Muenzaniso weKufamba Kwedenderedzwa

Mienzaniso gumi nerimwe yeMibvunzo yeKutenderera Kwedenderedzwa

1. Chinhu chine huremu hwe10 kg chinoremakufamba kwakafanana kwedenderedzwa nekumhanya kwe4 ms^-1Kana nharaunda yedenderedzwa iri mamita 0,5, saka:
(1) Kutenderera kwefrequency ndeye 4/π Hz
(2) Kukurumidza kwepakati32 ms^-2
(3) Simba repakati penyika i320 N
(4) Nguva yacho i4π s.
Mhinduro chaiyo ndeyekuti…
1. (1), (2), (3), uye (4)
2. (1), (2), uye (3)
3. (1), uye (3) chete
4. (2), uye (4) chete
5. (3), uye (4) chete
Kukurukurirana
2. Chinhu chinofamba mudenderedzwa rine radius yemamita matanhatu. Kana chinhu chikatenderera kagumi nematanhatu mumaminitsi maviri, saka kumhanya kwechinhu chacho kwakafanana...
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) uye angular velocity (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

3. 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

4. Kune chinhu chinofamba nenzira yakatenderera, kumhanya kwacho kwakanangana kunoenderana...
A. huremu nenharaunda yedenderedzwa
B. huremu nenguva
C. huremu uye frequency
D. nguva uye nharaunda yenzira
E. kumhanya kwekona uye nharaunda yedenderedzwa
Kukurukurirana

 

5. 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.

6. Mavhiri B naC akaiswa paekisi imwe chete uye vhiri A rinosangana nevhiri B sezvakaratidzwa pamufananidzo uri padivi. Kana radius yevhiri A yakafanana neradius yevhiri C = 30 cm, radius yevhiri B = 60 cm, chiyero chekumhanya kwakatwasuka pakati pemavhiri A, B, naC…

A. 1: 1: 1

B. 1 : 2 : 1

C. 1 : 4 : 1

D. 2 : 2 : 1

Chikamu 4: 1: 2

Kukurukurirana

Zvinozivikanwa kuti :

Dunhu revhiri A (r _A ) = 30 cm = 0,3 metres

Radiyo yevhiri B (r _B ) = 60 cm = 0,6 metres

Dunhu revhiri C (r _C ) = 30 cm = 0,3 metres

Zvinodiwa : Kuenzanisa kumhanya kwakatwasuka pakati pemavhiri A, B, naC

Mhinduro :

Kumhanya kwakatsetseka kwerimu revhiri A

Vhiri A nevhiri B zvakabatana sezviri pamufananidzo uri pamusoro, saka kumhanya kwevhiri A hakuna kufanana nekumhanya kwevhiri B. Izvi zvinodaro nekuti kutenderera kwevhiri B kwakakura kupfuura kwevhiri A. Munguva imwe chete, kana vhiri A rafamba mudenderedzwa kutenderera kamwe (360 ^o ), vhiri B harina kusvika pakutenderera kamwe (360 ^o ). Zvisinei, panguva imwe chete, daro rinofambwa nemupendero wevhiri A rakafanana nedaro rinofambwa nemupendero wevhiri B. Saka kumhanya kwemupendero wevhiri A (v _A ) kwakafanana nekumhanya kwemupendero wevhiri B (v _B ).

Kumhanya kwakatsetseka kwerimu revhiri A:

v _A = r _A ω _A = 0,3 ω _A

Kumhanya kwakatsetseka kwerimu revhiri B

Vhiri B nevhiri C zvakabatana, saka vhiri B nevhiri C zvinotenderera pamwe chete. Kana vhiri B richifamba mudenderedzwa kutenderera kumwe chete (360)^o) ipapo panguva imwe chete vhiri C rinofambawo mudenderedzwa kutenderera kumwe chete (360^o). Nekuti zvinotenderera pamwe chete, kumhanya kwevhiri B (ω) kunoenderana nekona._B) yakaenzana nekumhanya kwevhiri C (ω)_C) = ω. Asi kumhanya kwakanangana kwerimu revhiri B (v)_B) hazvina kufanana nekumhanya kwakanangana kwemucheto wevhiri C (v)_C)

Kumhanya kwakatsetseka kwemucheto wevhiri B:

v _B = r _B ω _B = 0,6 ω _B = 0,6 ω

Kumhanya kwakatsetseka kwemucheto wevhiri C:

v _C = r _C ω _C = 0,3 ω _C = 0,3 ω

Kumhanya kwakanangana kwemupendero wevhiri A (v _A ) kwakafanana nekumhanya kwakanangana kwemupendero wevhiri B (v _B )

v _A = v _B

0,3 ω _A = 0,6 ω

ω _A = 0,6 ω / 0,3

ω _A = 2 ω

Kumhanya kwakatsetseka kwerimu revhiri A

v _A = 0,3 ω _A = 0,3 ( 2 ω) = 0,6 ω

Kuenzanisa kumhanya kwakatwasuka pakati pemavhiri A, B, naC

v _A : v _B : v _C

0,6 ω : 0,6 ω : 0,3 ω

0,6: 0,6: 0,3

6: 6: 3

2: 2: 1

Mhinduro chaiyo ndiD.

