Masiku ano miyoyo yathu yakhala yosavuta komanso yomasuka chifukwa cha kukhalapo kwa magalimoto okhala ndi mawilo, zida zamakono monga majenereta, makina opera, mafani, makina odulira udzu, zothira maluwa ndi zina zotero. Magalimoto okhala ndi mawilo monga njinga, njinga zamoto, magalimoto ndi ndege sangathe kuyenda ngati alibe mawilo kapena ngati mawilo sazungulira. Ma helikopita kapena ndege sizingayendenso ngati ma propeller awo sazungulira. Zombo sizingayende ngati majenereta awo kapena ma propeller awo sazungulira. Usiku, nyumba imakhala yakuda kwambiri ndipo palibe zosangalatsa ngati jenereta kapena malo opangira magetsi sagwira ntchito. Zinthu zambiri zimayenda mozungulira tsiku lililonse. Ngakhale osazindikira, dziko lapansi lomwe tikukhalamo, mwezi womwe umatiunikira usiku, ma satellite opanga monga ma satellite olumikizirana omwe amatumiza mafunde amagetsi pa wailesi yakanema, wailesi, foni yam'manja, ndi mawailesi apa intaneti, amazungulira nthawi zonse, omwe amadziwikanso kuti amayenda mozungulira nthawi zonse.
Chinthu chimanenedwa kuti chimayenda mozungulira ngati njira yake ndi yozungulira. Kuchuluka kwa thupi mu kuyenda kozungulira kumakhala ndi kuchuluka kwa angular (kuchuluka kwa kuyenda kozungulira) ndi kuchuluka kwa mzere (kuchuluka kwa kuyenda kozungulira). Kuchuluka kwa angular kumaphatikizapo kusuntha kwa angular, liwiro la angular, ndi kuthamanga kwa angular. Kuchuluka kwa mzere ndi kuchuluka monga kuyenda molunjika, kuphatikiza kusuntha (kutalika), liwiro (liwiro), ndi kuthamanga. Mosiyana ndi zimenezi, kuchuluka kwa kuyenda kozungulira nthawi zambiri kumatchedwa kuchuluka kwa angular . Mu kuyenda kozungulira, kuchuluka kwa mzere kumakhudzana ndi kuchuluka kwa angular.
Sinthani mayunitsi a ngodya (madigiri, ma radians, ma revolutions)
1. ¼ kutembenukira = ….. o (madigiri)?
Zokambirana
Kuzungulira 1 = 360o
½ kutembenukira = 180o
¼ kutembenukira = 90o
2. ½ kutembenukira = …….. ma radians?
Zokambirana
Chizunguliro chimodzi = ma radians awiri a pi = ma radians awiri (3,14) = ma radians 6,28
½ kutembenukira = pi radians = 3,14 radians
3. 180o (Madigiri 180) = ….. kuzungulira kapena revolution ?
Zokambirana
360o = 1 kuzungulira (1) revolution)
180o = ½ kutembenukira (1/2) revolution)
4. 90o = ….. ma radians?
Zokambirana
360o = 2 pi radians = 2(3,14) radians = 6,28 radians
180o = ma radians a pi = ma radians 3,14
90o = ½ pi radian = ½ (3,14) = 1,57
5. Ma radians 60 = ….. kuzungulira?
Zokambirana
Ma radians 6,28 = 1 revolution
Ma radians 60/6,28 = ma revolutions 9,55
6. Ma radians 40 = ….. o (madigiri)?
Zokambirana
6,28 radian = 360o
Ma radians 40/6,28 = (6,37)(360o= = 2292,99o
Liwiro la angular
Chitsanzo cha mavuto.
1. Gudumu limazungulira mozungulira wotchi, ndikupanga ngodya ya 180o kwa masekondi awiri ndi 90o kwa sekondi imodzi. Dziwani kukula ndi komwe liwiro lapakati la angular likuyendera!
Zokambirana
Chachikulu = 9o/chiwiri = …. kusintha/chiwiri = ….. radian/sekondi ?
