Nguva yeInertia Formula
Nguva yekusagadzikana ipfungwa yakakosha mufizikisi ine chekuita nekutenderera kwezvinhu. Inotsanangura kugoverwa kwehukuru muchinhu maererano ne axis yayo yekutenderera uye inoshanda seanorongedzero yekutenderera kwehukuru mukufamba kwakatwasuka. Chinyorwa chino chichaongorora tsananguro yenguva yekusagadzikana, fomura yekutanga yenguva yekusagadzikana kwezvinhu zvakasiyana-siyana, nzira dzekuverenga nguva yekusagadzikana, uye mashandisirwo ayo muhupenyu hwezuva nezuva netekinoroji.
Kunzwisisa Nguva Yekusagadzikana
Nguva yekusashanda, inowanzonzi "kutenderera kwekusashanda" kana "nguva yekusashanda," ndiyo nzira yekuyera kuoma kwazvinoita kushandura kumhanya kwekutenderera kwechinhu. Nekunzwisisa, nguva yekusashanda yakakura, ndipo pazvinoita kuti zviome kukurumidzisa kana kuderedza kutenderera kwechinhu. Nguva yekusashanda inoenderana nekupararira kwechinhu uye daro racho kubva pa axis yekutenderera.
Fomura Yekutanga yeNguva Yekusagadzikana
Pamasvomhu, nguva yekusashanda (\( I \)) yechinhu chine huremu \( m \) chiri kure \( r \) kubva ku axis yekutenderera inoratidzwa se:
\[ Ini = mr^2 \]
Kune muviri wakasimba une zvidimbu zvakawanda, nguva yese yekusagadzikana ndiyo huwandu hwenguva dzekusagadzikana kwechikamu chimwe nechimwe. Kana muviri uchionekwa sekupararira kwehuwandu kunoramba kuripo, saka nguva yekusagadzikana inoratidzwa sechinhu chakakosha:
\[ I = \int r^2 \, dm \]
Di mana:
– \( I \) inguva yekusaita chinhu (kirogiramu mita yakaenzana nemativi mana, kg·m²),
– \( r \) idaro kubva pachinhu chikuru \( dm \) kusvika pa axis yekutenderera (mita, m),
– \( dm \) chinhu chidiki chine huremu hwechinhu (kilogiramu, kg).
Nguva Yekusagadzikana Kwezvinhu Zvakasiyana-siyana
Nguva yekusagadzikana inoenderana nechimiro uye kupararira kwehuwandu hwechinhu uye axis yacho yekutenderera. Heano mafomati enguva yekusagadzikana kwemamwe maumbirwo echinhu akajairika achienzaniswa neaxis yakapihwa:
1. Hunde yakatetepa
– Akisi iri kumagumo etsvimbo (kureba \( L \), huremu \( M \)):
\[ I = \frac{1}{3} ML^2 \]
– Akisi iri pakati pehunde:
\[ I = \frac{1}{12} ML^2 \]
2. Mhete yakatetepa kana Denderedzwa
– Akisi nepakati uye yakatwasuka kuenda mundege:
\[ Ini = MR^2 \]
3. Sirinda Yakasimba kana Dhisiki
– Akisi inopinda nepakati uye yakabatana neakisi refu:
\[ I = \frac{1}{2} MR^2 \]
4. Bhora Rakasimba
- Akisi nepakati:
\[ I = \frac{2}{5} MR^2 \]
5. Bhora kana Goko reHole
- Akisi nepakati:
\[ I = \frac{2}{3} MR^2 \]
Nzira Yekuverenga Nguva Yekusagadzikana
Kuverenga nguva yekusagadzikana kwechinhu chimwe nechimwe kuti uwane maumbirwo akaomarara kunoda kushandiswa kwekuverenga uye nzira yekubatanidza. Nzira mbiri dzakajairika dzekuverenga nguva yekusagadzikana kwechinhu chimwe nechimwe inzira yekubvisa chimiro uye nzira yekubatanidza.
1. Nzira yekuora
Nzira iyi inosanganisira kupatsanura chinhu kuita zvikamu zvidiki, zviri nyore, chimwe nechimwe chine nguva inozivikanwa yekusaita chinhu, uye wobva wapfupisa mipiro inobva muchikamu chimwe nechimwe.
