Te Tātai Hurihuri: Te Whakamārama, te Tātai, me te Whakamahinga
Ko te hihiri hurihuri he peka o te hangarau e ako ana i te nekehanga hurihuri o ngā mea me ngā kaha e puta ai, e awe ai rānei i taua nekehanga. He rite tonu ki te hihiri whakawhiti, e ako ana i te nekehanga o ngā mea i roto i te rārangi tika. I roto i tēnei tuhinga, ka matapakihia e mātou te whakamāramatanga o te hihiri hurihuri, ngā tātai e pā ana ki te hihiri hurihuri, me ētahi tauira o ōna whakamahinga i roto i te oranga o ia rā me te hangarau.
Te Mārama ki ngā Āhuatanga Hurihuri
Ko te hihiri hurihuri te ako i te āhua o te hurihuri o ngā mea huri noa i tētahi pūwāhi, i tētahi tuaka rānei. Ko ngā ariā matua o ngā hihiri hurihuri ko te taipana, te wā o te korekore, te koki hurihuri, te tere koki, me te whakaterenga koki. He rite ēnei ki te kaha, te papatipu, te nekehanga, te tere, me te whakaterenga i roto i ngā hihiri whakawhiti.
Ko ētahi o ngā ariā matua o ngā whanaketanga hurihuri ko:
– Taipana (τ): Te kaha e puta ai te hurihanga. Koinei te āhua hurihanga o te kaha i roto i ngā nekehanga whakawhiti.
– Te Wā Ātete o te Āhuakore (I): Te ātete o te mea ki ngā huringa o tōna tere hurihuri, he rite ki te papatipu i roto i te nekehanga whakawhiti.
– Tere Koki (ω): Te tere o te huringa o te koki hurihuri, he rite ki te tere o te nekehanga whakawhiti.
– Te Whakaterenga Koki (α): Te tere o te huringa o te tere koki, he rite ki te whakaterenga i roto i te nekehanga whakawhiti.
Ngā Tātai Āhuatanga Hurihuri
1. Taipana (τ)
Ko te taipana he kaha hurihuri e pā ana ki tētahi mea, ā, ka huri ai. Ko te tātai mō te taipana ko:
\[ \tau = r \times F \sin(\theta) \]
Kei hea:
– Ko te taipana te \( \tau \),
– Ko te \( r \) te tawhiti mai i te pūwāhi hurihuri ki te wāhi e pāngia ai te kaha,
– Ko te kaha e whakamahia ana ko \( F \),
– Ko te koki i waenganui i te rārangi mahi a te kaha me te rārangi e hono ana i te pūwāhi hurihuri ki te pūwāhi pā o te kaha ko \( \theta \).
2. Te Wā o te Āhuakore (I)
Ko te wā o te korekore he ine i te ātete o tētahi mea ki ngā huringa o tōna tere hurihuri. Ko te tātai whānui mō te wā o te korekore ko:
\[ I = \tapeke m_i r_i^2 \]
Kei hea:
– Ko te wā o te korekore o te \( I \)
– Ko te papatipu o ngā huānga iti o te mea ko \( m_i \),
– Ko te \( r_i \) te tawhiti o te huānga iti mai i te tuaka hurihuri.
Mō ngā mea he āhua motuhake, he tātai motuhake tō te wā o te korehau, pēnei i:
– Ka huri te tokotoko angiangi i te pito: \( I = \frac{1}{3} mL^2 \)
– Ka huri te rango totoka i waenganui: \( I = \frac{1}{2} mR^2 \)
– Ka huri te pōro totoka i waenganui: \( I = \frac{2}{5} mR^2 \)
3. Whārite Nekehanga Hurihuri
He rite te whārite o te nekehanga hurihuri ki te Ture Tuarua a Newton mō te nekehanga whakawhiti, engari e pā ana ki te hurihanga:
\[ \tau = I \alpha \]
Kei hea:
– Ko te taipana te \( \tau \),
– Ko te wā o te korekore o te \( I \)
– Ko te whakaterenga koki ko \( \alpha \).
4. Pūngao Kinetic Hurihuri
Ko te pūngao nekeneke hurihuri ko te pūngao kei roto i tētahi mea hurihuri. Ko te tātai mō te pūngao nekeneke hurihuri ko:
\[ E_k = \frac{1}{2} I \omega^2 \]
Kei hea:
– Ko te pūngao nekeneke hurihuri a \( E_k \),
– Ko te wā o te korekore o te \( I \)
– Ko te tere koki te \( \omega \).
5. Te Momentum Koki (L)
Ko te nekehanga koki te rite o te hurihanga o te nekehanga raina. Ko te tātai mō te nekehanga koki ko:
\[ L = I \omega \]
Kei hea:
– Ko te nekehanga koki te \( L \),
– Ko te wā o te korekore o te \( I \)
– Ko te tere koki te \( \omega \).
