Angular momentum

Angular momentum

Huwandu hwekufamba kwese, hwakafanana nehuremu (m) mukufamba kwese, ndiyo nguva yekusaita (I). Huwandu hwekufamba kwese, hwakafanana nevelocity (v) mukufamba kwese, ndiyo angular velocity (ω). Saka, chinhu chinotenderera chine angular momentum inogona kuverengerwa uchishandisa equation:

L = I ω

L = angular momentum (kg m ² /s), I = nguva yekusaita basa (kg m ² ), ω = angular velocity (rad/s)

Matambudziko emuenzaniso we angular momentum

Dambudziko remuenzaniso 1.

Chidimbu chine huremu hwe 0.5 gramu chinofamba mudenderedzwa chine angle velocity inogara iripo ye 2 rad/s. Sarudza angle momentum yechinhu kana radius yenzira yechinhu iri 10 cm.

Solution:

Nguva yekusagadzikana kwechikamu:

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

Kumhanya kwekona kwechinhu ichi:

ω = 2 rad/s

Kufamba kwekona kwechikamu:

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

Mutemo wekuchengetedza angular momentum

Mutemo wekuchengetedza angular momentum unotaura kuti kana nguva yesimba rinobuda pamuviri wakasimba painotenderera iri zero, saka angular momentum yemuviri wakasimba painotenderera inogara iri nguva dzose. Mutemo wekuchengetedza angular momentum unogona kuwanikwa nemasvomhu nekushandura equation yemutemo wechipiri waNewton we angular momentum. Heino equation yemutemo wechipiri waNewton pa angular momentum:

Kana nguva yesimba inobuda iri zero, saka equation iri pamusoro inoshanduka kuita:

I _t = nguva yekupedzisira yekusashanda, I _o = nguva yekutanga yekusashanda, ω _t = kumhanya kwekupedzisira kwekona, ω _o = kumhanya kwekutanga kwekona, L _t = kumhanya kwekupedzisira kwekona, L _o = kumhanya kwekutanga kwekona.

Matambudziko emuenzaniso wemutemo wekuchengetedza angular momentum

Dambudziko remuenzaniso 1.

Dhisiki resilinda rakaenzana rinotanga kutenderera padivi paro nekumhanya kwe4 rad/s. Huremu neredhiyumu yedhisiki zviri 1 kg ne 0.5 m. Kana pamusoro peplate pakaiswa rin'i ine huremu neredhiyumu ye 0.2 kg ne 0.1 m uye pakati perin'i,

pamusoro pepakati pedhisiki, ipapo dhisiki nerin'i zvinotenderera pamwe chete nekumhanya kwekona kwe…..

Solution:

Nguva yekusashanda kwe silinda yakasimba: I = 1⁄2 mr ² = 1⁄2 (1 kg)(0.5 m) ² = (0.5)(0.25) = 0.125 kg m ²

Nguva yekusashanda kwemhete: I = mr ² = (0.2 kg)(0.1 m) ² = (0.2)(0.01) = 0.002 kg m ²

Mwenje wekutanga wekona (L ₁ ) = Mwenje wekupedzisira wekona (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

