Fomura Yekukurumidza Kwenguva Yenguva
Pendauluan
Angular momentum ipfungwa yakakosha mufizikisi ine chekuita nekufamba kwechinhu. Pfungwa iyi yakafanana ne linear momentum mukufamba kwekushandura. Angular momentum ine basa guru muzvikamu zvakasiyana zvefizikisi, kubva kuma mechanics ekare kusvika kuma quantum mechanics. Chinyorwa chino chichakurukura tsananguro ye angular momentum, mafomula ane hukama, mashandisirwo muhupenyu hwezuva nezuva, uye mienzaniso yekuwedzera kunzwisisa.
Tsanangudzo yeAngular Momentum
Angular momentum inhamba yevector inotsanangura maitiro echinhu kuramba chichitenderera panzvimbo kana axis. Angular momentum (\(\vec{L}\)) inoenderana nezvinhu zviviri zvikuru: linear momentum (\(\vec{p}\)) uye relative position (\(\vec{r}\)) ye reference point. Angular momentum inotsanangurwa se:
\[ \vec{L} = \vec{r} \times \vec{p} \]
di mana:
– \(\vec{L}\) ndiyo angular momentum.
– \(\vec{r}\) ndiyo vhekitari yenzvimbo inoenderana nenzvimbo yekunongedzera.
– \(\vec{p}\) ndiyo linear momentum (\(\vec{p} = m \vec{v}\), apo \(m\) iri huremu uye \(\vec{v}\) iri velocity).
– \(\times\) inomiririra chigadzirwa chakasanganiswa pakati pemaveki maviri.
Fomura Yekukurumidza Kwenguva Yenguva
Kune muviri wakasimba unotenderera ne angular velocity (\(\omega\)) inenge yakagadzika axis, angular momentum (\(L\)) inogona kuratidzwa seizvi:
\[ L = I \omega \]
di mana:
– \(L\) ndiyo angular momentum.
– \(I\) inguva yekusashanda kwechinhu chiri pamusoro pe axis yekutenderera.
– \(\omega\) ndiyo angled velocity.
Nguva yeInertia
Nguva yekusashanda (\(I\)) chiyero chekuramba kwechinhu kuchinja kwekufamba kwacho. Nguva yekusashanda inoenderana nekugoverwa kwehukuru hwechinhu maererano ne axis yekutenderera. Kune chinhu chakasimba, nguva yekusashanda inogona kuverengerwa uchishandisa fomura:
\[ I = \sum m_i r_i^2 \]
di mana:
– \(m_i\) huremu hwechikamu che\(i\)th.
– \(r_i\) ndiko kureba kwechikamu che\(i\)th kubva pachikamu chekutenderera.
Kune zvinhu zviri nyore, nguva yekusaita chinhu ine fomura yayo. Mimwe mienzaniso ndeiyi:
– Sirinda ine Hollow: \(I = mr^2\)
– Sirinda Yakazara: \(I = \frac{1}{2} mr^2\)
– Full Sphere: \(I = \frac{2}{5} mr^2\)
Nheyo Yekuchengetedza Kumhanya Kwemakona
Nheyo yekuchengetedza angular momentum inoti kana pasina torque yekunze inoshanda pane imwe system, angular momentum yese ye system icharamba yakadaro. Izvi zvinoreva:
\[ \vec{L}_{kutanga} = \vec{L}_{end} \]
kana
\[ Ini_{initial} \omega_{initial} = Ini_{yekupedzisira} \omega_{yekupedzisira} \]
Nheyo iyi inokosha zvikuru muzviitiko zvakasiyana-siyana zvemuviri, zvakaita sekufamba kwemapuraneti, mapirouette evatambi, uye kugadzikana kwemagyroscopes.
