Mibvunzo neKukurukurirana kweRotational Dynamics
Kutenderera kwesimba inyaya inokosha mufizikisi, inobata nekufamba kwezvinhu zvinotenderera. Chiitiko ichi chinosanganisira pfungwa dzakawanda, dzakadai se moment of inertia, torque, mutemo wechipiri waNewton wekutenderera, rotational kinetic energy, nezvimwewo. Chinyorwa chino chichapa matambudziko akati wandei nehurukuro pamusoro pekuchinja kwesimba kuti tijekese kunzwisisa kwedu pfungwa idzi.
1. Nguva yeKusagadzikana uye Kusimba
Mubvunzo:
Mhete yakatetepa ine huremu \(2\) kg uye radius \(0.5\) m inotenderera pakati pe axis yayo. Verenga nguva yekusashanda kwemhete, uye kana torque ye \(6\) Nm ikaiswa pairi, chii chinokonzera kumhanyisa kwe angular?
Kukurukurirana:
Nguva yekusaita chinhu (inertia) yerin'i yakatetepa yakatenderedza axis yayo yepakati ndeiyi:
\[ Ini = MR^2 \]
Ne \(M = 2\) kg uye \(R = 0.5\) m, ipapo:
\[I = 2 \nguva (0.5)^2 \]
\[I = 2 \kawa 0.25 \]
\[ I = 0.5 \, \text{kg} \, \text{m}^2 \]
Kukurumidza kweAngular (\(\alpha\)) kunogona kuverengerwa uchishandisa torque (\(\tau\)) uye nguva yekusagadzikana (\(I\)):
\[ \tau = I \alpha \]
\[ \alpha = \frac{\tau}{I} \]
Ne \(\tau = 6\) Nm uye \(I = 0.5\) kg m²:
\[ \alpha = \frac{6}{0.5} \]
\[ \alpha = 12 \, \text{rad/s}^2 \]
Saka, nguva yekusashanda kweringi ndeye \(0.5\) kg m² uye kumhanyisa kwekona kunoitika ndeye \(12\) rad/s².
2. Simba reKinetic rinotenderera
Mubvunzo:
Sirinda yakasimba ine huremu hwe \(4\) kg uye radius ye \(0.3\) m inotenderera ne angular velocity ye \(10\) rad/s. Verenga simba re rotational kinetic resirinda.
Kukurukurirana:
Simba rekinetic rinotenderera (\(K\)) rakagadzirwa seizvi:
\[ K = \frac{1}{2} I \omega^2 \]
Apo \(\omega\) iri angular velocity, uye \(I\) iri nguva yekusashanda. Kune silinda yakasimba (\(I = \frac{1}{2}MR^2\)):
\[ I = \frac{1}{2} \kawa 4 \kawa (0.3)^2 \]
\[I = 2 \kawa 0.09 \]
\[ I = 0.18 \, \text{kg} \, \text{m}^2 \]
Isa kukosha kwe \(I\) uye \(\omega\) mu equation ye rotational kinetic energy:
\[ K = \frac{1}{2} \times 0.18 \times (10)^2 \]
\[ K = 0.09 \kawa 100 \]
\[ K = 9 \, \mashoko{J} \]
Saka, simba rekufamba kwesimba resilinda yakasimba ndi \(9\) Joules.
3. Mutemo wechipiri waNewton wekutenderera
Mubvunzo:
Vhiri repulley rine radius ye \(0.4\) m uye nguva yekusashanda kwe \(0.8\) kg m². Simba \(F\) re \(20\) N rinoiswa tangentially kumucheto kwevhiri. Verenga kumhanyisa kwevhiri kwekona.
Kukurukurirana:
Kutanga, tinoverenga torque \(\tau\):
\[ \tau = F \times R \]
\[ \tau = 20 \kawa 0.4 \]
\[ \tau = 8 \, \text{Nm} \]
Wobva washandisa mutemo wechipiri waNewton pakutenderera:
\[ \tau = I \alpha \]
\[ \alpha = \frac{\tau}{I} \]
Ne \(\tau = 8 \, \text{Nm}\) uye \(I = 0.8 \, \text{kg m}^2\):
\[ \alpha = \frac{8}{0.8} \]
\[ \alpha = 10 \, \text{rad/s}^2 \]
Saka, kumhanyisa kwevhiri kwekona ndeye \(10\) rad/s².
4. Hukama huripo pakati peTangent neTranslation
Mubvunzo:
Bhora rine huremu hwe \(1\) kg uye radius ye \(0.2\) m rinotenderera risingatsvedzeri pasi rine angular velocity ye \(5\) rad/s. Verenga linear velocity yepakati pehuremu hwebhora.
Kukurukurirana:
Hukama huripo pakati pe angular velocity (\(\omega\)) uye linear velocity (\(v\)) mu rolling motion pasina kutsvedza ndehwekuti:
\[ v = \omega R \]
Ne \(\omega = 5\) rad/s uye \(R = 0.2\) m:
\[ v = 5 \kawa 0.2 \]
\[ v = 1 \, \text{m/s} \]
Saka, kumhanya kwepakati pehukuru hwebhora i \(1\) m/s.
5. Musanganiswa weSimba reKushandura uye reKutenderera reKinetic
Mubvunzo:
Sirinda yakasimba ine huremu hwe \(2\) kg uye radius ye \(0.1\) m inokotama pasi pakakwirira yakatsamira \(3\) m. Verenga kumhanya kwesirinda painosvika pasi pepuranga yakatsamira.
Kukurukurirana:
Kana silinda ikatenderera isingatsvedze, simba regiravhiti rinoshandurwa kuita simba rekinetic rinoshandura uye simba rekinetic rinotenderera. Simba rose \(E\) rinogona kuratidzwa seizvi:
\[ E = mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2 \]
Tichifunga nezve \(I\) silinda yakasimba = \(\frac{1}{2}MR^2\), uye \(\omega = \frac{v}{R}\), equation inova:
\[ mgh = \frac{1}{2}mv^2 + \frac{1}{2}\left(\frac{1}{2}MR^2\right)\left(\frac{v^2}{R^2}\right) \]
\[ 2 \nguva 9.8 \nguva 3 = \frac{1}{2} \nguva 2 \nguva v^2 + \frac{1}{2} \left( \frac{1}{2} \nguva 2 \nguva v^2 \kurudyi) \]
\[ 58.8 = v^2 + \frac{1}{2}v^2 \]
\[ 58.8 = \frac{3}{2}v^2 \]
\[ v^2 = \frac{58.8 \kawa 2}{3} \]
\[ v^2 = 39.2 \]
\[ v = \sqrt{39.2} \]
\[ v \inenge 6.26 \, \text{m/s} \]
Saka, kumhanya kwesilinda painosvika pasi penzvimbo yakatsveyama inenge iri pa (6.26) m/s.
Mhedziso
Kuburikidza nematambudziko aya, takaongorora pfungwa dzinoverengeka dzakakosha mukuchinjana kwesimba, kusanganisira nguva yekusagadzikana, torque, simba rekutenderera rinotenderera, mutemo wechipiri waNewton wekutenderera, uye hukama huripo pakati pekufamba kwekutenderera nekushandura. Kunzwisisa kwakanaka kwepfungwa idzi kuchatibatsira kuongorora nekugadzirisa matambudziko chaiwo anosanganisira kufamba kwekutenderera.