Mibvunzo nemhinduro zvepfungwa

1. Chii chinonzi angular momentum?
   Pindura: Angular momentum chiyero chehuwandu hwekutenderera kwechinhu, tichifunga nezvehukuru hwacho nechimiro chacho. Ndiyo analog yekutenderera kwe linear momentum.
2. Ko angular momentum inotsanangurwa sei nemasvomhu?
   Pindura: Angular momentum (L) inotsanangurwa se $L=r\times p$, apo $r$ ndiyo vhekitari yenzvimbo kubva pa axis yekutenderera kusvika pakushandiswa, uye $p$ ndiyo simba rakatsetseka.
3. Ko angular momentum i scalar kana kuti vector quantity here?
   Pindura: Angular momentum inhamba yevector.
4. Chii chinonzi "angular momentum" muSI system?
   Pindura: Chikamu che angular momentum muSI system chinoyera kilogram-mita sikweya pasekondi (kg·m).²/s).
5. Simba re angular rinochengetedzwa sei?
   Pindura: Muhurongwa hwakavharwa husina ma torque ekunze, simba rese re angular rinoramba riripo.
6. Ndeipi nheyo yekuchengetedza angular momentum?
   Pindura: Nheyo yacho inotaura kuti simba rese re angular system rakavharwa rinoramba riripo kunze kwekunge rashandiswa ne external torque.
7. Kutenderera kwemutambi anotsvedza muchando kunoenderana sei nekufamba kwenguva kwemuchina?
   Pindura: Kana munhu anotsvedza achidhonza maoko nemakumbo ake pedyo nemuviri wake panguva yekutenderera, anoderedza nguva yake yekusagadzikana, zvichiita kuti atenderere nekukurumidza. Izvi zvinoratidza kuchengetedza kwekufamba kwemakona.
8. Chii chiri hukama huripo pakati pe torque ne angular momentum?
   Pindura: Torque ($\tau$) ndiyo mwero wekuchinja kwe angular momentum. Panyaya yemasvomhu, τ=dL/sekondi​.
9. Zvinokwanisika here kuti chinhu chive ne angular momentum isina angular velocity?
   Pindura: Kwete, kana chinhu chine angular momentum, chine angular velocity. Hukuru uye gwara re angular momentum zvinoenderana nenguva yekusashanda zvakanaka uye angular velocity.
10. Nguva yekusagadzikana inokanganisa sei angular momentum?
    Pindura: Angular momentum (L) imhedzisiro yenguva yekusashanda (I) uye angular velocity (ω). US $L=I\omega$, kuwedzera kwekusashanda zvakanaka kwekukurumidza kwe angular kunowedzera angular momentum.
11. Ndeupi musiyano uripo pakati pe spin ne orbital angular momentum mu quantum mechanics?
    Pindura: Spin angular momentum imhando yezvikamu, semaerekitironi, uye haibvi mukufamba muchadenga. Orbital angular momentum, kune rumwe rutivi, inobva mukufamba kwezvikamu zvakatenderedza nzvimbo yepakati.
12. Ibasa rei iro angular momentum rinoita mukuumbwa kwemapuraneti?
    Pindura: Sezvo gore remamorekuru richidonha kuti riumbe nyeredzi nemapuraneti, kuchengetedzwa kwekufamba kwemakona kunoita kuti zvinhu zviteteke kuita dhisiki rakatenderedza nyeredzi ichangoberekwa, iyo mapuraneti anogona kuumbwa kubva mairi.
13. Gyroscope inoramba yakatarisa sei muchadenga?
    Pindura: Gyroscope inotenderera ine angular momentum. Kana torque yekunze ichiedza kuchinja mafambiro ayo, gyroscope inoenderera mberi, kana kuchinja axis yayo yekutenderera, nenzira yakatarisana netorque inoshandiswa nekuda kwekuchengetedzwa kwe angular momentum.
14. Chii chinokonzera precession mu top inotenderera?
    Pindura: Kufamba kwechikamu chepamusoro chinotenderera kunokonzerwa ne torque inokonzerwa ne gravity inoshanda pakati pehukuru hwepamusoro, iyo inobviswa kubva panzvimbo yayo ye pivot. Iyi torque inokonzera shanduko munzira ye angular momentum yepamusoro, zvichiita kuti imhanye.
15. Sei nyeredzi dzichitsvedza pamipendero yadzo?
    Pindura: Nyeredzi padzinotenderera, dzinoona simba repakati nepakati richisundira zvinhu kunze. Izvi zvinosimba paequator kupfuura pamativi, zvichiita kuti pave nechimiro chakatsetseka kana kuti chakati sandara.
16. Ko angular momentum ine chekuita sei nemutemo wechipiri waKepler?
    Pindura: Mutemo wechipiri waKepler unoti chikamu chemutsetse chinobatanidza nyika nezuva chinobvisa nzvimbo dzakaenzana panguva dzakaenzana. Izvi zvinokonzerwa nekuchengetedzwa kwekufamba kwemakona.
17. Sei katsi ichigara ichingomira netsoka dzayo kana yadonha?
    Pindura: Katsi dzinoshandisa kuchengetedza simba rekufamba kwemhuka. Nekutenderedza miviri yadzo uye kuchinja nguva dzadzo dzekusaita chinhu dziri mumhepo, dzinogona kuzvitenderedza kuti dzimire netsoka dzadzo pasina kutyora mitemo yekuchengetedza mhuka.
18. Nguva yemagineti inoenderana sei ne angular momentum mumaerekitironi?
    Pindura: Nguva yemagineti yeerekitironi inobva mukutenderera kwayo uye kutenderera kwayo kwe-orbital angular momentum. Nguva yemagineti inoenderana ne-angular momentum yeerekitironi.
19. Chii chinonzi angular momentum maererano nema polar coordinates?
    Pindura: Mu polar coordinates, angular momentum $L$ poindi imwe inogona kuratidzwa se $L=mrv$, apo $m$ ndiyo misa, $r$ ndiyo daro re radial, uye $v$ ndiyo kumhanya kwetangential.
20. Chii chinoitika ku angular momentum ye closed system kana zvinhu zviviri zvikabonderana?
    Pindura: Muhurongwa hwakavharwa apo zvinhu zviviri zvinosangana, simba rese rekona risati rasangana rakaenzana ne simba rese rekona mushure mekusangana, tichifunga kuti hapana ma torque ekunze anobata basa racho.

