ʻO ka manaʻo kihikihi

ʻO ka manaʻo kihikihi

ʻO ka nui o ka neʻe ʻana o ka wili, e like me ka nuipa (m) i ka neʻe linear, ʻo ia ka manawa o ka inertia (I). ʻO ka nui o ka neʻe ʻana o ka wili, e like me ka wikiwiki (v) i ka neʻe linear, ʻo ia ka wikiwiki angular (ω). No laila, loaʻa i ka mea wili ka momentum angular e hiki ke helu ʻia me ka hoʻohana ʻana i ka hoohalike:

L = I ω

L = ka momentum angular (kg m ² /s), I = ka manawa o ka inertia (kg m ² ), ω = ka wikiwiki angular (rad/s)

Nā pilikia laʻana o ka momentum angular

Laʻana pilikia 1.

Neʻe kahi ʻāpana me ke kaumaha o 0.5 grams i loko o kahi pōʻai me ka wikiwiki angular mau o 2 rad/s. E hoʻoholo i ka momentum angular o ka ʻāpana inā he 10 cm ka radius o ke ala o ka ʻāpana.

pāʻoihana:

ʻO ka manawa o ka inertia o ka ʻāpana:

ʻO 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

ʻO ka wikiwiki kihi o ka ʻāpana:

ω = 2 rad/s

ʻO ka momentum angular o ka ʻāpana:

L = (0.5 x 10 ^-5 kg ​​​​m² ⁾ (2 rad/s) = 1 x 10 ^-5 kg ​​​​m² ^/ s

Ke kānāwai o ka mālama ʻana i ka momentum angular

ʻŌlelo ke kānāwai o ka mālama ʻana i ka momentum angular inā ʻo ka hopena o ka manawa o ka ikaika ma luna o ke kino paʻa i ka wā e wili ana he zero, a laila mau ka momentum angular o ke kino paʻa i ka wā e wili ana. Hiki ke loaʻa ke kānāwai o ka mālama ʻana i ka momentum angular ma ke ʻano makemakika ma ka hoʻololi ʻana i ka hoohalike o ke kānāwai ʻelua o Newton o ka momentum angular. Eia ka hoohalike o ke kānāwai ʻelua o Newton ma ka momentum angular:

Inā he ʻole ka hopena o ka manawa o ka ikaika, a laila e loli ke kaulike ma luna nei i:

ʻO I _t = ka manawa hope loa o ka inertia, ʻO I _o = ka manawa mua o ka inertia, ʻO ω _t = ka wikiwiki kihi hope loa, ʻO ω _o = ka wikiwiki kihi mua, ʻO L _t = ka momentum kihi hope loa, ʻO L _o = ka momentum kihi mua.

Nā pilikia laʻana o ke kānāwai o ka mālama ʻana i ka momentum angular

Laʻana pilikia 1.

Ke hoʻomaka nei kahi diski cylinder paʻa like ma kona axis me ka wikiwiki o 4 rad/s. ʻO ke kaumaha a me ke radius o ka diski he 1 kg a me 0.5 m. Inā ma luna o ka pā i kau ʻia kahi apo nona ke kaumaha a me ke radius o 0.2 kg a me 0.1 m a ʻo ke kikowaena o ke apo,

ma luna pono o ke kikowaena o ka diski, a laila e wili pū ka diski a me ke apo me ka wikiwiki angular o…..

pāʻoihana:

Manawa o ka inertia o ka cylinder paʻa: I = 1⁄2 mr2 ⁼ 1⁄2 (1 kg)(0.5 m) ² = (0.5)(0.25) = 0.125 kg ^m2

Manawa o ka inertia o ke apo: I = mr ² = (0.2 kg)(0.1 m) ² = (0.2)(0.01) = 0.002 kg m ²

Ka momentum kihi mua (L ₁ ) = Ka momentum kihi hope loa (L ₂ )

ʻO I ₁ ω ₁ = ʻO I ₂ ω ₂

(0.125 kg m² ⁾ (4 rad/s) = (0.125 kg m² ⁺ 0.002 kg m² ⁾ ( _ω² )

