1. Ivili eliyimitha e-1 kwiradiyumu likhawuleza ngokulinganayo kwi-2 rad/s2. Misela i ukukhawulezisa iiangular kwaye i isantya se-angular yevili, emva kwemizuzwana emi-2.
Yaziwa:
Irediyasi (r) = 1 imitha
Ukukhawulezisa kwe-angular (α)) = 2 rad/s2
Ufuna: ukukhawulezisa kwe-angular kunye nesantya se-angular emva kwemizuzwana emi-2.
Isisombululo:
(a) Ukukhawulezisa kwe-angular kwimizuzwana emi-2
Ukukhawulezisa kwe-angular kuhlala kuhleli, ngoko ke emva kwemizuzwana emi-2, ukukhawulezisa kwe-angular kwevili yi-2 rad/s2.
(B) Isantya se-angular kwimizuzwana emi-2
Ukukhawulezisa kwe-angular 2 rad/s2 kuthetha ukuba isantya se-angular sonyusa iiradians ezi-2/isekhondi rhoqo emva kwesekhondi e-1. Emva kwesekhondi e-1, isantya se-angular = iiradians ezi-2/isekhondi. Emva kwemizuzwana emi-2, isantya se-angular = iiradians ezi-4/isekhondi.
2. Isuntswana likhawuleza ngokulinganayo ukusuka ekuphumleni ukuya kwi-60 rpm kwimizuzwana eli-10. Chonga ubungakanani bokukhawulezisa kwe-angular!
Yaziwa:
Isantya sokuqala se-angular (ωo= 0
Isantya sokugqibela se-angular (ωt) = 60 rpm = iirevolutions ezingama-60 / imizuzwana engama-60 = ujikelezo olu-1 / isekhondi = iiradians eziyi-6,28/isekhondi
Ixesha eliphakathi (t) = imizuzwana eli-10
Ifunwa: Ukukhawulezisa kwe-angular (α)
Isisombululo:
ωo = isantya sokuqala se-angular, ωt = isantya sokugqibela se-angular, α = ukukhawulezisa kwe-angular, t = ixesha eliphakathi, θ = i-engile.
ωt = ωo + α t
6.28 = 0 + α (10)
6.28 = 10 α
α = 6.28/10
α = 0.628 rad/s2
Ubukhulu bokukhawuleziswa kwe-angular = 0.628 rad/s2
3. Into iyancipha ukusuka kwi-20 rad/s ukuya kwi-10 rad/s kwimizuzwana emi-4. Fumana ubungakanani bokukhawuleziswa kwe-angular!
Yaziwa:
Ixesha eliphakathi (t) = imizuzwana eli-4
Isantya sokuqala se-angular (ωo ) = 20 rad/s
Isantya sokugqibela se-angular (ωt) = 10 rad/s
wayefuna : ubukhulu bokukhawulezisa kwe-angular (α)
Isisombululo:
ωt = ωo + α t
10 = 20 + α (4)
10 - 20 = 4 α
-10 = 4 α
α = -10 / 4
α = – 2.5 rad/s2
Ubukhulu bokukhawuleziswa kwe-angular yi--2.5 rad/s2Uphawu olunegative luthetha ukuba into iyacotha. Ukukhawulezisa = isantya se-angular siyanda, ukucotha = isantya se-angular siyancipha.
4. Into ikhawuleziswa imizuzwana emi-2 ukusuka kwi-10 rad/s ukuya kwi-2 rad/s2Chonga i-engile ejikelezwe yinto!
Yaziwa:
isantya sokuqala se-angular (ωo ) = 10 rad/s
ukukhawuleziswa kwe-angular (α) = 2 rad/s2
ixesha eliphakathi (t) = imizuzwana emi-2
Ifunwa: i-engile (θ)
Isisombululo:
θ = ωo + ½ α t2
θ = (10)(2) + ½ (2)(22)
θ = 20 + (1)(4) = 20 + 4
θ = iirediyani ezingama-24
5. Ivili lemoto liyehla ukusuka kwi-20 rad/s ukuya kuthi ga emva kwee-radians ezijikeleze i-20. Fumana ubungakanani bokukhawuleziswa kwevili nge-angular!
Yaziwa:
isantya sokuqala se-angular (ωo) = 20 rad/s
isantya sokugqibela se-angular (ωt= 0
Iengile (θ) = iiradiyani ezingama-20
Ifunwa: ubukhulu bokukhawuleziswa kwe-angular (α)
Isisombululo:
ωt2 = ωo2 + 2 α θ
0 = 202 + 2 α (20)
0 = 400 + 40 α
400 = – 40 α
α = – 400 / 40
α = – 10 rad/s2
6. I-rod PQ enobude obuyi-60 cm ijikeleza malunga nenqaku Q njenge-axis yokujikeleza kunye ne-PQ njenge-radius yesangqa. I-rod PQ ikhawuleza ukusuka ekuphumleni ukuya kwi-0.3 rad/s2Ithini isantya esithe ngqo senqaku P kwi-t = imizuzwana eli-10, ukuba indawo yokuqala ye-angular yi-0.