7. Mavhiri matatu akabatana sezvakaratidzwa mumufananidzo uri pazasi.

Kana R _A = 10 cm, R _B = 4 cm uye R _C = 40 cm, saka chiyero chekumhanya kwevhiri A nevhiri C ndeche…

A. 1: 1

B. 1: 2

C. 1 : 4

D. 2: 1

Chikamu 4: 1

Kukurukurirana

Zvinozivikanwa kuti :

Dura revhiri A (r _A ) = 10 cm

Radiyo yevhiri B (r _B ) = 4 cm

Dunhu revhiri C (r _C ) = 40 cm

Mubvunzo : Chiyero chekumhanya kwevhiri A nevhiri C

Mhinduro :

Kumhanya kwevhiri A neC kwekona

Kutenderera kwevhiri A kwakakura zvikuru kupfuura kutenderera kwevhiri C. Kana vhiri C rafamba mudenderedzwa kutenderera kamwe (360 ^o ), panguva imwe chete vhiri A harisati rasvika kutenderera kamwe (360 ^o ). Saka, kumhanya kwevhiri A hakuna kufanana nekumhanya kwevhiri C.

Zvisinei, mavhiri A naC akabatana netambo kana cheni. Nekuti akabatana, panguva imwe chete, daro rinofambwa nemupendero wevhiri A rakafanana nedaro rinofambwa nemupendero wevhiri C. Saka kumhanya kwemupendero wevhiri C (v _C ) kwakafanana nekumhanya kwemupendero wevhiri A (v _A ).

v _A = v _C

r _A ω _A = r _C ω _C

10 ω _A = 40 ω _C

ω _A / ω _C = 40 / 10

ω _A / ω _C = 4 / 1

Mhinduro chaiyo ndiE.

8.

Mavhiri matatu A, B naC akabatana sezvakaratidzwa mumufananidzo. Kana radii yemavhiri A, B naC iri 20 cm, 8 cm uye 4 cm zvichiteerana, uye vhiri B richitenderera nekumhanya kwe10 rad.s.^-1, ipapo vhiri C rinotenderera ne angled velocity ye...

A. 80 rad.s^-1
B. 50 rad.s^-1
C. 40 rad.s^-1
D. 20 rad.s^-1
E. 10 rad.s^-1

Kukurukurirana
Zvinozivikanwa :
Radiyo yevhiri A (r)_A) = 20 cm = 0,2 mamita
Radiyo yevhiri B (r)_B) = 8 cm = 0,08 mamita
Nharaunda yevhiri C (r)_C) = 4 cm = 0,04 mamita
Kumhanya kwevhiri B (ω)_B) = 10 rad/s
Akabvunzwa : Kumhanya kwevhiri C (ω)_C)
Jawab :

Kumhanya kwekona uye kumhanya kwakanangana kwerimu revhiri A
Vhiri A nevhiri B zvakabatana, saka vhiri A nevhiri B zvinotenderera pamwe chete. Kana vhiri B richifamba mudenderedzwa kutenderera kumwe chete (360)^o) ipapo panguva imwe chete vhiri A rinofambawo mudenderedzwa kutenderera kumwe (360^oNekuti zvinotenderera pamwe chete ipapo kumhanya kwekona vhiri A (ω)_A) yakaenzana nekumhanya kwevhiri B (ω)_B).
Kumhanya kwevhiri A kwekona :
ω_A = ω_B = 10 radians/sekondi
Kumhanya kwakatsetseka kwerimu revhiri A :
Hukuru hwekumhanya kwemutsara wemucheto wevhiri A hunoverengerwa uchishandisa fomura yehukama huripo pakati pekumhanya kwemutsara uye kumhanya kwekona, v = r ω.
v_A =r_A ω_A = (0,2 m)(10 rad/s) = 2 m/s

Kumhanya kwekona uye kumhanya kwakanangana kwerimu revhiri C
Kutenderera kwevhiri A kwakakura kupfuura kutenderera kwevhiri C. Kana vhiri C rafamba mudenderedzwa, kutenderera kamwe chete (360)^o), panguva imwe chete vhiri A harina kutenderera kamwe chete (360^oSaka, kumhanya kwevhiri A kwakasiyana nekumhanya kwevhiri C.
Zvisinei, mavhiri A naC akabatana netambo kana cheni. Nekuti akabatana, panguva imwe chete, daro rinofambwa nemucheto wevhiri A rakafanana nedaro rinofambwa nemucheto wevhiri C. Saka kumhanya kwemutsetse kwemucheto wevhiri C (v)_C) yakaenzana nekumhanya kwakatsetseka kwemucheto wevhiri A (v)_A).
Kumhanya kwakatsetseka kwerimu revhiri C :
v_C =v_A = 2 m/s
Kumhanya kwevhiri C kwekona :
v_C =r_C ω_C
ω_C =v_C /r_C = 2 / 0,04 = 50 radians/sekondi = 50 rad.s^-1.
Mhinduro chaiyo ndeiyi B.