Kushandiswa kweAngular Momentum muhupenyu hwezuva nezuva
Kufamba Kwepasi
Mapuraneti ari mudenga rezuva anotenderera zuva uye ane momentum yakafanana neangular. Kuchinja kudiki mumomentum yakafanana neangular kunogona kukonzera shanduko mukufamba kwepasi. Izvi zvinodaro nekuti simba regiravhiti rinoshanda papasi hariburitse torque yakakwana, zvichiita kuti angular momentum irambe iripo.
Mutambi weBallet Pirouette
Mutambi weballet anogona kuwedzera kumhanya kwekutenderera kwake nekudhonza maoko nemakumbo ake pedyo nemuviri wake. Izvi zvinodaro nekuti nguva yekusaita chinhu inoderera, saka kuti arambe aine simba rakafanana, kumhanya kwekona kunofanira kuwedzera.
Gyroscope
Gyroscope chishandiso chinoshandisa musimboti we angular momentum kuchengetedza kugadzikana. MaGyroscope anoshandiswa mumhando dzakasiyana-siyana, dzakadai sekufamba mundege, ngarava, uye mafoni.
Mibvunzo nemhinduro dzemuenzaniso
Muenzaniso Mubvunzo 1
Dhisiki ine huremu hwe2 kg uye radius ye 0,5 metres inotenderera ne angular velocity ye 10 rad/s. Verenga angular momentum yedhisiki.
Mhinduro:
Nguva yekusashanda kwediski (\(I\)) inopiwa nefomura:
\[ I = \frac{1}{2} mr^2 \]
Isa kukosha kwakapihwa:
\[ I = \frac{1}{2} \nguva 2 \, \text{kg} \nguva (0,5 \, \text{m})^2 = \frac{1}{2} \nguva 2 \nguva 0,25 = 0,25 \, \text{kg} \cdot \text{m}^2 \]
Angular momentum (\(L\)) ndiyo:
\[ L = I \omega = 0,25 \, \text{kg} \cdot \text{m}^2 \times 10 \, \text{rad/s} = 2,5 \, \text{kg} \cdot \text{m}^2/\text{s} \]
Muenzaniso Mubvunzo 2
Mutambi ane nguva yekutanga yekusagona kumhanya ye0,8 kg·m² ari kutenderera nekakunguru ye5 rad/s. Kana akadzosera maoko ake kumashure uye nguva yake yekusagona kumhanya ikaderera kusvika pa0,4 kg·m², chii chiri kumhanya kwake kwekupedzisira kwekakunguru?
Mhinduro:
Kushandisa musimboti wekuchengetedza angular momentum:
\[ Ini_{initial} \omega_{initial} = Ini_{yekupedzisira} \omega_{yekupedzisira} \]
Isa kukosha kwakapihwa:
\[ 0,8 \, \text{kg} \cdot \text{m}^2 \times 5 \, \text{rad/s} = 0,4 \, \text{kg} \cdot \text{m}^2 \times \omega_{end} \]
\[ 4 \, \text{kg} \cdot \text{m}^2/\text{s} = 0,4 \, \text{kg} \cdot \text{m}^2 \times \omega_{end} \]
\[ \omega_{end} = \frac{4 \, \text{kg} \cdot \text{m}^2/\text{s}}{0,4 \, \text{kg} \cdot \text{m}^2} = 10 \, \text{rad/s} \]
Mhedziso
Angular momentum ipfungwa inokosha ine chekuita nekufamba kwezvinhu. Mafomula ekutanga e angular momentum, \(\vec{L} = \vec{r} \times \vec{p}\) uye \(L = I \omega\), anopa hwaro hwekunzwisisa zviitiko zvakasiyana-siyana zvepanyama. Nheyo yekuchengetedza angular momentum inobatsira kutsanangura nekufanotaura maitiro ehurongwa hwekutenderera mumamiriro ezvinhu akawanda, kubva pakufamba kwepuraneti kusvika ku ballet. Nekunzwisisa pfungwa uye mashandisirwo e angular momentum, tinogona kunzwisisa zviri nani runako nekuoma kwekufamba kwekutenderera muchadenga.