(0.5) = (0.127)(ω ₂ )

ω ₂ = 0.5 : 0.127

ω ₂ = 4 rad/s

Nā nīnau a me nā pane manaʻo

1. He aha ka momentum angular?
   pane mai: ʻO ke momentum angular ke ana o ka nui o ka wili ʻana o kahi mea, e noʻonoʻo ana i kona nuipa a me kona ʻano. ʻO ia ke analog rotational o ka momentum linear.
2. Pehea e hoʻoholo ʻia ai ka momentum angular ma ka makemakika?
   pane mai: Ua wehewehe ʻia ka momentum angular (L) e like me $L=r\times p$, kahi $r$ ʻo ia ke vector kūlana mai ke axis o ka wili a i ke kiko o ka noi, a $p$ ʻo ia ka momentum linear.
3. He nui scalar a he nui vector paha ka momentum angular?
   pane mai: He nui vector ka momentum angular.
4. He aha ke anakahi o ka momentum angular i loko o ka ʻōnaehana SI?
   pane mai: ʻO ke anakahi o ka momentum angular i loko o ka ʻōnaehana SI he kilokani-mika huinahā i kekona (kg·m²/s).
5. Pehea e mālama ʻia ai ka momentum angular?
   pane mai: I loko o kahi ʻōnaehana pani me ka ʻole o nā torques o waho, e mau ana ka momentum angular holoʻokoʻa.
6. He aha ke kumumanaʻo o ka mālama ʻana i ka momentum angular?
   pane mai: ʻŌlelo ke kumumanaʻo e mau ana ka momentum angular holoʻokoʻa o kahi ʻōnaehana pani ke ʻole e hana ʻia e kahi torque o waho.
7. Pehea e pili ai ka wili o kahi mea heʻe kiʻi i ka momentum angular?
   pane mai: Ke huki ka mea heʻe kiʻi i ko lākou mau lima a me nā wāwae a kokoke i ko lākou kino i ka wā o ka milo, hoʻemi lākou i ko lākou manawa o ka inertia, e hoʻoulu ai iā lākou e milo wikiwiki. Hōʻike kēia i ka mālama ʻana o ka momentum angular.
8. He aha ka pilina ma waena o ka torque a me ka momentum angular?
   pane mai: ʻO ka ikehu ($\tau$) ʻo ia ka wikiwiki o ka loli o ka momentum angular. Ma ke ʻano makemakika, τ=dL/kekona​.
9. Hiki i kahi mea ke loaʻa ka momentum angular me ka ʻole o ka velocity angular?
   pane mai: ʻAʻole, inā he momentum angular ko kahi mea, he velocity angular kona. Pili ka nui a me ke kuhikuhi o ka momentum angular i ka moment of inertia a me ka velocity angular.
10. Pehea ka hopena o ka manawa o ka inertia i ka momentum angular?
    pane mai: ʻO ka momentum angular (L) ka huahana o ka manawa o ka inertia (I) a me ka wikiwiki angular (ω). US $L=I\omega$, ʻo ka hoʻonui ʻana i ka manawa o ka inertia no kahi wikiwiki angular i hāʻawi ʻia e hoʻonui i ka momentum angular.
11. He aha ka ʻokoʻa ma waena o ka spin a me ka orbital angular momentum i ka mechanics quantum?
    pane mai: ʻO ka momentum angular spin kahi waiwai kūloko o nā ʻāpana, e like me nā electrons, a ʻaʻole ia e kū mai ka neʻe ʻana i ka lewa. ʻO ka momentum angular orbital, ma ka ʻaoʻao ʻē aʻe, e kū mai ana mai ka neʻe ʻana o kahi ʻāpana a puni kahi kiko waena.
12. He aha ke kuleana o ka momentum angular i ke kūkulu ʻia ʻana o nā ʻōnaehana honua?
