Ngā Mahi Wetereo: Ngā Ariā me ngā Whakamahinga i roto i te Pāngarau me ngā Pūtaiao Whaihua
Pendahuluan
Ko te tikanga, he mea pāngarau te whārite, he rahi, he ahunga hoki. He maha ngā whakamahinga o ngā whārite hei tohu i ngā āhuatanga rerekē o te pūtaiao me te hangarau, tae atu ki te ahupūngao, te hangarau, me te pāngarau. I roto i tēnei tuhinga, ka matapakihia e tātou te ariā taketake o ngā whārite, ngā mahi ka taea te mahi mā rātou, me te whakamahinga o ēnei mahi i roto i ngā mara rerekē.
Te Mārama ki ngā Wētere
I roto i ngā kupu māmā noa, ka taea te whakaatu i tētahi whārite hei pere i roto i te wāhi rua-ahu, toru-ahu rānei. He roa tēnei pere e rite ana ki te rahi o te whārite, me te ahunga e tohu ana i tētahi ahunga. Ko te tuhipoka noa mō tētahi whārite he reta iti me te pere i runga ake, he reta matotoru rānei, pērā i te \(\vec{v}\) me te v rānei. Ka taea te whakaatu i ngā whārite i roto i ngā wāhanga, hei tauira, i roto i ngā āhuatanga e rua, ka taea te whakaatu i te whārite \(\vec{v}\) hei \(\vec{v} = v_x \hat{i} + v_y \hat{j}\), ko \(v_x\) me \(v_y\) ngā wāhanga tauine o te whārite i te taha o ngā tuaka-X me te-Y, ā, ko \(\hat{i}\) me \(\hat{j}\) ngā whārite wae i te taha o ngā tuaka-X me te-Y.
Ngā Mahi Taketake i runga i ngā Wetere
Tāpiritanga Wetere
Ko te tāpiritanga whāka tētahi o ngā mahi taketake e whakamahia whānuitia ana. I roto i ngā āhuatanga e rua, mēnā he whāka e rua ā tātou \(\vec{a}\) me \(\vec{b}\), ia whāka he wāhanga \(\vec{a} = a_x \hat{i} + a_y \hat{j}\) me \(\vec{b} = b_x \hat{i} + b_y \hat{j}\), ko te tapeke o ēnei whāka e rua ko:
\[
\vec{a} + \vec{b} = (a_x + b_x) \hat{i} + (a_y + b_y) \hat{j}
\]
I runga i te āhuahanga, ka taea te whakaahua i te tāpiritanga whārite mā te tikanga "upoko-ki-te-hiku", e whakanohoia ai te hiku o te whārite tuarua ki te pito o te upoko o te whārite tuatahi, ā, ko te whārite ka puta he pere e hono ana i te hiku o te whārite tuatahi ki te upoko o te whārite tuarua.
Te Tangohanga Wetereo
Ka mahia te tangohanga whāka mā te tāpiri i ngā whāka rerekē. Hei tauira, mō ngā whāka \(\vec{a}\) me \(\vec{b}\), ko te tangohanga \(\vec{a} – \vec{b}\) he rite ki \(\vec{a} + (-\vec{b})\), ko \(-\vec{b}\) te whāka e anga kē ana \(\vec{b}\). I roto i te kupu wāhanga, ko te whakamaoritanga o tēnei ko:
\[
\vec{a} – \vec{b} = (a_x – b_x) \hat{i} + (a_y – b_y) \hat{j}
\]
Whakareatanga Tauine
Ko te whakarea tauine te mahi whakarea i tētahi whārite ki tētahi tauine (he tau tūturu). Hei tauira, mēnā he whārite a \(\vec{v}\) ā, he tauine a \(k\), ko \(k \vec{v}\) he whārite hou me ngā wāhanga \(k v_x \hat{i} + k v_y \hat{j}\). Ka whakarerekē tēnei whakarea i te roa (te rahi) o te whārite me te kore e whakarerekē i tōna ahunga mēnā kāore a \(k\) i te kino, ā, i roto i tēnā wā ka hurihia tōna ahunga.
