Mienzaniso gumi nerimwe yeMatambudziko Ekufamba Kwedenderedzwa Yakafanana
1. Chidimbu chinofamba mudenderedzwa chine kumhanya kwekona kunogara kuripo kwe10 rad/s. Tsvaga (a) kumhanya kwekona kwechinhu mushure memasekonzi gumi (b) kona yakaderedzwa nechinhu mushure memasekonzi gumi.
Kukurukurirana
(a) kumhanya kwekona mushure memasekonzi gumi
Chidimbu chinofamba chakaita denderedzwa rakafanana = chidimbu chinofamba nekufamba kwe angular kusingachinji. Saka kumhanya kwe angular mushure memasekonzi gumi kunoramba kuri 10 radians/sekondi.
(b) kona yakavharirwa mushure memasekonzi gumi
Kumhanya kwekona kunogara kuripo kwemaradians gumi/sekondi zvinoreva kuti sekondi imwe neimwe, chidimbu chinotenderera kona yemaradians gumi. Mushure memasekonzi maviri, chidimbu chinotenderera kona ye2 x 10 = 20 radians. Mushure memasekonzi gumi, chidimbu chinotenderera kona ye10 x 10 radians = 100 radians.
2. Poindi iri pamucheto wesirinji inofamba yakatenderera nekumhanya kwakasimba kwe10 m/s. Radiyumu yesirinji = mita imwe. Tsvaga (a) kumhanya kwemucheto wesirinji mushure memasekonzi mashanu (b) daro rakafambwa nemupendero wesirinji mushure memasekonzi mashanu (c) kukurumidza kwepakati pemapoinzi ari 0,5 metres uye mita imwe kubva pa axis yekutenderera.
Kukurukurirana
(A) kumhanya kwenzvimbo pamucheto wesilinda mushure memasekonzi mashanu
Sirinda inofamba yakatenderera nekumhanya kwakafanana, saka mushure memasekonzi mashanu, kumhanya kwemucheto wesirinda kunoramba kuri mamita gumi pasekondi.
(B) daro rakafambwa nepfungwa pamucheto wesilinda mushure memasekonzi mashanu
Pasina fomura
Kumhanya kwemamita gumi pasekondi zvinoreva kuti sekondi imwe chete yega yega, poindi iri pamucheto wesirinji inofamba mamita gumi. Mushure mesekondi imwe chete, poindi iri pamucheto wesirinji inofamba mamita gumi. Mushure memasekonzi maviri, poindi iri pamucheto wesirinji inofamba mamita makumi maviri. Mushure memasekonzi mashanu, poindi iri pamucheto wesirinji inofamba mudenderedzwa remamita makumi mashanu.
Kushandisa fomura :
v = s/t
s = vt = (10)(5) = mamita gumi
(C) kukurumidza kwepakati (as)
Kukurumidza kwepakati penzvimbo iri mita imwe kubva pa axis ndekwekuti:
as =v2 / r = 102 / 0,5 = 100 / 0,5 = 200 m/s2
Kukurumidza kwepakati penzvimbo iri mita imwe kubva pa axis ndekwekuti:
as =v2 / r = 102 / 0,5 = 100 / 1 = 100 m/s2
3. Turntable ine radius yemamita maviri inofamba nekumhanya kwekona kusingachinji kwe60 rpm. Tsvaga (a) kumhanya kwekona kweturntable mushure memasekonzi maviri (b) kona yakavharirwa neturntable mushure meminiti imwe (b) kumhanya kwekona, kukurumidza kwepakati nepakati uye daro rakafambwa nepoindi imwe mita kubva pa axis of rotation (c) kumhanya kwekona, kukurumidza kwepakati nepakati nedaro rakafambwa nepoindi iri pamucheto weturntable.
Kukurukurirana
Zvinozivikanwa :
Jawab :
(A) kumhanya kwekona ( ) mushure memasekonzi maviri
Kumhanya kwekona hakuchinji saka mushure memasekonzi maviri, kumhanya kwekona kwekona ye turntable kunoramba kuri 6,28 radians/second.
(B) kona ( ) yakakomberedzwa ne turntable mushure meminiti imwe
Kumhanya kwekona kwe1 revolution/sekondi zvinoreva kuti sekondi yega yega turntable inoita kutenderera kamwe chete. Mushure memasekonzi makumi matanhatu, turntable inenge yaita kutenderera makumi matanhatu. Kana, neimwe nzira,
Kumhanya kwekona kwe6,28 radians/sekondi zvinoreva kuti sekondi yega yega turntable inotenderera kona ye6,28 radians. Mushure memasekonzi makumi matanhatu, turntable inenge yatenderera kona ye376,8 radians.
