Ūn-tōng-liōng

Soàn-sêng ūn-tōng-liōng (Hàn-jī: 線型運動量; Eng-gí: linear momentum), ia̍h sī kán-chheng ūn-tōng-liōng (運動量; momentum), ê chi̍t chióng le̍k-ha̍k ê bu̍t-lí-liōng, i biâu-su̍t bu̍t-thé sóa-tāng ê chêng-hêng.

It-poaⁿ só͘ kóng ê ūn-tōng-liōng sī hiòng-liōng, kòan-sì iōng lâi tāi-piáu, án-ne i ê tōa-sè tō sī , hong-hiòng tō sī .

Newton tē-jī ūn-tōng tēng-lu̍t kóng, bu̍t-thé ūn-tōng-liōng ê piàn-hòa-lu̍t pêⁿ-pêⁿ i siū-tio̍h ê si tī i sin-khu-téng ê chēng-la̍t.

Ūn-tōng-liōng chīn-chāi bu̍t-thé ê chham-khó-hē, put-jî-kò, tùi jīm-hô ê chham-khó-hē lâi khòaⁿ, ūn-tōng-liōng sī siú-hêng-liōng (守恆量; conserved), che tō sī kóng, siat-sú chi̍t-ê ba̍t-hē-thóng bô khì hō͘ gōa-le̍k éng-hióng--tio̍h, nā-án-ne i ê chóng ūn-tōng-liōng lóng bē ū piàn-hòa. Tī te̍k-sû siong-tùi-lūn, tiān-tōng-le̍k-ha̍k, liōng-chú le̍k-ha̍k, liōng-chú tiûⁿ-lūn, it-poaⁿ siong-tùi-lūn tang-tiong, ūn-tōng-liōng sui-jiân lóng ū bô-kâng ê hêng-sek, in chóng--sī siú-hêng-liōng. Kî-si̍t, ūn-tōng-liōng sī chi̍t chióng khong-kan kap sî-kan ê ki-pún tùi-thīn: sóa-ūi tùi-thīn (徙位對伨; translational symmetry.)

Newton Le̍k-ha̍kSiu-kái

Chit-tiámSiu-kái

Newton Le̍k-ha̍k tiong, ko͘-chi̍t-ê chit-tiám ê ūn-tōng-liōng chiū tēng-gī chòe i ê chit-liōng   kap sok-tō͘   ê hē-só͘-chek (係數積):

 

Tī it-chhù-goân (1D) ê chêng-hêng tiong,   kap   iōng si̍t-sò͘ piáu-sī tō hó:

 

in ê chèng-hū hû-hō tāi-piáu hong-hiòng. Ūn-tōng-liōng ê tan-ūi sī chit-liōng ê tan-ūi sêng sok-tō͘ ê tan-ūi. Phì-jû-kóng tī SI tan-ūi, chit-liōng ê tan-ūi sī kong-kin (kg), sok-tō͘--ê sī kong-chhioh múi bió (m/s), nā án-ne ūn-tōng-liōng--ê tō sī "kong-kin kong-chhioh múi bió (kg⋅m/s)." Tī cgs tan-ūi, chit-liōng ê tan-ūi sī kong-khek (g), sok-tō͘--ê sī kong-hun múi bió (cm/s), nā án-ne ūn-tōng-liōng--ê tō sī "kong-khek kong-hun múi bió (g⋅cm/s)."

Siat-sióng chi̍t tâi chhia ē-ēng-tit khòaⁿ-chòe sī chit-liōng 2000 kong-kin ê chit-tiàm, taⁿ chit tâi chhia í 36 km/h, iā tō sī 10 m/s, ê sok-tō͘ ǹg sai sái. Kiám-chhái kā tang-hong tèng chòe   hong-hiòng, chit tâi chhia ê ūn-tōng-liōng chiū-án-ne sī (2000 kg) × (−10 m/s) = 20000 kg⋅m/s, hū-hō tāi-piáu hong-hiòng ǹg sai.

Che Newton tē-jī ūn-tōng tēng-lu̍t

 

Chit-tiám Hē-thóngSiu-kái

Chi̍t tīn chit-tiám ē-sái cho͘-sêng chit-tiám hē-thóng (質點系統). Chit-ê hē-thóng ê ūn-tiōng-liōng tō sī ta̍k-ê chit-tiám ūn-tiōng-liōng ê hiòng-liōng-hô (向量和):

 

kî-tiong ē-thiam-jī (下添字)   sī chit-tiám ê phiau-thâu (標頭),  .

Chit-tiám hē-thóng ū chi̍t-ē chit-sim. I ê ūi-tì sī   ta̍k-ê chi̍t-tiám ê ūi-tì   í chit-liōng   ûi khoân-sò͘ ê ka-khoân-hô (加權和):

 

chia ê ē-thiam-jī   sī chit-sim (center-of-mass) ê ì-sù. Chit-sim sok-tō͘    ê bî-hun:

 

tān-sī   tō sī chit-liōng chóng-hô,   tú-á-hó tō sī  , só͘-í,

 

Che hām ko͘-chi̍t-ê chit-tiàm ê ūn-tōng-liōng ū kāng-khoán ê hêng-sek. Che piáu-sī kóng, chí-iàu chiong chit-tiàm hē-thóng iōng i ê chit-sim lâi tāi-piáu, ko͘-chit-tiàm ê Newton le̍k-ha̍k tùi i mā ē ha̍h-ēng.

