I-Rotational dynamics iyigatsha le-mechanics elifunda ukunyakaza kokujikeleza okubandakanya amandla, ubuningi, nezinye izinto ezithonya ukunyakaza kokujikeleza. Into iyajikeleza uma zonke izingxenye zento zihamba zizungeze i-axis noma i-pivot etholakala kwenye yezingxenye zento. Ukunyakaza kokujikeleza okufundwe kulesi sihloko kugxile ekunyakazeni kokujikeleza mayelana ne-axis ehleliwe. Ukunyakaza kwe-pulley, ifeni, ukunyakaza kwe-CD/DVD ekamelweni le-CD/DVD , ukunyakaza komnyango noma ifasitela, ukunyakaza kwesilinda senjini, i-helicopter noma i-propeller yendiza, noma i-propeller yomkhumbi ezinye zezibonelo zokunyakaza kokujikeleza mayelana ne-axis ehleliwe. Wake wayibona i-top ejikelezayo? Indawo ye-axis ye-rounding top ihlala ishintsha (ukuthambekela kwe-top kuvame ukushintsha), ngakho-ke ukunyakaza kokujikeleza okufana nalokho okubonwa yi-top ejikelezayo akufundiwe kulesi sihloko.
Ku-particle dynamics, into eshukumayo ekuhumusheni ibhekwa njenge-particle noma iphuzu elilodwa. Kungakhathaliseki ukuthi into inkulu kangakanani noma ukuthi iyinkimbinkimbi kangakanani, ibhekwa njengephuzu elilodwa. Ku-rotation dynamics, into ayibhekwa njengephuzu elilodwa kodwa ibhekwa kanjalo, uma kucatshangwa ukuthi isimo sayo nosayizi wayo kuhlala kungashintshi. Uma into ebhekwa njenge-particle iqukethe iphuzu elilodwa, khona-ke into ebhekwa njengomzimba oqinile iqukethe izinhlayiya eziningi, lapho indawo ye-particle ngayinye ihlala ingaguquki futhi ibanga eliphakathi kwazo lihlala lifana.
Isibonelo sezinkinga
1. I-pulley eyenziwe ngezinto eziqinile enentambo eboshwe ohlangothini lwayo lwangaphandle iboniswa njengoba kuboniswe esithombeni. Ukungqubuzana kwe-pulley kunganakwa. Uma umzuzu wokungapheleli kwe-pulley I = β futhi intambo idonswa ngamandla angaguquki F, khona-ke inani lika-F lilingana no….
A. F = α .β .R
B. F = α . β 2 . R
C. F = α . (β . R)-1
D. F = α . β . (R)-1
E. F = R. (α. β)-1
Ingxoxo
Kuyaziwa ukuthi:
Amandla okudonsa = F
Isikhathi sokungakhathali kwe-pulley = β
Ukusheshisa kwe-angular kwe-pulley = α
Irediyasi ye-Pulley = R
Umbuzo: Inani lika-F lilingana no….
Impendulo:
Ifomula yomthetho wesibili kaNewton yokunyakaza kokujikeleza:
Umzuzu wamandla ophumelayo osebenza ku-pulley:
Impendulo efanele ngu-D.
2. Induku enobude obungamamitha ayi-6 futhi enobunzima obuncane isetshenziswa amandla amathathu njengoba kuboniswe esithombeni. Ubukhulu besikhathi samandla enduku lapho ijikeleza phakathi nendawo yayo yobunzima ku-O bungu…
A. F
B. 3F
C. 4F
D. 5F
E. 6F
Ingxoxo
Kuyaziwa ukuthi:
I-axis yokujikeleza isendaweni ethi O.
Amandla 1 (F 1 ) = F
Ibanga eliphakathi kwephuzu lokusebenza F 1 kanye ne-axis yokujikeleza (r 1 ) = 3 amamitha
Amandla 2 (F 2 ) = 2F
Ibanga eliphakathi kwephuzu lokusebenza F 2 kanye ne-axis yokujikeleza (r 2 ) = 2 amamitha
Amandla 3 (F 3 ) = 2F
Ibanga eliphakathi kwephuzu lokusebenza F 3 kanye ne-axis yokujikeleza (r 3 ) = 3 amamitha
Umbuzo: Ubukhulu besikhathi samandla enduku lapho ijikeleza phakathi nendawo yayo yobunzima ku-O
Impendulo:
Isikhathi Samandla 1:
τ 1 = F 1 r 1 = (F)(3) = -3F
Umzuzu wamandla 1 ubangela ukuthi induku ijikeleze ngokwewashi ukuze lowo mzuzu wamandla 1 ube nophawu olubi.
Isikhathi Samandla 2:
τ 2 = F 2 r 2 = (2F)(2) = 4F
Umzuzu wamandla 2 ubangela ukuthi induku ijikeleze ngokuphambene newashi ukuze lowo mzuzu wamandla 2 ube nophawu oluhle.
