunja, mphamvu yonse ya angular imakhalabe yofanana.
6. Kodi mfundo yosungira mphamvu ya angular ndi iti?
   Yankho: Mfundoyi imati mphamvu yonse ya angular ya dongosolo lotsekedwa imakhalabe yofanana pokhapokha ngati mphamvu yakunja ikugwira ntchito.
7. Kodi kuzungulira kwa munthu wothamanga pa skate kumagwirizana bwanji ndi angular momentum?
   Yankho: Wosewera skater akakoka manja ndi miyendo yake pafupi ndi thupi lake panthawi yozungulira, amachepetsa nthawi yake yopuma, zomwe zimapangitsa kuti azizungulira mofulumira. Izi zikusonyeza kuti akupitirizabe kuyenda bwino.
8. Kodi pali ubale wotani pakati pa torque ndi angular momentum?
   Yankho: Torque ($\tau$) ndi liwiro la kusintha kwa mphamvu ya angular. Mwa masamu, τ=dL/sekondi​.
9. Kodi n'zotheka kuti chinthu chikhale ndi mphamvu ya angular popanda liwiro la angular?
   Yankho: Ayi, ngati chinthu chili ndi mphamvu ya angular, chimakhala ndi liwiro la angular. Kukula ndi komwe chimayenda zimadalira nthawi ya inertia komanso liwiro la angular.
10. Kodi nthawi ya inertia imakhudza bwanji mphamvu ya angular?
    Yankho: Mphamvu ya angular (L) ndi zotsatira za nthawi ya inertia (I) ndi liwiro la angular (ω). US $L=I\omega$, kuwonjezeka kwa mphindi ya inertia pa liwiro la angular loperekedwa kudzawonjezera mphamvu ya angular.
11. Kodi kusiyana pakati pa spin ndi orbital angular momentum mu quantum mechanics ndi kotani?
    Yankho: Mphamvu ya spin angular momentum ndi chinthu chapadera cha tinthu tating'onoting'ono, monga ma elekitironi, ndipo sichichokera ku kuyenda mumlengalenga. Mphamvu ya orbital angular momentum, kumbali ina, imachokera ku kuyenda kwa tinthu tating'onoting'ono mozungulira malo apakati.
12. Kodi mphamvu ya angular imagwira ntchito yotani pakupanga mapulaneti?
    Yankho: Pamene mtambo wa mamolekyu umagwa kupanga nyenyezi ndi mapulaneti, kusungidwa kwa mphamvu ya angular kumapangitsa kuti zinthuzo ziphwanyike kukhala diski yozungulira nyenyezi yobadwa kumene, yomwe mapulaneti angapangidwe kuchokera.
13. Kodi gyroscope imasunga bwanji malo ake mumlengalenga?
    Yankho: Gyroscope yozungulira imakhala ndi mphamvu ya angular. Pamene mphamvu yakunja ikuyesera kusintha momwe imayendera, gyroscope imapitiliza, kapena kusintha mzere wake wozungulira, molunjika ku mphamvu yomwe yagwiritsidwa ntchito chifukwa chosunga mphamvu ya angular.
14. Nchiyani chimayambitsa precession mu top yozungulira?
    Yankho: Kukwera kwa mphamvu pamwamba pa chinthu chozungulira kumachitika chifukwa cha mphamvu yokoka yomwe imagwira ntchito pakati pa chinthu chapamwamba, yomwe imasiyana ndi mfundo yake yozungulira. Mphamvu imeneyi imasintha njira ya mphamvu ya chinthu chapamwamba, zomwe zimapangitsa kuti chikwere.
15. N’chifukwa chiyani nyenyezi zimaphwanyika pamizere yawo?
    Yankho: Pamene nyenyezi zikuzungulira, zimakumana ndi mphamvu ya centrifugal yomwe imakankhira zinthu kunja. Izi zimakhala zolimba kwambiri ku equator kuposa ku ma poles, zomwe zimapangitsa kuti zikhale ngati oblate, kapena mawonekedwe osalala.
16. Kodi mphamvu ya angular ikugwirizana bwanji ndi lamulo lachiwiri la Kepler?
    Yankho: Lamulo lachiwiri la Kepler limati gawo la mzere lomwe limalumikiza dziko lapansi ndi Dzuwa limachotsa madera ofanana panthawi yofanana. Izi ndi zotsatira za kusunga mphamvu ya angular.
17. N’chifukwa chiyani mphaka nthawi zonse imagwa pansi ikagwa?
    Yankho: Amphaka amagwiritsa ntchito njira yosungira mphamvu ya angular. Mwa kupotoza matupi awo ndikusintha nthawi yawo ya kutopa mumlengalenga, amatha kudzisintha kuti akwere pansi popanda kuphwanya malamulo oteteza chilengedwe.
18. Kodi mphindi ya maginito imakhudzana bwanji ndi mphamvu ya angular mu ma electron?
    Yankho: Mphamvu ya maginito ya elekitironi imachokera ku mphamvu yake yozungulira ndi yozungulira. Mphamvu ya maginito imagwirizana ndi mphamvu ya angular ya elekitironi.
19. Kodi mphamvu ya angular momentum pankhani ya ma coordinates a polar ndi chiyani?
    Yankho: Mu ma coordinates a polar, angular momentum $L$ chifukwa cha mfundo imodzi, misa imodzi ikhoza kufotokozedwa ngati $L=mrv$, kumene $m$ ndi misa, $r$ ndi mtunda wa radial, ndipo $v$ ndi liwiro la tangential.
20. Kodi chimachitika ndi chiyani ndi mphamvu ya angular ya dongosolo lotsekedwa pamene zinthu ziwiri zigundana?
    Yankho: Mu dongosolo lotsekedwa pomwe zinthu ziwiri zimagundana, mphamvu yonse ya angular isanayambe kugundana imakhala yofanana ndi mphamvu yonse ya angular pambuyo pa kugundana, poganiza kuti palibe mphamvu yakunja yomwe ikugwira ntchito pa dongosololi.