Yaziwa:
Ubude bentonga ye-PQ = irediyasi yesangqa (r) = 60 cm = 60/100 m = 0.60 m
Isantya sokuqala se-angular (ωo) = 0 rad/s
Ukukhawulezisa kwe-angular (α) = 0.3 rad s-2
Indawo yokuqala ye-angular (θo= 0
Ifunwa: Isantya esithe ngqo (v) senqaku P kwi-t = imizuzwana eli-10
Isisombululo:
Isantya sokugqibela se-angular emva kwemizuzwana eli-10:
ωt = ωo + α t = 0 rad/s + (0.3 rad s-2)(10 s) = 3 rad/s
Isantya sokugqibela esithe ngqo emva kwemizuzwana eli-10:
v = r ω = (0.6 m)(3 rad/s) = 1.8 m/s
7. Into ijikeleza ngesantya sokuqala se-4 rad/s kwaye i-angular acceleration yi-0.5 rad/s2Ingakanani isantya sento emva kwemizuzwana emi-4?
Yaziwa:
Isantya sokuqala se-angular (ωo) = 4 rad/s
Ukukhawulezisa kwe-angular (α) = 0.5 rad/s2
Ixesha eliphakathi (t) = imizuzwana eli-4
Ifunwa: Isantya sento emva kwemizuzwana emi-4 (ωt)
Isisombululo:
ωt = ωo + α t
ωt = 4 + (0.5)(4)
ωt = 4 + 2
ωt = 6 rad/s
8. A Iwotshi yodonga enobubanzi obuyi-10 cm ineenaliti ezintathu, nganye ibonisa iiyure, imizuzu kunye nemizuzwana. Uthelekiso lwenani leemijikelo zenaliti yeyure: inaliti yomzuzu: inaliti yesibini.
A. 1: 3: 180
B. 1: 12: 720
C. 4 : 12 : 180
D. 4 : 12 : 720
Yaziwa:
Iyure e-1 = imizuzu engama-60
Iiyure ezili-12 = (12)(imizuzu engama-60) = imizuzu engama-720
Isantya se-angular senaliti yeyure = umjikelo o-1 / iiyure ezili-12 = umjikelo o-1 / imizuzu engama-720
Isantya se-angular senaliti yemizuzu = ukujikeleza oku-1 / iyure e-1 = ukujikeleza oku-1 / imizuzu engama-60
Isantya se-angular senaliti yesibini = ukujikeleza oku-1 / umzuzu o-1
Ufuna: Uthelekiso lwenani leemijikelo zenaliti yeyure: inaliti yomzuzu: inaliti yesibini
Isisombululo:
I-equation yentshukumo ejikelezayo:
Isantya se-angular = inani leenguqu / ixesha eliphakathi
Inani leenguqu = isantya se-angular x ixesha eliphakathi
Kwixesha elifanayo, umzekelo, umzuzu o-1, zingaphi iinguqu zenaliti yeyure, inaliti yemizuzu, kunye nenaliti yesibini.
Inani leenguqu zenaliti yeyure = isantya se-angular x ixesha eliphakathi = (umjikelo o-1 / imizuzu engama-720) (umzuzu o-1) = iinguqu eziyi-1/720
Inani leenguqu zenaliti yemizuzu = isantya se-angular x ixesha eliphakathi = (umjikelo o-1 / imizuzu engama-60) (umzuzu o-1) = iinguqu eziyi-1/60
Inani leenguqu zenaliti yesibini = isantya se-angular x ixesha eliphakathi = (umjikelo o-1 / umzuzu o-1)(umzuzu o-1) = umjikelo o-1/1
Uthelekiso lweenguqu ezininzi:
Inani leenguqu zenaliti yeyure: inani leenguqu zenaliti yemizuzu: inani leenguqu zenaliti yesibini.
1/720: 1/60: 1/1
1/720: 12/720: 720/720
1: 12: 720
Impendulo echanekileyo ngu-B.
9. Ibhola ebotshelelwe ngentambo. Ibhola iyajikeleziswa ukuze ihambe ngendlela ejikelezayo ehambelana nomphezulu womhlaba. Kule ntshukumo, ibhola iyakhawuleza kuba…..
A. Ukuqulunqa yomoya
B. ubunzima yebhola
C. Amandla oxinzelelo
Isisombululo:
Umthetho wesibini wesindululo sikaNewton ithi into ikhawuleziswa ukuba kukho amandla avelayo. Ibhola iqhagamshelwe kwintambo kwaye xa intambo ijikeleza, nebhola iyajikeleza. Xa ibhola ijikeleza (ibhola ihamba ngesangqa), ibhola idlula kwi-centripetal acceleration. Zonke izinto ezihambayo ziyi-circular centripetal acceleration. Ukukhawulezisa okuphakathi kubangelwa amandla asecentripetalAmandla asembindini kweli tyala ngamandla oxinzelelo.
Impendulo echanekileyo nguC.
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- Iingxaki zesampulu zokuguqula iiyunithi ze-engile ngezisombululo
- Iingxaki zesampulu zokufuduka kwe-angular kunye nesampulu yokufuduka ethe tye kunye nezisombululo
- Iingxaki zesampuli zesantya se-angular kunye nesantya esithe ngqo kunye nezisombululo
- Iingxaki zesampulu zokukhawulezisa ze-angular kunye nesampulu yokukhawulezisa ethe tye enezisombululo
- Iingxaki zesampuli zeentshukumo ezijikelezayo ezifanayo kunye nezisombululo
- Iingxaki zesampulu yokukhawulezisa iCentripetal kunye nezisombululo
- Iingxaki zesampuli zeentshukumo ezijikelezayo ezingalinganiyo kunye nezisombululo