    pane mai: I ka hiolo ʻana o ke ao molekala e hana i nā hōkū a me nā hōkūhele, ʻo ka mālama ʻana i ka momentum angular ke kumu o ka palahalaha ʻana o ka mea i loko o kahi disk a puni ka hōkū hānau hou, kahi e hiki ai i nā hōkūhele ke hana ʻia.
13. Pehea e hoʻonohonoho ai ka gyroscope i kona kuhikuhi ʻana i ka lewa?
    pane mai: He momentum angular ko ka gyroscope wili. Ke hoʻāʻo kahi torque waho e hoʻololi i kona kuhikuhi, neʻe mua ka gyroscope, a hoʻololi paha i kona axis o ka wili ʻana, ma kahi kuhikuhi kū pololei i ka torque i hoʻopili ʻia ma muli o ka mālama ʻana i ka momentum angular.
14. He aha ke kumu o ka precession i loko o kahi top milo?
    pane mai: Hoʻokumu ʻia ka precession i loko o kahi top wili e ka torque ma muli o ke umekaumaha e hana ana ma ke kikowaena nuipa o ka top, kahi i hoʻokaʻawale ʻia mai kona pivot point. ʻO kēia torque ka hopena o kahi loli i ke kuhikuhi o ka momentum angular o ka top, e hoʻoulu ai i ka precess.
15. No ke aha i pālahalaha ai nā hōkū ma ko lākou mau pou?
    pane mai: I ka hoʻohuli ʻana o nā hōkū, ʻike lākou i kahi ikaika centrifugal e hoʻokuke ana i nā mea i waho. ʻOi aku ka ikaika o kēia hopena ma ka equator ma mua o nā pou, e alakaʻi ana i kahi ʻano oblate, a i ʻole pālahalaha.
16. Pehea e pili ai ka momentum angular i ke kānāwai ʻelua o Kepler?
    pane mai: ʻŌlelo ke kānāwai ʻelua o Kepler ʻo kahi ʻāpana laina e hoʻohui ana i kahi honua a me ka Lā e hoʻopau i nā wahi like i nā wā like. He hopena kēia o ka mālama ʻana i ka momentum angular.
17. No ke aha e pae mau ai ka pōpoki ma luna o kona mau wāwae ke hāʻule?
    pane mai: Hoʻohana nā pōpoki i ka mālama ʻana i ka momentum angular. Ma ka wili ʻana i ko lākou kino a me ka hoʻololi ʻana i ko lākou mau manawa o ka inertia i ka lewa, hiki iā lākou ke hoʻololi iā lākou iho e pae ma ko lākou mau wāwae me ka ʻole o ka uhaki ʻana i nā kānāwai mālama.
18. Pehea e pili ai ka manawa magnetic i ka momentum angular i loko o nā electrons?
    pane mai: Kū mai ka manawa magnetic o kahi electron mai kona milo a me ka momentum angular orbital. Pili ka manawa magnetic i ka momentum angular o ka electron.
19. He aha ka momentum angular e pili ana i nā hoʻonohonoho polar?
    pane mai: Ma nā hoʻonohonoho polar, ka momentum angular $L$ no ka nuipa kiko hiki ke hōʻike ʻia e like me $L=mrv$, kahi $m$ ʻo ia ka nuipa, $r$ ʻo ia ka mamao radial, a $v$ ʻo ia ka wikiwiki tangential.
20. He aha ka mea e hana ʻia i ka momentum angular o kahi ʻōnaehana pani ke kuʻi ʻelua mau mea?
    pane mai: I loko o kahi ʻōnaehana pani kahi e kuʻi ai ʻelua mau mea, ua like ka huina o ka momentum angular ma mua o ke kuʻi ʻana me ka huina o ka momentum angular ma hope o ke kuʻi ʻana, me ka manaʻo ʻaʻohe torques o waho e hana ma ka ʻōnaehana.