Matambudziko uye Kugadziriswa

1. Dambudziko: Poindi yehuremu m = 2 kg inofamba nevelocity v = 3 m/s mudenderedzwa reradius r = 4 m. Verenga momentum yayo yekona iri pakati pedenderedzwa.

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

2. Dambudziko: Dunhu rakasimba rine huremu hwe 3 kg uye radius ye 0.5 m riri kutenderera dhayamita yaro ne angular velocity ω = 2 rad/s. Chii chinonzi angular momentum yaro?

Mhinduro: Kune bhora rakasimba, 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. Dambudziko: Huremu hwemakirogiramu matatu huri kufamba nekumhanya kwe4 m/s mumutsara wakatwasuka. Chii chiri kutenderera kwayo kwekona iri kure ne5 m kubva pamutsetse wayo wekufamba?

Solution:

$L=m\times v\times r$

L=3×4×5=60 kg.m ² /s

4. Dambudziko: Disiki ine huremu hwe5 kg uye radius ye3 m iri kutenderera nekumhanya kwe angular kwe2 rad/s. Verenga angular momentum yayo.

Mhinduro: Kune dhisiki, I = 1/2 ​m r ²

$L=I\times \omega$

L=1/2×5×3 ² ×2=45 kg.m ² /s

5. Dambudziko: Tsvimbo ine hurefu hwemamita mana uye huremu hwemakirogiramu maviri inotenderera mugumo mumwe chete ne angled velocity ye3 rad/s. Tsvaga angled momentum yayo.

Mhinduro: Patsvimbo inenge mugumo mumwe chete, I = 1/3 ​ml l ²

$L=I\times \omega$

L=1/3×2×4 ² ×3=96 kg.m ² /s

6. Dambudziko: Chii chinochinja mu angular momentum kana muviri unotenderera ukawedzera kaviri angular velocity yawo?

Mhinduro: Hukama huripo pakati pe angular momentum (L) ne angular velocity (ω) ndi $L=I\times \omega$ . Kana ω yakapetwa kaviri, angular momentum ichapetwawo kaviri.

7. Dambudziko: Kana nharaunda yenzira yakatenderera yechinhu chinofamba ikawedzera kaviri ukuwo ichiita kuti kumhanya kurambe kwakafanana, mafambiro emakona anochinja nei?

Mhinduro: Angular momentum, $L=m\times r\times v$ . Kana r ikapetwa kaviri, L ichapetwawo kaviri.

8. Dambudziko: Mwana ane huremu hunosvika 30 kg akamira pamucheto we merry-go-round iri pakadzikama. Radius ye merry-go-round i2 m. Kana mwana akatanga kumhanya nekumhanya kwe2m/s pasi pamucheto, tsvaga angular momentum yemwana pakatarisana nepakati.

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

9. Dambudziko: Silinda ine huremu hwe 6 kg uye radius ye 2 m iri kutenderera pakati pe axis yayo ne angular velocity ye 5 rad/s. Verenga angular momentum yayo.

Mhinduro: Kune sirinda, I = 1/2 m r ²

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

10. Dambudziko: Chii chichava simba idzva remuviri kana nguva yaro yekusaita basa ikadzikiswa nehafu uye kumhanya kwaro kweakona kukapetwa katatu?