Mavuto ndi Mayankho

1. Vuto: Kulemera kwa mfundo m = 2 kg kumayenda ndi liwiro v = 3 m/s mu bwalo la radius r = 4 m. Werengani mphamvu yake ya angular momentum pakati pa bwalo.

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

2. Vuto: Chipilala cholimba cha kulemera kwa 3 kg ndi utali wa 0.5 m chikuzungulira pafupifupi dayamita yake ndi liwiro la angular ω = 2 rad/s. Kodi mphamvu yake ya angular ndi yotani?

Yankho: Pa bwalo lolimba, I = 2/5 ​m r ²

$L=Ine\times \omega$

L=2/5×3×(0.5) ² ×2=0.6kg.m ² /s

3. Vuto: Kulemera kwa mfundo ya 3 kg kukuyenda ndi liwiro la 4 m/s mu mzere wowongoka. Kodi mphamvu yake ya angular ndi yotani pafupifupi mfundo 5 m kuchokera pa mzere wake woyenda?

yankho;

$L=m\times v\times r$

L=3×4×5=60 kg.m ² /s

4. Vuto: Disiki yolemera makilogalamu 5 ndi utali wa mamita 3 ikuzungulira ndi liwiro la angular la 2 rad/s. Werengani mphamvu yake ya angular.

Yankho: Pa diski, I = 1/2 ​m r ²

$L=Ine\times \omega$

L=1/2×5×3 ² ×2=45 kg.m ² /s

5. Vuto: Ndodo yautali wa mamita 4 ndi kulemera kwa makilogalamu 2 imazungulira mbali imodzi ndi liwiro la angular la 3 rad/s. Pezani mphamvu yake ya angular.

Yankho: Pa ndodo pafupifupi mbali imodzi, I = 1/3 ​ml l ²

$L=Ine\times \omega$

L=1/3×2×4 ² ×3=96 kg.m ² /s

6. Vuto: Kodi kusintha kwa mphamvu ya angular ndi kotani ngati thupi lozungulira liwonjezera liwiro lake la angular?

Yankho: Ubale pakati pa angular momentum (L) ndi angular velocity (ω) ndi $L=I\times \omega$ . Ngati ω yawirikiza kawiri, angular momentum nayonso idzawirikiza kawiri.

7. Vuto: Ngati utali wa njira yozungulira ya tinthu toyenda ukuwonjezeka kawiri pamene liwiro likupitirirabe, ndi chifukwa chiyani mphamvu ya angular imasintha?

Yankho: Angular momentum, $L=m\times r\times v$ . Ngati r iwirikiza kawiri, L idzawirikizanso kawiri.

8. Vuto: Mwana wolemera makilogalamu 30 wayima m'mphepete mwa merry-go-round yomwe ili pamalo opumulira. Utali wa merry-go-round ndi mamita awiri. Ngati mwanayo wayamba kuthamanga pa liwiro la 2m/s poyerekeza ndi nthaka m'mphepete mwake, pezani mphamvu ya mwanayo poyerekeza ndi pakati.

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

9. Vuto: Silinda yolemera makilogalamu 6 ndi utali wa mamita 2 ikuzungulira mozungulira mzere wake wapakati ndi liwiro la angular la 5 rad/s. Werengani mphamvu yake ya angular.