Isikhathi Samandla 3:
τ 3 = F 3 r 3 isono 30 o = (2F)(3)(0,5) = 3F
Umzuzu wamandla 3 ubangela ukuthi induku ijikeleze ngokuphambene newashi ukuze lowo mzuzu wamandla 3 ube nophawu oluhle.
Umzuzu wamandla ophumela:
Στ = τ 1 + τ 2 + τ 3
Στ = -3F + 4F + 3F
Στ = 4F
Ubukhulu besikhathi samandla buyi-4F Newton metres. Isikhathi esihle samandla sisho ukuthi induku ijikeleza ngokuphambene newashi.
Impendulo efanele ngu-C.
3. Bheka isithombe!
Uma isisindo senduku ye-AC singanakwa, α = 30 o , ubude AB = BC = 1 imitha, umzuzu wamandla wesistimu nge-axis endaweni A u…
A. 10√3 Nm ngokwewashi 
B. 10 √3 Nm ngokuphambene newashi
C. 20 Nm ngokwewashi
D. 20 √3 Nm ngokuphambene newashi
E. 20 √3 Nm ngokwewashi
Ingxoxo
Kuyaziwa ukuthi:
I-axis yokujikeleza isendaweni A.
Amandla 1 (F 1 ) = 10 N
Ibanga eliphakathi kwephuzu lokusebenza F 1 kanye ne-axis yokujikeleza (r 1 ) = 1 amamitha
Amandla 2 (F 2 ) = 10 N
Ibanga eliphakathi kwephuzu lokusebenza F 2 kanye ne-axis yokujikeleza (r 2 ) = 1 amamitha
Amandla 3 (F 3 ) = 20 N
Ibanga eliphakathi kwephuzu lokusebenza F 3 kanye ne-axis yokujikeleza (r 3 ) = 2 amamitha
Umbuzo: Isikhathi samandla esistimu nge-axis ephuzwini A
Impendulo:
Isikhathi Samandla 1:
τ 1 = F 1 r 1 sin 30 o = (10)(1)(0,5) = 5 amamitha e-Newton
Umzuzu wamandla 1 ubangela ukuthi induku ijikeleze ngokuphambene newashi ukuze lowo mzuzu wamandla 1 ube nophawu oluhle.
Isikhathi Samandla 2:
τ 2 = F 2 r 2 sin 30 o = (10)(1)(0,5) = -5 amamitha e-Newton
Umzuzu wamandla 2 ubangela ukuthi induku ijikeleze ngokwewashi ukuze lowo mzuzu wamandla 2 ube nophawu olubi.
Isikhathi Samandla 3:
τ 3 = F 3 r 3 sin 60 o = (20)(2)(0,5 √3 ) = -20 √3 amamitha e-Newton
Umzuzu wamandla 2 ubangela ukuthi induku ijikeleze ngokwewashi ukuze lowo mzuzu wamandla 2 ube nophawu olubi.
Umzuzu wamandla ophumela:
Στ = τ 1 + τ 2 + τ 3
Στ = 5 – 5 – 20 √3
Στ = – 20 √3 amamitha e-Newton
Ubukhulu besikhathi samandla bungama- 20 √3 amamitha amaNewton . Isikhathi samandla esingesihle sisho ukuthi induku ijikeleza ngokwewashi.
Impendulo efanele ngu-E.
4. Bheka isithombe ohlangothini!
I-pulley eyenziwe ngezinto eziqinile (I = 2/5 MR 2 ) inesisindo esingu-2 kg. Uma isikhathi samandla ku-pulley singu-4 Nm, khona-ke ukusheshisa okuqondile kwe-pulley kungu…. (g = 10 ms -2 )
A. 50 ms -2
B. 25 ms -2
C. 20 ms -2
D. 16 ms -2
E. 8 ms -2
Ingxoxo
Kuyaziwa ukuthi:
Isikhathi sokungahlali kahle kwe-pulley eqinile (I) = 2/5 MR 2
Isisindo se-Pulley (M) = 2 kg
Isikhathi samandla ( τ) = 4 Nm
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 ms -2
Irediyasi ye-Pulley (R) = 20 cm = 0,2 m
Umbuzo: Ukusheshisa okuqondile (a)
Impendulo:
Bala isikhathi sokungabi namandla kwe-pulley (I):
I = 2/5 MR 2 = 2/5 (2)(0,2) 2 = 2/5 (2)(0,04) = 2/5 (0,08) = 0,16/5 = 0,032 kg m 2
Bala ukusheshisa kwe-angular ( α):
τ = I α
α = τ/I = 4/0,032 = 125 rad.s -2
Bala ukusheshisa okuqondile (a):
a = R α = (0,2)( 125) = 25 ms -2
Ukusheshisa okuqondile komphetho we-pulley kungu- 25 ms -2.
Impendulo efanele ingu-B.
5. Bheka isithombe ohlangothini! I-pulley yebhola eliqinile ijikeleza ngokusheshisa okungu-2 ms -2 , uma u-g = 10 ms -2 , khona-ke isikhathi sokungaqhubeki kwe-pulley ....
