Usoro Momentum Angular
Pendahuluan
Momentum angular bụ echiche dị mkpa na fiziki metụtara mmegharị ntụgharị nke ihe. Echiche a yiri momentum ahịrị na mmegharị ntụgharị. Momentum angular na-arụ ọrụ dị mkpa n'ọtụtụ ngalaba fiziki, site na mekaniki oge gboo ruo na mekaniki quantum. Isiokwu a ga-atụle nkọwa nke momentum angular, usoro ndị metụtara ya, ojiji na ndụ kwa ụbọchị, na ihe atụ iji mee ka nghọta dịkwuo omimi.
Nkọwa nke Angular Momentum
Momentum angular bụ ọnụọgụ vektọ nke na-akọwa etu ihe si aga n'ihu na-agbagharị gburugburu isi ihe ma ọ bụ axis. Momentum angular (\(\vec{L}\)) dabere na isi ihe abụọ: momentum linear (\(\vec{p}\)) na ọnọdụ relative (\(\vec{r}\)) nke ebe ntụaka. A na-akọwa momentum angular dị ka:
\[ \vec{L} = \vec{r} \times \vec{p} \]
Ebe:
– \(\vec{L}\) bụ ọsọ nkuku.
– \(\vec{r}\) bụ vektọ ọnọdụ metụtara ebe ntụaka.
– \(\vec{p}\) bụ momentum linear (\(\vec{p} = m \vec{v}\), ebe \(m\) bụ oke na \(\vec{v}\) bụ ọsọ).
– \(\times\) na-anọchite anya ngwaahịa obe n'etiti vektọ abụọ.
Usoro Momentum Angular
Maka ahụ siri ike nke na-agbagharị na ọsọ angular (\(\omega\)) gburugburu axis a kapịrị ọnụ, enwere ike ịkọwa momentum angular (\(L\)) dị ka:
\[ L = I \omega \]
Ebe:
– \(L\) bụ ọsọ nkuku.
– \(I\) bụ oge nke inertia nke ihe ahụ gbasara axis nke ntụgharị.
– \(\omega\) bụ ọsọ akụkụ.
Oge nke Inertia
Oge nke inertia (\(I\)) bụ ihe atụ nke iguzogide ihe na mgbanwe na mmegharị ntụgharị ya. Oge nke inertia dabere na nkesa nke oke ihe ahụ ma e jiri ya tụnyere axis nke ntụgharị. Maka ihe siri ike, enwere ike ịgbakọ oge inertia site na iji usoro:
\[ I = \sum m_i r_i^2 \]
Ebe:
– \(m_i\) bụ oke nke ihe dị n'ime ya.
– \(r_i\) bụ anya nke ihe dị n'ime ya site na axis nke ntụgharị.
Maka ihe dị mfe, oge nke inertia nwere usoro nke ya. Ụfọdụ ihe atụ bụ:
– Silinda oghere: \(I = mr^2\)
– Silinda zuru ezu: \(I = \frac{1}{2} mr^2\)
– Gburugburu zuru ezu: \(I = \frac{2}{5} mr^2\)
Ụkpụrụ nke Nchekwa nke Angular Momentum
Ụkpụrụ nke nchekwa nke angular momentum na-ekwu na ọ bụrụ na ọ dịghị ike mpụga na-arụ ọrụ na sistemụ, mkpokọta angular momentum nke sistemụ ahụ ga-anọgide na-adịgide adịgide. Nke a pụtara:
\[ \vec{L}_{start} = \vec{L}_{njedebe} \]
ma ọ bụ
\[ I_{mmalite} \omega_{mmalite} = I_{mkpeazụ} \omega_{mkpeazụ} \]
Ụkpụrụ a dị oke mkpa n'ọtụtụ ihe dị iche iche a na-ahụ anya, dịka mmegharị nke mbara ala, pirouettes nke ndị na-agba egwú, na nkwụsi ike nke gyroscopes.
Itinye Angular Momentum n'ọrụ na Ndụ Kwa Ụbọchị
Mmegharị mbara ala
Mbara ala dị na sistemụ anyanwụ na-agba gburugburu anyanwụ ma nwee ike ịdịgide n'akụkụ. Mgbanwe dị nta na ike angular nwere ike ibute mgbanwe na gburugburu mbara ala. Nke a bụ n'ihi na ike ndọda na-arụ ọrụ na mbara ala anaghị emepụta ike net, na-eme ka ike angular na-aga n'ihu.