Yankho: Pa silinda, I = 1/2 ​m r ²

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

10. Vuto: Kodi mphamvu yatsopano ya angular ya thupi idzakhala yotani ngati mphindi yake ya inertia yachepetsedwa ndi theka ndipo liwiro lake la angular lawonjezeka katatu?

Yankho: Popeza $L=I\times \omega$ , ngati $ndichepetsedwa$ pakati ndipo $\omega \; ndi\; katatu,$$L$ yatsopano idzakhala 1/2×3=1.5 × yoyambirira.

11. Vuto: Chizunguliro cha kulemera kwa 2kg ndi radius ya 1m chikuzungulira ndi liwiro la angular la 4 rad/s. Werengani mphamvu yake ya angular.

Yankho: Pa hoop, I = m r ²

$L=Ine\times \omega$

L=2×1 ² ×4=8 kg.m ² /s

12. Vuto: Fani ili ndi masamba a 0.5m kutalika kwake ndipo kulemera kwake konse ndi 1kg. Ngati ikuzungulira ndi liwiro la 10 rad/s, dziwani mphamvu yake ya angular.

Yankho: Poganiza kuti masamba a fan ali ngati ndodo zomwe zimazungulira mbali imodzi, I = 1/3 ​ml l ²

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

13. Vuto: Werengani mphamvu ya dziko lapansi mozungulira mzere wake chifukwa cha kuzungulira kwake. Mwapatsidwa: Kulemera kwa dziko lapansi = 5.972×10 ²⁴ kg , Radius $r=6371\text{km}$ , ω = 7.27 × 1 0 ⁻⁵ rad/s.

Yankho: Poganiza kuti dziko lapansi ndi lozungulira lolimba, I = 2/5 ​m r ²

$L=Ine\times \omega$ =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. Vuto: Mwana akusunthira pakati pa nsanja yozungulira. Kodi mphamvu ya angular imawonjezeka, imachepa kapena imakhalabe yomweyo?

Yankho: Mphamvu ya angular imasungidwa. Pamene mwana akupita pakati, nthawi ya inertia imachepa. Kuti asunge mphamvu ya angular, liwiro la angular limawonjezeka. Motero, mphamvu ya angular imakhalabe yomweyo.

15. Vuto: Ngati mphamvu ya kinetic ya thupi lozungulira yawirikiza kawiri, ndi chifukwa chiyani mphamvu yake ya angular imasintha?

Yankho: Mphamvu ya kinetic K = 1/2 ​I ω ² ndi Angular momentum $L=I\omega$ . Ngati mphamvu ya kinetic yawirikiza kawiri ndipo $I$ ikhalabe yokhazikika, ω ² imawirikiza kawiri. Izi zikutanthauza kuti $\omega$ imawonjezeka ndi factor ya √ 2 ​.$Chifukwa\; chake,\; L$ imawonjezekanso ndi factor ya √ 2 ​.

16. Vuto: Gudumu la njinga la radius 0.3 m lili ndi mzere wolemera makilogalamu 1.5. Ngati likuzungulira ndi liwiro la angular la 5 rad/s, pezani mphamvu yake ya angular.

Yankho: Poganiza kuti mkomberowo ndi hoop, 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. Vuto: Wosewera pa ayezi amakoka manja ake mkati pamene akuzungulira. Kodi chimachitika n’chiyani ndi mphamvu yake yozungulira?

Yankho: Mphamvu ya wokwera phiri imasungidwa. Mwa kukoka manja ake, amachepetsa nthawi yake ya kutopa, motero amazungulira mofulumira (kuwonjezeka kwa liwiro la angular) kuti asunge mphamvu yake ya angular.

18. Vuto: Chiwongolero cha flywheel chili ndi nthawi yochepa ya 0.2 kg.m ² kg.m ² ndipo chikuzungulira ndi liwiro la angular la 10 rad/s. Pezani mphamvu yake ya angular.

yankho;

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

L = 0.2 × 10 = 2 kg.m ² / s

19. Vuto: Dongosolo lili ndi mphamvu yakunja ya zero yomwe imagwira ntchito pa ilo. Kodi munganene chiyani za mphamvu yake ya angular?

Yankho: Ngati mphamvu yakunja yonse ndi zero, ndiye kuti malinga ndi kusunga mphamvu ya angular, mphamvu yonse ya angular ya dongosololi imakhalabe yofanana.

20. Vuto: Kulemera kwa mfundo m = 5 kg kumayenda ndi liwiro v = 3 m/s molunjika ku mzere wolumikizana ndi mfundo P. Ngati mtunda wochokera ku mfundo P uli 4 m, pezani mphamvu yake ya angular pafupi ndi mfundo P.

yankho;

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

L = 5 × 4 × 3 = 60 kg.m ² / s