Ajụjụ na Mkparịta ụka gbasara Mgbanwe Mgbanwe
Mgbanwe ntụgharị bụ isiokwu dị mkpa na fiziki, na-eleba anya na mmegharị nke ihe na-agbagharị agbagharị. Ihe a na-eme gụnyere ọtụtụ echiche, dịka oge nke inertia, torque, iwu nke abụọ nke ntụgharị nke Newton, ike ntụgharị nke ntụgharị, na ihe ndị ọzọ. Isiokwu a ga-egosi ọtụtụ nsogbu na mkparịta ụka gbasara mgbanwe ntụgharị iji mee ka nghọta anyị banyere echiche ndị a doo anya.
1. Oge nke Inertia na Torque
Ajụjụ:
Mgbaaka dị gịrịgịrị nke ibu \(2\) kg na radius \(0.5\) m na-agbagharị gburugburu axis etiti ya. Gbakọọ oge nke inertia nke mgbanaka ahụ, ọ bụrụkwa na etinyere ike nke \(6\) Nm na ya, gịnị bụ ọsọ nkuku na-esi na ya apụta?
Azịza:
Oge nke inertia \(I\) maka mgbanaka dị gịrịgịrị gburugburu axis etiti ya bụ:
\[ I = MR^2 \]
Site na \(M = 2\) kg na \(R = 0.5\) m, mgbe ahụ:
\[ I = ugboro abụọ (0.5)^2 \]
\[ I = ugboro abụọ 0.25 \]
\[ I = 0.5 \, \ederede{kg} \, \ederede{m}^2 \]
Enwere ike ịgbakọ osooso angular (\(\alpha\)) site na iji torque (\(\tau\)) na oge inertia (\(I\)):
\[ \tau = I \alpha \]
\[ \alpha = \frac{\tau}{I} \]
Na \(\tau = 6\) Nm na \(I = 0.5\) kg m²:
\[ \alpha = \frac{6}{0.5} \]
\[ \alpha = 12 \, \ederede{rad/s}^2 \]
Ya mere, oge nke inertia nke mgbanaka ahụ bụ \(0.5\) kg m² na osooso akụkụ nke na-esi na ya apụta bụ \(12\) rad/s².
2. Ike Kinetic nke na-agbagharị agbagharị
Ajụjụ:
Sịlinda siri ike nke nwere oke ibu nke kilogram (4) na radius nke mita (0.3) na-agbagharị na ọsọ akụkụ nke rad/s (10) nke silinda. Gbakọọ ike kinetic nke silinda ahụ.
Azịza:
A na-ahazi ike kinetic nke ntụgharị (\(K\)) dị ka:
\[ K = \frac{1}{2} I \omega^2 \]
Ebe \(\omega\) bụ ọsọ angular, na \(I\) bụ oge inertia. Maka silinda siri ike (\(I = \frac{1}{2}MR^2\)):
\[ I = \frac{1}{2} \ugboro anọ \ugboro (0.3)^2 \]
\[ I = ugboro abụọ 0.09 \]
\[ I = 0.18 \, \ederede{kg} \, \ederede{m}^2 \]
Tinye uru nke \(I\) na \(\omega\) n'ime usoro maka ike kinetic rotational:
\[ K = \frac{1}{2} \ugboro 0.18 \ugboro (10)^2 \]
\[ K = ugboro anọ 100 \]
\[ K = 9 \, \ederede{J} \]
Ya mere, ike kinetic nke silinda siri ike bụ joules.
3. Iwu nke Abụọ nke Mgbanwe nke Newton
Ajụjụ:
Wheel pulley nwere radius nke \(0.4\) m na oge nke inertia nke \(0.8\) kg m². A na-etinye ike \(F\) nke \(20\) N n'ụzọ tangential na nsọtụ wiil ahụ. Gbakọọ ọsọ nkuku nke wiil ahụ.