4. Vhiri remota rinogara richitenderera ka120 mumasekonzi makumi matanhatu ega ega. Chii chinonzi kumhanya kwevhiri? Nyora izvi mu: (a) kumukirana paminiti (rpm) kana kutenderera paminiti (b) madhigirii pasekondi (o/s) (c) radians pasekondi (rad/s)
Kukurukurirana
(A) kumhanya kwevhiri muzvikamu zvekutenderera paminiti (rpm)
Kutenderera 120 / masekondi 60 = 120 kutenderera / miniti 1 = 120 kutenderera / miniti = 120 rpm
(B) kumhanya kwevhiri mumakiromita / sekondi (o/ s)
Kutenderera kamwe chete = 360o, 120 kutendeuka = 43200o
Saka 120 revolutions / 60 seconds = (120)(360o) / masekondi makumi matanhatu = 43200o / Masekondi makumi matanhatu = 720o/chepiri
(C) kumhanya kwevhiri mu radians/second (rad/s)
Kutenderera kumwe chete = 6,28 radians
Saka 120 revolutions / 60 seconds = (120)(6,28) radians / 60 seconds = 753,6 radians / 60 seconds = 12,56 radians/second
5. Marble inotenderedzwa mundiro yakatenderera ine dhayamita ye 1 m. Kana marble ikatenderera kumucheto kwendiro nekumhanya kwakafanana kwe 50 rpm, saka kumhanya kwakanangana uye kukurumidza kwepakati pemarble ndizvo….
A. 50 ms-1 uye 2500 ms-2
B. 5π ms-1 uye 25π2 Ms.-2
C. 5π/3 ms-1 uye 25π2/18 ms-2
D. 5π/6 ms-1 uye 25π2/18 ms-2
E. 5π/12 ms-1 uye 25π2/36 ms-2
Kukurukurirana
Zvinozivikanwa kuti:
Dhayamita yedenderedzwa (D) = mita imwe
Nharaunda yedenderedzwa (r) = 0,5 metres
Kumhanya kweAngular (ω) = 50 rpm = 50 revolutions / 1 miniti
1 revolution = 2π radians
Kutenderera makumi mashanu = 50 (2π radians) = 100π radians
Miniti imwe = masekondi makumi matanhatu
Kumhanya kwekona (ω) = 100π radians / masekondi 60 = (10π/6) radians/sekondi
Mubvunzo: Kumhanya kwemutsetse (v) uye kukurumidza kwepakati (a)s)
Mhinduro:
Kumhanya kwemutsetse (v):
v = r ω = (0,5)(10π/6) = 5π/6 m/s
Kukurumidza kwepakati pepakati (a)s):
as =v2/r = (5π/6)2 : 0,5 = 25π2/36 : 0,5 = (25π2/36)(1/0,5)
as = (25π2/18) m/s2
Mhinduro chaiyo ndiD.
6. Chinhu chinofamba mudenderedzwa rine radius ye50 cm. Kana chinhu chikatenderera pa120 rpm, zvinoreva kuti nguva yekutenderera uye kumhanya kwechinhu zvakateerana….
A. 0,5 s uye 2π ms-1
B. 0,5 s uye 0,2π ms-1
C. 0,5 s uye π ms-1
D. 2 s uye 5π ms-1
E. 2 s uye 10π ms-1
Kukurukurirana
Zvinozivikanwa kuti:
Nharaunda (r) = 50 cm = 0,5 metres
Kumhanya kweAngular (ω) = 120 rpm = 120 revolutions / 1 miniti = 120 revolutions / 60 maminitsi = 2 revolutions / 1 sekondi
1 revolution = 2π radians
Kumhanya kwekona (ω) = 2 (2π radians) / 1 sekondi = 4π radians/sekondi
Mubvunzo: Nguva yekutenderera (T) uye kumhanya kwakatwasuka (v)
Mhinduro:
Nguva kana nguva yekufamba kwendege (T):
Nguva yacho inguva inotora chinhu kuti chipedzise kutenderera kamwe chete.
Chinhu chinoita ma revolution maviri pasekondi imwe chete = chinhu chinoita revolution imwe pamasekondi 0,5. Saka nguva yekutenderera kana kuti nguva yacho imasekondi 0,5.
Kumhanya kwechinhu (v):
v = r ω = (0,5 metres)(4π radians/second) = 2π metres/second
Mhinduro chaiyo ndiA.
Dzidza zviri muchinyorwa pamusoro pekufamba kwedenderedzwa uye kufamba kwedenderedzwa nguva dzose kuti unzwisise zviri nani hurukuro yemubvunzo uyu.
7. Vhiri rine radius ye 10 cm rinotenderera zvakaenzana, richipedzisa kutenderera 180 paminiti. Kumhanya kwakanangana kwenzvimbo iri pamucheto wevhiri ndekwe…
Kukurukurirana
Zvinozivikanwa kuti:
Akabvunzwa:
Kumhanya kwemutsetse (v) ?