Nā pilikia a me nā hoʻoponopono

1. Pilikia: Neʻe kahi nuipa kiko m = 2 kg me ka wikiwiki v = 3 m/s i loko o kahi pōʻai me ka radius r = 4 m. E helu i kona momentum angular a puni ke kikowaena o ka pōʻai.

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

2. Pilikia: Ke wili nei kahi poepoe paʻa me ke kaumaha he 3 kg a me ka radius he 0.5 m a puni kona anawaena me ka wikiwiki angular ω = 2 rad/s. He aha kona momentum angular?

Hoʻonā: No kahi poepoe paʻa, 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. Pilikia: Ke neʻe nei kahi nuipa kiko o 3 kg me ka wikiwiki o 4 m/s ma kahi laina pololei. He aha kona momentum angular e pili ana i kahi kiko 5 m ka mamao mai kona laina neʻe?

pāʻoihana:

$L=m\times v\times r$

L=3×4×5=60 kg.m ² /s

4. Pilikia: Ke wili nei kahi diski me ke kaumaha he 5 kg a me ka radius he 3 m me ka wikiwiki angular o 2 rad/s. E helu i kona momentum angular.

Hoʻonā: No kahi diski, I = 1/2 ​m r ²

$L=I\times \omega$

L=1/2×5×3 ² ×2=45 kg.m ² /s

5. Pilikia: Ke wili nei kahi koʻokoʻo he 4 m ka lōʻihi a me ke kaumaha he 2 kg ma kahi o hoʻokahi wēlau me ka wikiwiki angular o 3 rad/s. E huli i kona momentum angular.

Hoʻonā: No ke koʻokoʻo ma kekahi ʻaoʻao, I = 1/3 ​m l ²

$L=I\times \omega$

L=1/3×2×4 ² ×3=96 kg.m ² /s

6. Pilikia: He aha ka loli o ka momentum angular inā e pāpālua ke kino e wili ana i kona wikiwiki angular?

Hoʻonā: ʻO ka pilina ma waena o ka momentum angular (L) a me ka wikiwiki angular (ω) ʻo $L=I\times \omega$ . Inā pāpālua ʻia ʻo ω, e pāpālua pū ka momentum angular.

7. Pilikia: Inā pālua ka radius o ke ala pōʻai o kahi ʻāpana e neʻe ana me ka mālama ʻana i ka wikiwiki mau, ma o ka mea hea e loli ai ka momentum angular?

Hoʻonā: Ka momentum angular, $L=m\times r\times v$ . Inā pālua ʻo r, e pālua pū ʻo L.

8. Pilikia: Ke kū nei kekahi keiki me ke kaumaha he 30 kg ma ka lihi o kahi merry-go-round e hoʻomaha ana. ʻO ke radius o ka merry-go-round he 2 m. Inā hoʻomaka ke keiki e holo ma ka wikiwiki o 2m/s e pili ana i ka honua ma ka lihi, e ʻimi i ka momentum angular o ke keiki e pili ana i ke kikowaena.

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

9. Pilikia: Ke kaʻapuni nei kahi cylinder me ke kaumaha o 6 kg a me ka radius 2 m a puni kona axis waena me ka wikiwiki angular o 5 rad/s. E helu i kona momentum angular.

Hoʻonā: No kahi paukūʻolokaʻa, I = 1/2 ​m r ²

$L=I\times \omega$ =1/2×6×0.52 ^× 5=120 kg.m2 ^/ s

10. Pilikia: He aha ka momentum angular hou o ke kino inā e hoʻemi ʻia kona momena inertia i ka hapalua a e hoʻonui ʻia kona wikiwiki angular i ʻekolu?

Pākuʻi: Hāʻawi ʻia ʻo $L=I\times \omega$ , inā e hapalua ʻia $ʻo\; I$ a e pākolu ʻia ʻo $\omega$ , ʻo ka $L$ hou he 1/2×3=1.5 × ka mea mua.

11. Pilikia: Ke wili nei kahi ʻōwili me ke kaumaha o 2kg a me ka radius 1m me ka wikiwiki angular o 4 rad/s. E helu i kona momentum angular.

Hoʻonā: No ka ʻōwili, I = m r ²

$L=I\times \omega$

L=2×1 ² ×4=8 kg.m ² /s

12. Pilikia: He 0.5m ka lōʻihi o nā lau o ka peʻahi a he 1kg ka nuipaʻa. Inā e wili ana me ka wikiwiki angular o 10 rad/s, e hoʻoholo i kona momentum angular.