Azịza:
Nke mbụ, anyị na-agbakọ ike \(\tau\):
\[ \tau = F \times R \]
\[ \tau = 20 \ugboro 0.4 \]
\[ \tau = 8 \, \ederede{Nm} \]
Jiri iwu nke abụọ nke Newton mee ntụgharị:
\[ \tau = I \alpha \]
\[ \alpha = \frac{\tau}{I} \]
Na \(\tau = 8 \, \text{Nm}\) na \(I = 0.8 \, \text{kg m}^2\):
\[ \alpha = \frac{8}{0.8} \]
\[ \alpha = 10 \, \ederede{rad/s}^2 \]
Ya mere, osooso akụkụ nke wiil ahụ bụ \(10\) rad/s².
4. Mmekọrịta dị n'etiti Tangent na Nsụgharị
Ajụjụ:
Bọọlụ nwere oke ibu nke kilogram (1) na radius nke mita (0.2) na-atụgharị n'enweghị ịmịda n'ala nwere ọsọ nkuku nke rad/s. Gbakọọ ọsọ kwụ ọtọ nke etiti oke nke bọọlụ ahụ.
Azịza:
Mmekọrịta dị n'etiti ọsọ angular (\(\omega\)) na ọsọ linear (\(v\)) n'ime mmegharị mpịakọta na-enweghị ịmịda bụ:
\[ v = \omega R \]
Na \(\omega = 5\) rad/s na \(R = 0.2\) m:
\[ v = 5 \ugboro 0.2 \]
\[ v = 1 \, \ederede{m/s} \]
Ya mere, ọsọ kwụ ọtọ nke etiti oke nke bọọlụ ahụ bụ \(1\) m/s.
5. Njikọta nke Ike Kinetic Ntụgharị na nke Rotary
Ajụjụ:
Sịlinda siri ike nke nwere ibu nke kilogram (2) na radius nke mita (0.1) na-agbada n'elu elu dị elu nke mita (3) gbakọọ ọsọ nke silinda ahụ mgbe ọ ruru ala nke oghere dị elu.
Azịza:
Mgbe silinda ahụ na-atụgharị n'enweghị mmịpụ, ike ike ndọda ahụ na-agbanwe ka ọ bụrụ ike ntụgharị uche na ike ntụgharị uche. Enwere ike ịkọwa ike niile dị ka:
\[ E = mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2 \]
N'ịtụle \(I\) maka silinda siri ike = \(\frac{1}{2}MR^2\), na \(\omega = \frac{v}{R}\), nha nhata ahụ ga-aghọ:
\[ mgh = \frac{1}{2}mv^2 + \frac{1}{2}\left(\frac{1}{2}MR^2\right)\left(\frac{v^2}{R^2}\right) \]
\[ 2 \ugboro 9.8 \ugboro 3 = \frac{1}{2} \ugboro 2 \ugboro v^2 + \frac{1}{2} \left( \frac{1}{2} \ugboro 2 \ugboro v^2 \nri) \]
\[ 58.8 = v^2 + \frac{1}{2}v^2 \]
\[ 58.8 = \frac{3}{2}v^2 \]
\[ v^2 = \frac{58.8 \ugboro 2}{3} \]
\[ v^2 = 39.2 \]
\[ v = \sqrt{39.2} \]
\[ v \ihe dịka 6.26 \, \text{m/s} \]
Ya mere, ọsọ nke silinda mgbe ọ rutere ala nke ụgbọelu ahụ gbagọrọ agbagọ bụ ihe dị ka m (6.26) m/s.
Mmechi
Site na nsogbu ndị a, anyị enyochaala ọtụtụ echiche dị mkpa na mgbanwe ntụgharị, gụnyere oge nke inertia, torque, ike kinetic rotation, iwu nke abụọ nke ntụgharị nke Newton, na mmekọrịta dị n'etiti mmegharị ntụgharị na ntụgharị. Nghọta dị mma nke echiche ndị a ga-enyere anyị aka inyocha ma dozie nsogbu ndị dị n'ụwa n'ezie metụtara mmegharị ntụgharị.