A. 1,0 kg.m2
B. 0,8 kg.m 2
C. 0,6 kg.m 2
D. 0,2 kg.m 2
E. 0,1 kg.m 2
Ingxoxo
Kuyaziwa ukuthi:
Ukusheshisa okuqondile komphetho we-pulley (a) = 2 ms -2
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 ms -2
Irediyasi ye-Pulley (R) = 10 cm = 0,1 m
Isisindo somthwalo (w) = mg = (4)(10) = 40 N
Umbuzo: Isikhathi sokungahlali kahle kwe-pulley
Impendulo:
Bala isikhathi samandla ( τ):
τ = FR = w R = (40)(0,1) = 4 Nm
Bala ukusheshisa kwe-angular kwe-pulley ( α ):
a = R α
α = a/R = 2/0,1 = 20 rad.s -2
Bala isikhathi sokungabi namandla kwe-pulley (I):
τ = I α
I = τ/ α = 4/20 = 0,2 kg m 2
Impendulo efanele ngu-D.
6. Bheka isithombe ohlangothini!
I-pulley idonswa ngendlela yokuthi i-pulley ihambe ngokusheshisa okungu-1 ms -2 . Uma i-radius ye-pulley ingu-10 cm, khona-ke isikhathi sokungaqhubeki kwe-pulley….
A. 4,00 kg.m2
B. 2,00 kg.m 2
C. 0,04 kg.m 2
D. 0,02 kg.m 2
E. 0,01 kg.m 2
Ingxoxo
Kuyaziwa ukuthi:
Ukusheshisa okuqondile komphetho we-pulley (a) = 1 ms -2
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 ms -2
Irediyasi ye-Pulley (R) = 10 cm = 0,1 m
Amandla okudonsa (F) = 4 N
Umbuzo: Isikhathi sokungahlali kahle kwe-pulley
Impendulo:
Bala isikhathi samandla ( τ):
τ = FR = (4)(0,1) = 0,4 Nm
Bala ukusheshisa kwe-angular kwe-pulley ( α ):
a = R α
α = a/R = 1/0,1 = 10 rad.s -2
Bala isikhathi sokungabi namandla kwe-pulley (I):
τ = I α
I = τ/ α = 0,4/10 = 0,04 kg m 2
Impendulo efanele ngu-C.
7. I-pulley yediski eqinile enesisindo esingu-1 kg kanye ne-radius engu-10 cm inentambo eboshwe onqenqemeni lwayo, futhi isisindo esingu-1 kg silenga kolunye uhlangothi lwentambo. Ake sithi intambo ayinasisindo. Ukusheshisa kokunyakaza komthwalo phansi… (g = 10 m/s2)
A. 10 m/s2
B. 12 m/s2
C. 15 m/s2
D. 20 m/s2
E. 22 m/s2
Ingxoxo:
Kuyaziwa ukuthi:
F = w = mg = (1 kg)(10 m/s2) = 10 Newton
r = 0,1 imitha
Kubuziwe:
Ukusheshisa kokunyakaza komthwalo
Impendulo:
I-Hitung Isikhathi Sokungabi Naso dan Isikhathi Sesitayela kuqala.
Impendulo efanele ngu-D.
8. I-pulley yediski eqinile enobunzima obungu-2M kanye ne-radius engu-R, igoqwa onqenqemeni ngentambo, bese umthwalo onobunzima obungu-m ulengiswe kolunye uhlangothi lwentambo. Lapho umthwalo ukhishwa, i-pulley ijikeleza ngokusheshisa kwe-angular okungu-. Uma into enobunzima obungu-M inamathele ku-pulley, khona-ke ukuze i-pulley ijikeleze ngokusheshisa okufanayo kwe-angular, isisindo somthwalo kumele senziwe... (I-pulley = ½ mr2).
A. ¾ m kg
B. 3/2 m kg
C. 2 m kg
D. 3 m kg
E. 4 m kg
Ingxoxo:
Kuyaziwa ukuthi:
Isisindo se-pulley yediski eqinile: 2M
Irediyasi yepulley yediski eqinile: R
Isisindo somthwalo: m
Kubuziwe :
Isisindo somthwalo?
Impendulo:
Bala isikhathi sokungabi namandla kwe-pulley yediski eqinile, ngaphambi nangemva kokuthi into enesisindo u-M inamathele kuyo:
Isikhathi Sokungabi Naso Isikhathi 1: I = ½ mr2 = ½ (2M)(R)2 = MR2
Isikhathi Sokungabi Naso Isikhathi 2: I = ½ mr2 = ½ (2M + M)(R)2 = ½ (3M)(R)2 = 1,5 MR2
Umthombo wombuzo:
Imibuzo Yefiziksi Yezivivinyo Zikazwelonke Zesikole Samabanga Aphezulu/Isikole Samabanga Aphezulu Sokufundela Umsebenzi