Hua Ira
Ko te hua ira he mahi i waenganui i ngā whārite e rua e hua ake ai he hua tauine. Mena he rua ā tātou whārite \(\vec{a}\) me \(\vec{b}\), ko tā rāua hua ira ko:
\[
\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y
\]
I roto i ngā āhuatanga e toru, ka uru te wāhanga z ki te tātai, ā, ka noho ko:
\[
\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y + a_z b_z
\]
He maha ngā wā ka whakamahia te hua ira hei tatau i te koki i waenganui i ngā whārite e rua, hei whakatau rānei mēnā he poutū (he poutū) ngā whārite e rua.
Hua Whakawhiti
Ko te hua whakawhiti he mahi kua tautuhia i roto i te wāhi toru-ahu anake, ā, ka puta he whārite anō. Mena he whārite e rua a \(\vec{a}\) me \(\vec{b}\) i roto i te wāhi toru-ahu, ko tā rāua hua whakawhiti ko:
\[
\vec{a} \times \vec{b} = (a_y b_z – a_z b_y) \hat{i} + (a_z b_x – a_x b_z) \hat{j} + (a_x b_y – a_y b_x) \hat{k}
\]
Ko te whārite e puta mai ana i te hua whakawhiti he poutū ki ngā whārite taketake e rua, ā, ko tōna ahunga ka whakatauhia e te ture ringa-matau.
Ngā Taupānga Mahi Wetereo
Ahupūngao me te Hangarau
I roto i te ahupūngao, ka whakamahia ngā whārite hei tohu i ngā rahinga rerekē, pērā i te tere, te whakaterenga, me te kaha. He mea noa te tāpiri me te tango i ngā whārite i roto i te tātaritanga o te nekehanga me te hihiri. Hei tauira, ko te kaha katoa e pā ana ki tētahi mea ko te tapeke whārite o ngā kaha takitahi katoa e pā ana ki taua mea.
E whakamahia ana te hua ira i roto i te hikohiko hei tatau i te mahi i mahia e te kaha, ko te hua whakawhiti ia e whakamahia ana i roto i te miihini hei tatau i te ia o te kaha, i te taipana rānei.
Whakairoiro Rorohiko
I roto i ngā whakairoiro rorohiko, he mea nui ngā whārite mō ngā panonitanga āhuahanga, pērā i te hurihanga, te tauine, me te whakawhiti i ngā mea. He maha ngā wā ka whakamahia ngā matihiko panonitanga me ngā mahi whārite hei whakarerekē i te tūranga me te aronga o ngā mea i roto i te wāhi toru-ahu.
Tātari Raraunga me te Ako Mīhini
I roto i te tātari raraunga me te ako mīhini, ka whakamahia ngā whārite hei tohu raraunga. Ko ngā whārite āhuatanga he whakaaturanga tau o ngā raraunga e āhei ai ngā rauropi ki te tautuhi i ngā tauira me te matapae. Ko ngā mahi whārite, pērā i te tāpiri me te whakarea tauine, ka whakamahia pinepinetia i roto i ngā rauropi arotau me ngā tikanga ako hōhonu.
Te Whakatauira Pūtea
I roto i te ōhanga me te pūtea, ka whakamahia ngā whārite i roto i te whakatauira putea hei tohu i ngā huinga rawa rerekē. Ka āwhina ngā mahi whārite ki te tatau i te mōrearea me te hokinga mai o te putea, me te whakanui ake i ngā rawa hei arotau i ngā hokinga mai me te whakaiti i te mōrearea.
Whakamutunga
He mea nui te mahi a ngā mahi whārite i roto i ngā momo mara o te pūtaiao me te hangarau. He taputapu kaha ēnei mō te tātari me te whakatauira i ngā āhuatanga e pā ana ki ngā rahinga me te ahunga. Mā te mārama ki ngā mahi taketake pēnei i te tāpiri, te tango, te whakarea tauine, te hua ira, me te hua whakawhiti, ka taea e tātou te whakamahi i ēnei ariā ki te whānuitanga o ngā tono mahi, mai i te ahupūngao ki te ako mīhini. Ehara i te mea ko ngā whārite anake he taputapu pāngarau engari he piriti hoki e hono ana i te ariā ki ngā tono o te ao tūturu, e āhei ai tātou ki te mārama ake i te ao me te whakatau whakatau pai ake i runga i te tātari tupato.