Siú-hêngSiu-kái

Sio-lòngSiu-kái

Kóng-gī-hòaSiu-kái

Lagrange Le̍k-ha̍kSiu-kái

Hamilton Le̍k-ha̍kSiu-kái

Liân-sio̍k-thèSiu-kái

Siong-tùi-lūnSiu-kái

Ti te̍k-sû siong-tùi-lūn tiong, Lorentz piàn-ōaⁿ sī nn̄g-ê koàn-sèng chham-khó-hē chi-kan ê chò-piau piàn-ōaⁿ (pau-koat ūi-tì hām sî-kan.) Lorentz piàn-ōaⁿ chi-hā ê chit-liōng m̄-sī put-piān-liōng, tian-tò sī sûi chham-khó-hē chi-kan ê siong-tùi sok-tō͘   lâi piàn-hòa:

 

chia ê  ,  kng-sok,   kiò-chòe Lorentz in-chú;   kiò-chòe put-piàn chit-liōng, i sī bu̍t-thé chit-liōng tiong bē siū-tio̍h Lorentz piàn-ōaⁿ éng-hióng ê pō͘-hūn.

Chi̍t-ê koan-chhat-chiá khiā tī koàn-sèng-hē, teh khòaⁿ lēng-gōa chi̍t-ê koàn-sèng-hē téng-koân ê chit-tiàm. Nā chit-tiàm ū put-piàn chit-liōng  , koan-chhat-chiá khòaⁿ-tio̍h ê siong-lúi-lūn-sèng ūn-tōng-liōng (相對論性運動量, relativistic momentum) tō sī

 

kî-tiong ê   sī kò͘-iú-sî-kan (固有時間, proper time), tō sī tòe-tio̍h hit-ê chit-tiàm ê sî-cheng sò͘ sǹg ê sî-kan.

Sì-hiòng-liōng Hêng-sekSiu-kái

Sì-hiòng-liōng (四向量, four-vector) ê kài-liām tùi siong-tùi-lūn ê sì-chhù-goân sî-khong tiong kài hó-ēng. Chi̍t-ê sì-hiòng-liōng   ū sì-ê hun-liōng, piáu-sī ê hoat-tō͘ ū chē-chē-chióng:

 

tī chia ko͘-chi̍t-ê  tō ē-sái piáu-ta̍t sì ê hun-liōng, i ê téng-thiam-jī (頂添字) tio̍h ài iōng Hi-lia̍p-jī; Nā-sī   tāi-piáu “ná chhiūⁿ sî-kan” ê hun-liōng, nā-sī   tāi-piáu “ná chhiūⁿ khong-kan” ê hun-liōng. Siá-chòe   ê sî, lán tiāⁿ-tiāⁿ ē iōng Einstein koàn-lē.

Nn̄g-ê sì-hiòng-liōng   kap  Minkowski khong-kan tiong ê sûn-liōng-chek sī án-ne tēng-gī:

 

  sī Minkowski metric tensor, siong-tong (−, +, +, +) ê metric signature.

Sì-ūi-tì

 

 kng-sok,   sī sî-kan,  sam-chhù-goân khong-kan ūi-tì hiòng-liōng. Sì-sok-tō͘

 

  sī sam-chhù-goân khong-kan sok-tō͘ hiòng-liōng.Só͘-í sì-ūn-tōng-liōng tō sī

 

chia ê   sī chóng-lêng-liōng,   sī siong-lúi-lūn-sèng ūn-tōng-liōng. Sì-ūn-tōng-liōng kap i ka-kī ê sûn-liōng-chek sī

 

che ē thàu-kàu lêng-liōng ūn-tōng-liōng koan-hē:

 

Liōng-chú Le̍k-ha̍kSiu-kái

Tiān-tōng-le̍k-ha̍kSiu-kái

Le̍k-súSiu-kái

Tē-it ūi chèng-khak thê-chhut Ūn-tōng-liōng siú-hêng tēng-lí ê lâng sī Eng-kok sò͘-ha̍k-kā John Wallis. Tī 1670 ê chok-phín, Mechanica sive De Motu, Tractatus Geometricus, i kóng "m̄-koán mi̍h-kiāⁿ chi̍t-khai-sí sī khiā tiānn-tiānn ia̍h-sī teh tín-tāng, tāi-seng ê chōng-thài chhî-sio̍k chiâu-ûn," koh kóng "nā-sī le̍k-liōng khah tōa chó͘-le̍k, mi̍h-kiāⁿ tō ē khai-sí tín-tāng." Wallis kā ūn-tōng ê liōng hō-chòe momentum, le̍k-liōng hō-chòe vis.

Newton ê Chū-jiân Tiat-ha̍k ê Sò͘-ha̍k Goân-lí tī 1687 chhut-pán ê sî, i ê piat-ta̍t hām Wallis chin sio-siāng ê tēng-gī. Quantitas motus, "ūn-tōng ê liōng", chiū I ê tēng-gī tō sī "iû sok-tō͘ kap bu̍t-chit ê liōng sò͘ lâi--ê", che ē-sái khòaⁿ-chòe sī ūn-tōng-liōng. Newton teh kái-soe Tē-jī Tēng-lu̍t ê sī sò͘ kóng ê mutatio motus, "ūn-tōng pia-hòa", sī chèng-pí sò͘ si ê la̍t. Só͘-í i tī hia kóng motus ê sî, ì-sù kî-si̍t i-pòaⁿ sī teh kóng ūn-tōng-liōng, m̄-sī ūn-tōng.