Mhinduro:
Nzvimbo iri pamucheto wevhiri iri 0,1 metres kubva pakati pevhiri.
Mhinduro chaiyo ndiA.
8. Chinhu chinofamba nekumhanya kunogara kuripo v munzira yakatenderera ine radius R ine centripetal acceleration (as). Zvekuti kukurumidza kwepakati kunowedzera katatu kupfuura kwekutanga ipapo...
A. v inogadzirwa ka4 uye R inogadzirwa kaviri zvakare
B. v inogadzirwa kaviri uye R inogadzirwazve ka4
C. v inogadzirwa kaviri uye R inogadzirwa kaviri zvakare
D. v inosara uye R inopetwa kaviri zvakare
E. v yakapetwa kaviri zvakare uye R inoramba iripo
Kukurukurirana
Mhinduro chaiyo ndiC.
9. Mavhiri A, B naC akabatana sezvakaratidzwa mumufananidzo. Kana radii yemavhiri A, B naC iri 10 cm, 4 cm uye 2 cm zvichiteerana, uye vhiri B richitenderera nekumhanya kwe5 rad.s-1 ipapo vhiri C rinotenderera ne angled velocity ye….
A. 80 rad.s-1
B. 55 rad.s-1
C. 40 rad.s-1
D. 25 rad.s-1
E. 10 rad.s-1
Kukurukurirana
Zvinozivikanwa kuti:
Mhinduro:
Hukama huripo pakati pevhiri A nevhiri B
Mavhiri A neB zvakabatana, saka zvinotenderera pamwe chete. Nekuti zvinotenderera pamwe chete, kumhanya kwevhiri A = kumhanya kwevhiri B.
Hukama huripo pakati pevhiri A nevhiri C
Kutenderera kwevhiri A kwakakura kupfuura kutenderera kwevhiri C. Kana vhiri C rakatora kona ye360o kana kutenderera kamwe chete, panguva imwe chete, vhiri A harina kusvika 360o kana kutenderera kamwe chete. Saka, kumhanya kwevhiri A kwakasiyana nekumhanya kwevhiri C.
Zvisinei, mavhiri A naC anobatanidzwa netambo. Nekuti anobatanidzwa netambo, panguva imwe chete, daro rinofambiswa nemucheto wevhiri A = daro rinofambiswa nemucheto wevhiri C. Saka kumhanya kwevhiri A = kumhanya kwemutsetse kwevhiri B.
Mhedziso:
Mhinduro chaiyo ndiD.
10. Chinhu chinekufamba kwakafanana kwedenderedzwa ine nharaunda yemamita matanhatu. Kana mumaminitsi maviri chinhu chikatenderera kagumi nematanhatu, saka kumhanya kwakatwasuka chinhu chacho….
A. 0,8 pm ms-1
B. 1,0 p ms-1
C. 1,2 pm ms-1
D. 1,4 p ms-1
E. 1,6 p ms-1
Kukurukurirana
Zvinozivikanwa kuti:
Nharaunda (r) = mamita makumi mashanu
Kumhanya kweAngular (ω) = 16 revolutions / 2 minutes = 8 revolutions / minute = 8 revolutions / 60 seconds = 0,13 revolutions / second.
Akabvunzwa: kumhanya kwemutsetse (v)?
Mhinduro:
Fomura yehukama huripo pakati pe linear velocity (v) ne kumhanya kwekona (ω):
v = r ω = (6 metres)(0,13 revolutions/second) = 0,8 revolutions mita/second
Mhinduro chaiyo ndiA.
Kana zvikataurwa muma radians:
1 revolution = 2π radians = 2(3,14) = 6,28 radians
Kumhanya kweAngular = 8 (6,28) radians / 60 seconds = 50,24 radians / 60 seconds = 0,84 radians/second
v = r ω = (6 metres)(0,84 radians/second) = 5,04 radians/second
11. Fan propeller ine radius ye 20/π cm inogona kutenderera ka4 musekondi imwe chete. Kumhanya kwakanangana kwemuromo wepropeller ndekwe…
A. 3,2 ms-1
B. 1,6 ms-1
C. 1,3 ms-1
D. 1,0 ms-1
E. 0,8 ms-1
Kukurukurirana
Zvinozivikanwa kuti:
Nharaunda (r) = 20/π m = 20 / 3,14 cm = 6,4 cm = 0,064 mamita
Kumhanya kwekona (ω) = 4 revolutions / 1 second = 4 revolutions/second
1 revolution = (2)(3,14) radians = 6,28 radians
Kumhanya kweAngular (ω) = (4)(6,28) radians/second = 25,12 radians/second
Mubvunzo: kumhanya kwakanangana (v) kwemuromo wepropeller?
Mhinduro:
v = r ω = (0,064 metres)(25,12 radians/sekondi) = 1,6 metres/sekondi
Mhinduro chaiyo ndeiyi B.