Njira yolowera = njira yolowera mozungulira wotchi.
2. Gudumu limazungulira mozungulira wotchi, ndikupanga ngodya ya 360o kwa masekondi 4, kenako gudumu limazungulira madigiri 180o kwa masekondi awiri motsatizana ndi wotchi. Zingati liwiro lapakati la angular gudumu?
Zokambirana
Chachikulu = 3o/chiwiri = …. kusintha/chiwiri = ….. radian/sekondi ?
Njira yolowera = njira yolowera mozungulira wotchi.
Liwiro la Angular Lofulumira
Kukula kwa liwiro la angular instantaneous = kukula kwa liwiro la angular lomwe limayenda panthawi yochepa kwambiri.
Mu kuyenda molunjika kapena molunjika, liwilo lalikulu angatchedwe liwiro Karen kusamuka kwakukulu mtengo wofanana ndi mtunda ngati ndi yaying'ono kwambiri. Yozungulira, liwiro lalikulu la angular angatchedwe liwiro la angular Karen kusuntha kwakukulu kwa ngodya mtengo wofanana ndi mtunda ngodya ngati ndi kakang'ono kwambiri.
Kuthamanga kwa Angular kwapakati
Chitsanzo cha mavuto.
1. Mphero ya mphepo yomwe poyamba imakhala chete kwa kanthawi kenako imazungulira chifukwa cha mphepo. Pambuyo pa masekondi awiri, liwiro la angular limawonjezeka kufika pa 90°.o/s. Ndalama zingati? kuthamanga kwapakati kwa angular makina opumira mphepo?
Zokambirana
Pa avareji, liwiro lalikulu la angular makina oyendera mphepo awonjezeka ndi 45o/s sekondi imodzi iliyonse.
2. Poyamba, propeller imazungulira ndi liwiro la ngodya 180o/s, patatha masekondi awiri imasiya kuzungulira. Kodi ingati kuchepa kwapakati kwa angular makina opumira mphepo?
Zokambirana
Pa avareji, liwiro lalikulu la angular makina oyendera mphepo achepetsedwa ndi 90o/s sekondi imodzi iliyonse.
Kuthamanga kwa Angular nthawi yomweyo
Kuthamanga kwa angular nthawi yomweyo nthawi zambiri kumafupikitsidwa ngati kuthamanga kwa angular. Kuthamanga kwa angular nthawi yomweyo ndi kusintha kwa liwiro la angular pakapita nthawi yochepa kwambiri. Mwa masamu:
Nthawi ndi Kuchuluka kwa Kuyenda Kozungulira
Nthawiyo imanena nthawi yomwe imafunika kuti tinthu tigwire ntchito imodzi kuti tizungulire, pomwe nthawi yomwe imachitika nthawi yomweyo imanena kuchuluka kwa kuzungulira kwa sekondi iliyonse.
Ubale pakati pa nthawi ndi kuchuluka kwa nthawi umafotokozedwa kudzera mu equation:
f = 1/T
Gawo la padziko lonse la nthawi ndi lachiwiri, gawo la dongosolo la padziko lonse la pafupipafupi ndi 1/sekondi kapena hertz.
Kuthamanga ndi Kuthamanga kwa Angular
Liwiro la tangential ndi liwiro la angular la tinthu tomwe tikuyenda mozungulira zitha kufotokozedwa malinga ndi nthawi ndi kuchuluka kwake.
Kukula kwa liwiro la tinthu tomwe tikuchita kayendedwe kozungulira kumafotokozedwa ndi equation iyi:
Kukula kwa liwiro la angular la tinthu tomwe tikuyenda mozungulira kumafotokozedwa ndi equation iyi:
Zambiri:
Chitsanzo cha mavuto
1. Mawilo awiri A ndi B okhala ndi mano 20 ndi 50 motsatana amayikidwa kuti giya iliyonse ikhale yolumikizana. Ngati gudumu A lizungulira nthawi 50 mu sekondi imodzi, liwiro la gudumu B ndi….