Mhinduro: Kana $L=I\times \omega$ , kana $ndikaderedzwa$ nehafu uye $\omega \; ikapetwa\; katatu,$$L$ itsva ichava 1/2×3=1.5 × yekutanga.

11. Dambudziko: Hoop ine huremu hwe2kg uye radius ye1m iri kutenderera nekumhanya kwekona kwe4 rad/s. Verenga momentum yayo yekona.

Mhinduro: Kune hoop, I = m r ²

$L=I\times \omega$

L=2×1 ² ×4=8 kg.m ² /s

12. Dambudziko: Fan ine mapanga akareba 0.5m uye huremu hwese hunosvika 1kg. Kana ikatenderera nekumhanya kwe angle kwe 10 rad/s, sarudza momentum yayo ye angle.

Mhinduro: Tichifunga kuti mabhenefiti akafanana nematanda anotenderera kumucheto mumwe chete, I = 1/3 ​m l ²

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

13. Dambudziko: Verengai momentum yenyika ine kona iri pedyo ne axis yayo nekuda kwekutenderera kwayo. Zvichipiwa: Huremu hwenyika =5.972×10 ²⁴ kg , Radius $r=6371\text{km}$ , ω = 7.27 × 1 0 ⁻⁵ rad/s.

Mhinduro: Tichifunga kuti nyika idenderedzwa rakasimba, 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. Dambudziko: Mwana ari kufamba akananga pakati pepuratifomu inotenderera. Ko angular momentum inowedzera, inoderera here kana kuti inoramba yakadaro?

Mhinduro: Angular momentum inochengetedzwa. Mwana paanofamba achienda pakati, nguva yekusaita basa inoderera. Kuti achengetedze angular momentum, angular velocity inowedzera. Saka, angular momentum inoramba yakafanana.

15. Dambudziko: Kana simba rekufamba kwemuviri rinotenderera rakapetwa kaviri, simba rayo rekona rinochinja nei?

Mhinduro: Kinetic energy K = 1/2 ​I ω ² uye Angular momentum $L=I\omega$ . Kana kinetic energy yakapetwa kaviri uye $I$ ikaramba yakadaro, ω ² yakapetwa kaviri. Izvi zvinoreva kuti $\omega$ yakawedzerwa ne factor ye √ 2 ​.$Saka,\; L$ inowedzerawo ne factor ye √ 2 ​.

16. Dambudziko: Vhiri rebhasikoro rine radius 0.3 m rine rim ine huremu hwe1.5 kg. Kana richitenderera nekumhanya kwe5 rad/s, tsvaga angular momentum yaro.

Mhinduro: Tichifunga kuti rim iri 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. Dambudziko: Munhu anotsvedza muchando anodhonza maoko ake mukati achitenderera. Chii chinoitika kukufamba kwake kwekona?

Mhinduro: Simba remutambi anotsvedza rinochengetedzwa. Nekudhonza maoko ake mukati, anoderedza nguva yake yekusaita basa, uye nokudaro anotenderera nekukurumidza (kuwedzera kumhanya kwekona) kuchengetedza simba rake rekona.

18. Dambudziko: Chinotenderera chine nguva yekusashanda zvakanaka ye 0.2 kg.m. ² kg.m. ² uye chiri kutenderera ne angular velocity ye 10 rad/s. Tsvaga angular momentum yaro.

Solution:

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

L = 0.2 × 10 = 2 kg.m ² / s

19. Dambudziko: Sisitimu ine torque yekunze ye zero inoshanda pairi. Ungati chii nezve angular momentum yayo?

Mhinduro: Kana torque yekunze yakakwana iri zero, saka zvichienderana nekuchengetedzwa kwe angular momentum, angular momentum yese yesystem inoramba yakadaro.

20. Dambudziko: Poindi huremu m = 5 kg inofamba nevelocity v = 3 m/s yakatarisana nemutsetse unoibatanidza nepoindi P. Kana daro kubva papoindi P riri 4 m, tsvaga angular momentum yayo pamusoro pepoindi P.

Solution:

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

L = 5 × 4 × 3 = 60 kg.m ² / s