Ko te tūāpapa tuatahi mō te taurite o te tinana pakari :
E ai ki te Ture Tuarua a Newton, mēnā kāore te kaha hua e pā ana ki tētahi mea (e kiia ana te mea he matūriki) e ōrite ki te kore, ka neke te mea me te whakaterenga pumau ina rite te ahunga o te nekehanga o te mea ki te ahunga o te kaha hua. Mēnā he kore te kaha hua, kei te okioki te mea, kei te neke rānei te mea i te tere pumau.
Ina noho pūmau, ina neke rānei te mea i te tere pumau, kāore he whakaterenga (a) o te mea. Nā te mea ko te whakaterenga (a) = 0, ka huri te whārite i runga ake nei ki:
Ka taea te wehewehe i tēnei whārite ki ōna wāhanga i runga i te tuaka-x, te tuaka-y me te tuaka-z.
Mena ka mahi ngā kaha i te taha whakapae anake, ka whakamahia te whārite 1. Mena ka mahi ngā kaha i te taha poutū anake, ka whakamahia te whārite 2. Mena ka mahi ngā kaha i runga i te papa (e rua ngā ahu), ka whakamahia ngā whārite 1 me te 2. Mena ka mahi ngā kaha i roto i te wāhi (e toru ngā ahu), ka whakamahia ngā whārite 1, 2 me te 3.
He rahinga whārite te kaha, he nui, he ahunga hoki tōna. E pā ana ki ngā taunga Cartesian (tuaka x, y, me z) ā, e ai ki ngā ture, mēnā he rite te kaha ki te tuaka-x kino (ki te taha maui) he rite rānei te kaha ki te tuaka-y kino (ki raro), kāti he kino te kaha. I tetahi atu taha, mēnā he rite te kaha ki te tuaka-x pai (ki te taha matau) he rite rānei te kaha ki te tuaka-y pai (ki runga), kāti he pai te kaha.
Tauira 1.
Taitara:
F = te kaha kume, fg = te kaha waku, N = te kaha noa, w = te kaha ā-papatipu, m = te papatipu, g = te whakaterenga nā te kaha ā-papatipu.
Kei te okioki te mea nā te mea ko te tapeke o ngā kaha katoa e pā ana ki te mea he kore.
Arotakehia ia kaha e pā ana ki te mea.
Ngā kaha e mahi ana i te ahunga whakapae (tuaka-x):
Te kaha kume (F) me te kaha waku (fg) he rite te rahi engari he rerekē ngā ahunga. Ko te ahunga o te kaha kume kei te taha matau, kei te taha rānei o te tuaka-x pai (kaha pai), ko te ahunga o te kaha waku kei te taha maui, kei te taha rānei o te tuaka-x kino (tohu kino). Nā te mea he rite te rahi o ngā kaha e rua (e tohuhia ana e te roa o te pere) ā, he rerekē te ahunga o ngā kaha e rua, ko te tapeke o ēnei kaha e rua he rite ki te kore.
Ngā kaha e mahi ana i te ahunga poutū (tuaka-y):
I te wāhanga poutū (tuaka-y) kei reira te kaha ā-papa (w) me te kaha noa (N). Ko te ahunga o te kaha ā-papa he poutū ki te pokapū o Papatūānuku, i te ahunga rānei o te tuaka-y kino (kaha me te tohu kino), ko te kaha noa kei te ahunga o te tuaka-y pai (kaha me te tohu pai). He rite te rahi o ēnei kaha e rua engari he rerekē ō rāua ahunga, nō reira ka whakakorea e ngā kaha e rua tetahi i tetahi.
Kei te okioki te mea i te tauira i runga ake nei nā te mea ko te kaha hua e pā ana ki te mea, i te tuaka whakapae me te tuaka poutū, he ōrite ki te kore.
Tauira 2.
Kāore e whakaaturia te kaha ā-papa me ngā kaha noa e pā ana ki tēnei mea nā te mea ka whakakorea e rāua tetahi i tetahi. Mēnā ka pāngia ngā pito e rua o te mea e whakaaturia ana i te pikitia he kaha F, he ōrite te rahi o ngā kaha e rua engari he rerekē ngā ahunga. Ka noho pūmau tonu te mea?
Hei āwhina i a koe ki te mārama ki tēnei, whakatakotoria he pukapuka ki runga i tētahi tēpu. I te tīmatanga, kāore te pukapuka e nekeneke ana nā te mea he kore te kaha e puta mai ana i runga i te pukapuka. Muri iho, whakamahia he kaha ki ngā taha e rua o te pukapuka, e whakaaturia ana i te pikitia. Mena ka pāngia te pito o te pukapuka e te kaha me te ahunga e whakaaturia ana i te pikitia, he rite tonu tēnei ki te hurihanga i te pukapuka, ā, ko te tikanga ka huri te pukapuka. Ka huri te pukapuka nā te mea he āputa kaha kei te hua mai i te kaha F. Kei waenganui o te pukapuka te tuaka hurihanga. Mena kāore he kaha waku e pā ana ki te mea, ko te āputa kaha e puta mai ana ko te tapeke o ngā āputa kaha i puta mai i ngā kaha e rua F. Ko te ahunga hurihanga o te mea he taha matau kia kino ai ngā āputa kaha e rua.
Ko te tuarua o ngā āhuatanga mō te taurite o tētahi tinana mārō
I runga i te tauira 2 i runga ake nei, ka taea te whakatau mēnā ehara te tere o te kaha i puta mai i runga i tētahi mea i te kore (e kiia ana te mea he mea pakari), ka huri te mea.
Kia kore ai te mea e hurihuri (e kore e neke), me kore te kaha e puta mai ana. Ina kore te mea e hurihuri ana, kāore he whakaterenga koki. Nā te mea he kore te whakaterenga koki, ka huri te whārite i runga ake nei ki:
Akohia ngā tauira o ngā raruraru taurite matūriki me ngā tauira o ngā raruraru taurite tinana mārō.