Zokambirana
Ndizodziwika kuti:
Chiwerengero cha mano pa gudumu A = 20
Chiwerengero cha mano pa gudumu B = 50
Liwiro la angular la gudumu A ( ω A ) = 50 revolutions/second
1 revolution = 2π radians
(50)(2π radians)/sekondi = 100π radians/sekondi
Funso: Liwiro la gudumu B ( ω B )
Yankho:
Liwiro la gudumu A: v A = r A ω A
Liwiro la gudumu B: v B = r B ω B
Mawilo awiriwa ali pafupi kotero liwiro lawo lolunjika ndi lofanana.
v A = v B
r A ω A = r B ω B
(20)( 100π rad/s) = (50)(ω B )
(2)(100π rad/s) = (5)(ω B )
(2)(20π rad/s) = ω B
ω B = 40π rad/s
2. Mafunso a Mayeso a Dziko Lonse a SMA/MA a 2017
Yang'anani chithunzi chotsatirachi.
Njinga yamoto ikuyenda pa curve yokhala ndi ngodya ya α (tan α = 2/5) mpaka paphewa la msewu. Liwiro lalikulu kwambiri loletsa njinga yamoto kuti isaterereke ndi 20 ms -1 . Kodi radius ya curve ndi yotani?
A. 50 m
B. 100 m
C. 200 m
D. 250 m
E. 400 m
Zokambirana
Amadziwika kuti:
Liwiro lalikulu (v) = 20 m/s
tangent α = 2/5
Chokwanira cha kusinthasintha kosasunthika (μ s ) = tangent α = 2/5
Funso: Radius of bend (r)
Yankho:
Fomula yofulumira ya Centripetal:
Zambiri:
a s = kuthamanga kwapakati, v = liwiro, r = utali wozungulira wa kupindika
Mphamvu yokhayo yopingasa yomwe imagwira ntchito pa galimoto ikatembenuka ndi kukangana kosasinthasintha. Njira ya kukangana kosasinthasintha ndi iyi:
Zambiri:
f s = mphamvu yokhazikika yokhazikika, μ s = coefficient ya kukhazikika kokhazikika, w = kulemera, m = kulemera, g = kuthamanga chifukwa cha mphamvu yokoka
Fomula yachiwiri ya lamulo la Newton yoyendetsera mozungulira:
Yankho lolondola ndi B.
3. Mafunso a Mayeso a Dziko Lonse a SMA/MA a 2017
Mawilo anayi alumikizidwa monga momwe zasonyezedwera pansipa!
Ulalo wa RA = 6 cm, RB = 3 cm, RC = 2 cm ndi RD = 5 cm ndipo gudumu A limazungulira pa liwiro la mzere wa 3 ms-1, ndiye kuti liwiro la angular la gudumu D ndi…
Zokambirana
Amadziwika kuti:
R A = 6 cm = 0,06 m, R B = 3 cm = 0,03 m, R C = 2 cm = 0,02 m, R D = 5 cm = 0,05 m.
v A = 3 ms -1
Funso: liwiro la angular la gudumu D ( ω D )
Yankho:
Liwiro la gudumu A:
v A = r A ω A
ω A = v A / r A = 3 / 0,06 = 50 rad/s
Mawilo A ndi B amazungulira pa liwiro lomwelo la angular.
ω A = ω B = 50 rad/s
Liwiro la gudumu B:
ω B = 50 rad/s
Liwiro la gudumu B:
v B = r B ω B
v B = (0,03)(50 rad/s)
v B = 1,5 m/s
Wheel B ndi wheel C ali ndi liwiro lofanana.
v B = v C = 1,5 m/s
Wheel C ndi wheel D ali ndi liwiro lofanana.
v C = v D = 1,5 m/s
Liwiro la gudumu D:
ω D = v D / r D = 1,5 / 0,05 = 30 rad/s