2. Nzira Yakabatana
Nzira iyi inoshandisa ma integrals kuverenga nguva yekusashanda kwehuwandu hwehuwandu hunoenderera mberi. Semuenzaniso, kune tsvimbo yakatetepa yehurefu \( L \) uye huremu \( M \):
\[ I = \int_0^L x^2 \left(\frac{M}{L}\right) dx = \frac{M}{L} \int_0^L x^2 \, dx = \frac{M}{L} \left[\frac{x^3}{3}\right]_0^L = \frac{1}{3} ML^2 \]
Dzidziso yeParallel Axis
Iyo parallel axis theorem, kana kuti Huygens-Steiner theorem, inotibvumira kuverenga nguva yekusashanda kwechinhu maererano neakisi yakafanana neakisi kuburikidza nepakati pehukuru hwechinhu. Zvichienderana neiyi theorem:
\[ Ini = Ini_{\text{cm}} + Md^2 \]
Di mana:
– \(I \) inguva yekusagadzikana kana tichienzanisa ne axis itsva,
– \( I_{\text{cm}} \) inguva yekusashanda zvakanaka kana tichienzanisa ne axis iri pakati pehukuru,
– \( M \) huremu hwechinhu,
– \( d \) idaro riri pakati pe axis itsva ne axis nepakati pehukuru.
Kushandiswa kweNguva yeKusagadzikana
Nguva yekusaita chinhu ine mashandisirwo akawanda akakosha muhupenyu hwezuva nezuva uye tekinoroji. Heano mimwe mienzaniso:
1. Mavhiri eMotokari
Mumotokari, nguva yekusashanda zvakanaka kwevhiri inokanganisa kukurumidza uye kushanda zvakanaka kwesimba. Mavhiri ane nguva yekusashanda zvakanaka ari nyore kukurumidza, izvo zvinovandudza mashandiro emotokari.
2. Injini neMota
Mumainjini nemamota, nguva yekusashanda zvakanaka kwerotor inokanganisa mhinduro uye kugadzikana kwesystem. Dhizaini yerotor yakanaka inotarisa nguva yekusashanda zvakanaka kuti iwane kushanda zvakanaka uye kudedera kwakaderera.
3. Gyroscope
Magyroscope anoshandisa nguva yekusaita chinhu kuti arambe akadzikama uye akatarisa. Nguva yekusaita chinhu yakakwira inobvumira gyroscope kuti irambe iri panzvimbo yayo pasinei nekukanganisika kwekunze.
4. Sisitimu yeZuva
Mukuongorora nyeredzi, nguva yekusaita chinhu inoshandiswa kunzwisisa kutenderera kwemapuraneti, mwedzi, nezvimwe zvinhu zviri muhurongwa hwezuva. Inobatsira mukudzidza chimiro chemukati uye kupararira kwehuwandu hwezvinhu izvi.
5. Zviridzwa zveMimhanzi
Muzviridzwa zvemimhanzi zvakaita seviolin negitare, nguva yekusagadzikana kwetambo inokanganisa frequency yekurira uye kunaka kweruzha rwunobuda. Dhizaini yakanaka yetambo inotarisa nguva iyi yekusagadzikana kuti ibudise toni inodiwa.
Mhedziso
Nguva yekusagadzikana ipfungwa huru mufizikisi inotsanangura kugoverwa kwehukuru hwechinhu zvichienderana ne axis of rotation yacho. Nekunzwisisa fomura yekutanga yenguva yekusagadzikana uye maitiro ekuiverenga kune akasiyana maumbirwo echinhu, tinogona kuongorora zviri nani nekugadzira masisitimu ane chekuita nekutenderera. Nheyo yekuchengetedza nguva yekusagadzikana, pamwe chete ne parallel axis theorem, inotibvumira kuverenga nguva yekusagadzikana mumamiriro ezvinhu akaomarara.
Mashandisirwo enguva yekusagadzikana anosvika munzvimbo dzakasiyana-siyana, kubva pakugadzira mota neinjini kusvika kuzvinhu zvenyeredzi nemimhanzi. Kunzwisisa kwakakwana nguva yekusagadzikana kwakakosha kwete chete kune fizikisi yedzidziso asiwo kune hunyanzvi hwetekinoroji uye mashandisirwo anoshanda muhupenyu hwezuva nezuva. Nekuramba tichiongorora nekunzwisisa pfungwa iyi, tinogona kuwana kufambira mberi kukuru mune zvakasiyana-siyana zvesainzi neinjiniya.