Hoʻonā: Ke manaʻo nei ua like nā lau peʻahi me nā koʻokoʻo e hoʻohuli ana a puni kekahi wēlau, I =1/3 ​m l ²

$L=I\times \omega$ =1/3×1×0.52 ^× 10=0.833 kg.m2 ^/ s

13. Pilikia: E helu i ka momentum angular o ka honua e pili ana i kona axis ponoʻī ma muli o kona wili ʻana. Hāʻawi ʻia: Mass o ka honua ⁼ 5.972× ¹⁰²⁴ kg , Radius $r=6371\text{km}$ , $\omega =7.27\times 10-5rad\text{/s}$.

Hoʻonā: Ke manaʻo nei he poepoe paʻa ka honua, 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. Pilikia: Neʻe kekahi keiki i ke kikowaena o kahi kahua e wili ana. Ke piʻi nei, ke emi nei a i ʻole ke mau nei ka momentum angular?

Hoʻonā: Mālama ʻia ka momentum angular. Ke neʻe ke keiki i ke kikowaena, emi iho ka manawa o ka inertia. No ka mālama ʻana i ka momentum angular, piʻi ka wikiwiki angular. No laila, ua like ka momentum angular.

15. Pilikia: Inā pāpālua ʻia ka ikehu kinetic o ke kino e wili ana, ma o ka mea hea e loli ai kona momentum angular?

Hoʻonā: Ikehu kinetic K = 1/2 ​I ω ² a me ka momentum angular $L=I\omega$ . Inā pāpālua ka ikehu kinetic a noho mau ʻo $I$ , pāpālua ʻo ω ^2.$ʻO\; ke\; ʻano\; o\; kēia,\; ua\; hoʻonui\; ʻia\; ʻo\; \omega$ e kahi kumu o √ 2 ​.$No\; laila,\; piʻi\; pū\; ʻo\; L$ e kahi kumu o √ 2 ​.

16. Pilikia: He 1.5 kg ke kaumaha o ka lihi o ka huila paikikala me ka radius 0.3 m. Inā e wili ia me ka wikiwiki angular o 5 rad/s, e ʻimi i kona momentum angular.

Hoʻonā: Ke manaʻo nei i ka lihi e like me ka hoop, I = m r ²

$L=I\times \omega$ =1.5×0.32×5=6.75 kg.m2 ^/ s

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

17. Pilikia: Huki ka mea holo hau i kona mau lima i loko i ka wā e milo ana. He aha ka mea e hana ʻia i kona momentum angular?

Hoʻonā: Ua mālama ʻia ka momentum angular o ka mea heʻe nalu. Ma ka huki ʻana i kona mau lima i loko, hoʻemi ʻo ia i kona momena o ka inertia, a pēlā ʻo ia e milo wikiwiki ai (hoʻonui ʻia ka wikiwiki angular) e mālama i kona momentum angular.

18. Pilikia: He 0.2 kg.m² ka manawa inertia o ka huila lele ^a ke wili ^nei me ka wikiwiki angular o 10 rad/s. E huli i kona momentum angular.

pāʻoihana:

$L=I\times \omega$ =0.2×10=2 kg.m2 ^/ s

L = 0.2 × 10 = 2 kg.m2 / s^​

19. Pilikia: Loaʻa i kahi ʻōnaehana kahi torque kūwaho net o ka ʻole e hana ana ma luna. He aha kāu e ʻōlelo ai e pili ana i kona momentum angular?

Hoʻonā: Inā ʻaʻohe ka torque waho ʻupena, a laila e like me ka mālama ʻana o ka momentum angular, e mau ana ka momentum angular holoʻokoʻa o ka ʻōnaehana.

20. Pilikia: Neʻe kahi nuipa kiko m = 5 kg me ka wikiwiki v = 3 m/s e kū pono ana i ka laina e hoʻohui ana iā ia i kahi kiko P. Inā he 4 m ka mamao mai ke kiko P, e ʻimi i kona momentum angular e pili ana i ke kiko P.

pāʻoihana:

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

L = 5 × 4 × 3 = 60 kg.m ² / s