Onye na-agba egwu ballet Pirouette
Onye na-agba egwu ballet nwere ike ime ka ọsọ ntụgharị ya dịkwuo elu site n'ịdọkpụ aka na ụkwụ ya nso n'ahụ ya. Nke a bụ n'ihi na oge nke inertia na-ebelata, yabụ iji nọgide na-enwe ike ịgbanwe agbanwe mgbe niile, ọsọ nke nkuku ga-amụba.
Gyroscope
Gyroscope bụ ngwaọrụ nke na-eji ụkpụrụ nke angular momentum iji nọgide na-enwe nkwụsi ike. A na-eji Gyroscopes eme ihe n'ọtụtụ ụzọ dị iche iche, dịka ụgbọelu, ụgbọ mmiri, na ekwentị mkpanaaka.
Ihe atụ ajụjụ na azịza
Ajụjụ Ihe Nlereanya nke 1
Diski nwere ibu nke kilogram abụọ na radius nke mita 0,5 na-agbagharị na ọsọ akụkụ nke 10 rad/s. Gbakọọ ọsọ akụkụ nke diski ahụ.
Ngwọta:
A na-enye oge nke inertia nke diski (\(I\)) site na usoro:
\[ I = \frac{1}{2} mr^2 \]
Tinye ụkpụrụ enyere:
\[ I = \frac{1}{2} \oge 2 \, \text{kg} \oge (0,5 \, \text{m})^2 = \frac{1}{2} \oge 2 \oge 0,25 = 0,25 \, \text{kg} \cdot \text{m}^2 \]
Momentum angular (\(L\)) bụ:
\[ L = I \omega = 0,25 \, \text{kg} \cdot \text{m}^2 \times 10 \, \text{rad/s} = 2,5 \, \text{kg} \cdot \text{m}^2/\text{s} \]
Ajụjụ Ihe Nlereanya nke 2
Onye na-agba skate nke nwere ike ịmalite ịgba ọsọ nke 0,8 kg·m² na-agbagharị na ọsọ akụkụ nke 5 rad/s. Ọ bụrụ na ọ dọghachi aka ya azụ ma oge ike ya belata ruo 0,4 kg·m², kedu ka ọsọ akụkụ ikpeazụ ya ga-adị?
Ngwọta:
Site n'iji ụkpụrụ nke nchekwa nke angular momentum:
\[ I_{mmalite} \omega_{mmalite} = I_{mkpeazụ} \omega_{mkpeazụ} \]
Tinye ụkpụrụ enyere:
\[ 0,8 \, \text{kg} \cdot \text{m}^2 \times 5 \, \text{rad/s} = 0,4 \, \text{kg} \cdot \text{m}^2 \times \omega_{end} \]
\[ 4 \, \text{kg} \cdot \text{m}^2/\text{s} = 0,4 \, \text{kg} \cdot \text{m}^2 \times \omega_{ngwụcha} \]
\[ \omega_{ngwụcha} = \frac{4 \, \text{kg} \cdot \text{m}^2/\text{s}}{0,4 \, \text{kg} \cdot \text{m}^2} = 10 \, \text{rad/s} \]
Mmechi
Momentum angular bụ echiche dị mkpa metụtara mmegharị ntụgharị nke ihe. Usoro bụ isi maka momentum angular, \(\vec{L} = \vec{r} \times \vec{p}\) na \(L = I \omega\), na-enye ntọala maka ịghọta ọtụtụ ihe dị iche iche nke anụ ahụ. Ụkpụrụ nke nchekwa momentum angular na-enyere aka ịkọwa ma buo amụma omume nke sistemụ na-agbagharị n'ọtụtụ ọnọdụ, site na mmegharị mbara ala ruo na ballet. Site n'ịghọta echiche na ojiji nke momentum angular, anyị nwere ike ịghọta nke ọma ịma mma na mgbagwoju anya nke mmegharị ntụgharị na eluigwe na ala.