6. Ture Tiaki i te Momentum Koki
E ai ki te ture tiaki i te nekehanga koki, ki te kore he taipana o waho e pā ki tētahi pūnaha, ka noho pūmau tonu te nekehanga koki o te pūnaha. He rite tēnei ki te ture tiaki i te nekehanga rārangi i roto i ngā whanaketanga whakawhiti.
\[ L_{\text{start}} = L_{\text{end}} \]
\[ I_{\text{start}} \omega_{\text{start}} = I_{\text{end}} \omega_{\text{end}} \]
Taupānga Hihiri Hurihanga
1. Mīra Hau
Ka whakamahia e ngā mira hau ngā mātāpono o te hihiri hurihuri hei huri i te pūngao hau hei pūngao miihini. Ka huri ngā mata o te mira hau nā te taipana e puta mai ana i te hau e pā ana ki a rātou. Ko te kaha o te inertia o ngā mata e whakatau ana i te tere me te neke.
2. Wīrokarapu
He taputapu te gyroscope e whakamahi ana i ngā mātāpono o te hihiri hurihuri hei pupuri i te aronga. Mā te kaha o te inertia o ngā wira hurihuri tere o te gyroscope ka pumau, ka mau tonu tōna tūranga ahakoa ngā raruraru o waho. E whakamahia ana i roto i ngā momo tono, tae atu ki te whakatere waka rererangi me te whakatere waea atamai.
3. Ngā Waka Motuka
I roto i ngā waka, ka huri ngā wira hei pana i te waka. Ka tukuna te taipana e hangaia ana e te miihini ki ngā wira mā te tuku hiko. He mea nui anō hoki ngā mahi hurihuri i roto i te hoahoa miihini me te pūnaha whakatārewatanga, ina whai wāhi nui te wā o te inertia ki te mahi me te whai huatanga o te waka.
4. Ngā Kēmu Orimipia
I roto i te maha o ngā hākinakina, he mea nui te hihiri hurihuri. Hei tauira, i roto i te mahi whakapakari tinana, ka mahi ngā kaitākaro i ngā takahurihuri me ngā huripokitanga, e uru ana ki te taipana, te ine o te koretake, me te nekehanga koki. Me whakarerekē e ngā kaitākaro te tūnga o ō rātou tinana kia rerekē ai te ine o te koretake me te whakahaere i ā rātou nekehanga i te wā e takahurihuri ana.
5. Teihana Rererangi
Ka whakamahia e ngā waka hurihuri ngā mātāpono o te hihiri hurihuri i roto i ā rātou hoahoa porowhita me te hurihanga. Ka pā te taipana me te wā o te korehau ki te tere me te hurihuri o te waka hurihuri huri noa i te ara. Mā te hoahoa tika ka maeneene, ka haumaru hoki te ekenga waka hurihuri.
Tauira Tātaitanga Āhuatanga Hurihuri
Tauira 1: Te Tātai i te Taipana
Me kī, ka huri tētahi wira he 0.5 mita te whānui ina pāngia he kaha 10 Newton ki tētahi pūwāhi i te taha o te wira, e poutū ana ki te whānui. He aha te taipana ka puta?
Mā te whakamahi i te tātai taipana:
\[ \tau = r \ngā F \]
\[ \tau = 0.5 \, \kuputuhi{m} \whakanuia kia 10 \, \kuputuhi{N} \]
\[ \tau = 5 \, \text{Nm} \]
Nō reira, ko te taipana i puta he 5 mita Newton.
Tauira 2: Te Tātai i te Wā Āhuakore
Me kī, he tokotoko angiangi e 2 kg te taumaha, ā, 1 mita te roa e hurihuri ana i tōna pito. He aha te tere o te inertia o te tokotoko?
Mā te whakamahi i te tātai o te wā ātete mō tētahi tokotoko angiangi e hurihuri ana i tōna pito:
\[ I = \frac{1}{3} mL^2 \]
\[ I = \frac{1}{3} \times 2 \, \text{kg} \times (1 \, \text{m})^2 \]
\[ I = \frac{2}{3} \, \text{kg} \cdot \text{m}^2 \]
Nō reira, ko te wā o te korekore o te tokotoko ko \(\frac{2}{3} \, \text{kg} \cdot \text{m}^2\).
Tauira 3: Te Tātai i te Pūngao Kinetic Hurihanga
Me kī, he rango totoka he 5 kg te taumaha, ā, he 0.2 mita te whānui e hurihuri ana i te tere koki o te 10 rad/s. He aha te pūngao nekeneke hurihuri o te rango?
Mā te whakamahi i te tātai pūngao nekeneke hurihuri:
\[ E_k = \frac{1}{2} I \omega^2 \]
Tuatahi, ka tatauhia e tātou te wā o te korehau mō tētahi rango totoka e hurihuri ana i waenganui:
\[ I = \frac{1}{2} mR^2 \]
\[ I = \frac{1}{2} \times 5 \, \text{kg} \times (0.2 \, \text{m})^2 \]
\[ I = 0.1 \, \text{kg} \cdot \text{m}^2 \]
Kātahi ka whakamahia tēnei uara hei tatau i te pūngao nekeneke hurihuri:
\[ E_k = \frac{1}{2} \times 0.1 \, \text{kg} \cdot \text{m}^2 \times (10 \, \text{rad/s})^2 \]
\[ E_k = \frac{1}{2} \times 0
