Ngā Pātai me te Kōrero mō ngā Āhuatanga Hurihuri
He kaupapa nui te hihiri hurihuri i roto i te ahupūngao, e pā ana ki te nekehanga o ngā mea hurihuri. He maha ngā ariā e pā ana ki tēnei āhuatanga, pērā i te wā o te korekore, te taipana, te ture tuarua o te hurihuri a Newton, te pūngao nekeneke hurihuri, me ētahi atu. Ka whakaatuhia e tēnei tuhinga ētahi raruraru me ngā matapakinga mō ngā hihiri hurihuri hei whakamārama i tō tātou māramatanga ki ēnei ariā.
1. Te Wā o te Āhuakore me te Taipana
Pātai:
Ka huri te mowhiti angiangi he taumaha \(2\) kg me te radius \(0.5\) m i tōna tuaka pokapū. Tātaihia te wā o te inertia o te mowhiti, ā, ki te whakamahia he taipana o \(6\) Nm ki runga, he aha te whakaterenga koki ka puta?
Kōrero:
Ko te wā o te inertia \(I\) mō tētahi mowhiti angiangi e karapoti ana i tōna tuaka pokapū ko:
\[ I = MR^2 \]
Me te \(M = 2\) kg me te \(R = 0.5\) m, kātahi:
\[ I = 2 \times (0.5)^2 \]
\[ I = 2 \whakareatia ki te 0.25 \]
\[ I = 0.5 \, \kuputuhi{kg} \, \kuputuhi{m}^2 \]
Ka taea te tatau i te whakaterenga koki (\(\alpha\)) mā te whakamahi i te taipana (\(\tau\)) me te wā o te korehau (\(I\)):
\[ \tau = I \alpha \]
\[ \ārepa = \frac{\tau}{I} \]
Me te \(\tau = 6\) Nm me te \(I = 0.5\) kg m²:
\[ \ārepa = \frac{6}{0.5} \]
\[ \alpha = 12 \, \text{rad/s}^2 \]
Nō reira, ko te wā o te inertia o te mowhiti he 0.5 kg m², ā, ko te whakaterenga koki ka puta ko 12 rad/s².
2. Pūngao Kinetic Hurihuri
Pātai:
Ka huri tētahi rango totoka, ko tōna taumaha he 4 kg, ā, ko tōna radius he 0.3 m, me te tere koki he 10 rad/s. Tātaihia te pūngao te nekenekehanga hurihuri o te rango.
Kōrero:
Ko te pūngao nekeneke hurihuri (\(K\)) ka hangaia penei:
\[ K = \frac{1}{2} I \omega^2 \]
Ko \(\omega\) te tere koki, ā, ko \(I\) te wā o te korekore. Mō te rango totoka (\(I = \frac{1}{2}MR^2\)):
\[ I = \frac{1}{2} \times 4 \times (0.3)^2 \]
\[ I = 2 \whakareatia ki te 0.09 \]
\[ I = 0.18 \, \kuputuhi{kg} \, \kuputuhi{m}^2 \]
Whakakapia ngā uara o \(I\) me \(\omega\) ki te whārite mō te pūngao nekeneke hurihuri:
\[ K = \frac{1}{2} \times 0.18 \times (10)^2 \]
\[ K = 0.09 \whakanuia ki te 100 \]
\[ K = 9 \, \text{J} \]
Nō reira, ko te pūngao nekeneke hurihuri o te rango totoka ko \(9\) Joules.
3. Te Ture Tuarua o te Hurihanga a Newton
Pātai:
Ko te radius o te wira porotaka he 0.4 m, ā, ko te moment of inertia he 0.8 kg m². Ka pāngia te taha o te wira he kaha 20 N. Tātaihia te whakaterenga koki o te wira.
Kōrero:
Tuatahi, ka tatauhia e mātou te taipana \(\tau\):
\[ \tau = F \ngā R \]
\[ \tau = 20 \whakareatia ki te 0.4 \]
\[ \tau = 8 \, \text{Nm} \]
Kātahi ka whakamahia Ngā ture a Newton tuarua mō te hurihanga:
\[ \tau = I \alpha \]
\[ \ārepa = \frac{\tau}{I} \]
Me \(\tau = 8 \, \text{Nm}\) me \(I = 0.8 \, \text{kg m}^2\):
\[ \ārepa = \frac{8}{0.8} \]
\[ \alpha = 10 \, \text{rad/s}^2 \]
Nō reira, ko te whakaterenga koki o te wira ko \(10\) rad/s².
4. Te Hononga i waenganui i te Pānga me te Whakamāoritanga
Pātai:
Ka hurihuri tetahi pōro he taumaha 1 kg me te radius 0.2 m i runga i te papa, kāore e paheke, he tere koki 5 rad/s. Tātaihia te tere rārangi o te pokapū o te taumaha o te pōro.
Kōrero:
Ko te whanaungatanga i waenga i te tere koki (\(\omega\)) me te tere rārangi (\(v\)) i roto i te nekehanga hurihuri me te kore e paheke ko:
\[ v = \omega R \]
Me te \(\omega = 5\) rad/s me te \(R = 0.2\) m:
\[ v = 5 \whakareatia ki te 0.2 \]
\[ v = 1 \, \text{m/s} \]
Nō reira, ko te tere rārangi o te pokapū papatipu o te pōro ko \(1\) m/s.
5. Te Huinga o te Pūngao Kinetic Whakawhiti me te Hurihanga
Pātai:
Ka hurihuri iho tētahi rango totoka, he taumaha 2 kg, ā, he radius 0.1 m te teitei, i tētahi papa piko he 3 m. Tātaihia te tere o te rango ina tae ki te pito o te papa piko.
Kōrero:
Ina hurihuri te rango me te kore e paheke, ka hurihia te pūngao pūmanawa ā-papa hei pūngao nekeneke whakawhiti me te pūngao nekeneke hurihuri. Ka taea te whakaatu i te pūngao katoa \(E\) penei:
\[ E = mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2 \]
I te whakaaro ki te \(I\) mō te rango totoka = \(\frac{1}{2}MR^2\), me te \(\omega = \frac{v}{R}\), ka pēnei te whārite:
\[ mgh = \frac{1}{2}mv^2 + \frac{1}{2}\left(\frac{1}{2}MR^2\right)\left(\frac{v^2}{R^2}\right) \]
\[ 2 \times 9.8 \times 3 = \frac{1}{2} \times 2 \times v^2 + \frac{1}{2} \left( \frac{1}{2} \times 2 \times v^2 \right) \]
\[ 58.8 = v^2 + \frac{1}{2}v^2 \]
\[ 58.8 = \frac{3}{2}v^2 \]
\[ v^2 = \frac{58.8 \times 2}{3} \]
\[ v^2 = 39.2 \]
\[ v = \sqrt{39.2} \]
\[ v \tata ki te 6.26 \, \kuputuhi{m/s} \]
Nō reira, ko te tere o te rango ina tae ki te pito o te papa whakarara he tata ki te \(6.26\) m/s.
Whakamutunga
Mā roto i ēnei raruraru, kua tūhuratia e mātou ētahi ariā nui o ngā whanaketanga hurihuri, tae atu ki te wā o te korekore, te taipana, te kaha nekeneke hurihuri, te ture tuarua o te hurihuri a Newton , me te whanaungatanga i waenga i te nekehanga hurihuri me te nekehanga whakawhiti. Mā te mārama pai ki ēnei ariā ka āwhina i a mātou ki te tātari me te whakaoti rapanga o te ao tūturu e pā ana ki te nekehanga hurihuri.