9.

Sisitimu yemavhiri ane sipo yeR_A = 2 cm ; R_B = 4 cm uye R_C = 10 cm yakabatana sezvakaratidzwa mumufananidzo. Vhiri B rinotenderera ne60 revolutions paminiti, saka kumhanya kwevhiri C kuri…

A. 8π cm.s^-1
B. 12 cm.s^-1
C. 12π cm.s^-1
Kureba kwe 24 cms^-1
E. 24π cm.s^-1

Kukurukurirana
Zvinozivikanwa :
Radiyo yevhiri A (r)_A) = 2 cm
Radiyo yevhiri B (r)_B) = 4 cm
Nharaunda yevhiri C (r)_C) = 10 cm
Kumhanya kwevhiri B (ω)_B) = 60 revolutions/minute = 60 revolutions/60 seconds = 1 revolution/second = 1(2π radian)/second = 2π rad/s
Akabvunzwa : Kumhanya kwakatsetseka kwevhiri C (v)_C)
Jawab :
Kumhanya kwakatsetseka kwerimu revhiri B
Kumhanya kwemupendero wevhiri B:
v_B =r_B ω_B = (4 cm)(2π rad/s) = 8π cm/s
Kumhanya kwakatsetseka kwerimu revhiri A
Vhiri A nevhiri B zvakabatana netambo saka kumhanya kwemupendero wevhiri A (v) kunoonekwa._A) yakaenzana nekumhanya kwakatsetseka kwemucheto wevhiri B (v)_B).
v_A =v_B = 8π cm/s
Kumhanya kwakatsetseka kwerimu revhiri C
Vhiri C nevhiri A zvakabatana netambo saka kumhanya kwemupendero wevhiri C kuri (v)._C) yakaenzana nekumhanya kwakatsetseka kwemucheto wevhiri A (v)_A).
v_C =v_A =v_B = 8π cm/s
Mhinduro chaiyo ndiA.

10.
Teerera kune zvinotevera zvinobatanidzwa nemavhiri! Radiyo yemavhiri iR_A = 25 cm, R_B = 15 cm, R_C = 40 cm uye vhiri C rinotenderera nekumhanya kwekutenderera kwe60 revolutions paminiti. Kumhanya kwekona kwevhiri A ndiko…
A. 2,5π rad.s^-1
B. 3π rad.s^-1
C. 3,2π rad.s^-1
D. 3,5π rad.s^-1
E. 3,8π rad.s^-1
Kukurukurirana
Zvinozivikanwa :
Radiyo yevhiri A (r)_A) = 25 cm = 0,25 mamita
Radiyo yevhiri B (r)_B) = 15 cm = 0,15 mamita
Nharaunda yevhiri C (r)_C) = 40 cm = 0,4 mamita
Kumhanya kwevhiri C (ω)_C) = 60 revolutions/minute = 60 revolutions/60 seconds = 1 revolution/second = 1(2π radian)/second = 2π rad/s
Akabvunzwa : Kumhanya kwevhiri A (ω)_A)
Jawab :
Kumhanya kwakatsetseka kwerimu revhiri C
Kumhanya kwakatsetseka kwerimu revhiri C:
v_C =r_C ω_C = (0,4 m)(2π rad/s) = 0,8π m/s
Kumhanya kwakatsetseka kwerimu revhiri B
Vhiri C nevhiri B zvakabatana netambo saka kumhanya kwemupendero wevhiri C kuri (v)._C) yakaenzana nekumhanya kwakatsetseka kwemucheto wevhiri B (v)_B).
v_B =v_C = 0,8π m/s
Kumhanya kwekona uye kumhanya kwakanangana kwerimu revhiri A
Vhiri A nevhiri B zvakabatana sezvakaratidzwa mumufananidzo uri pamusoro, saka kumhanya kwevhiri A hakuna kufanana nekumhanya kwevhiri B. Izvi zvinodaro nekuti kutenderera kwevhiri A kwakakura kupfuura kwevhiri B. Munguva imwe cheteyo, kana vhiri A rafamba mudenderedzwa remavhiri rimwe chete (360).^o), vhiri B harisati rasvika pakutenderera kamwe chete (360^oZvisinei, panguva imwe cheteyo, daro rinofambwa nemupendero wevhiri A rakafanana nedaro rinofambwa nemupendero wevhiri B. Saka kumhanya kwakanangana kwemupendero wevhiri A (v)_A) yakaenzana nekumhanya kwakatsetseka kwemucheto wevhiri B (v)_B).
Kumhanya kwakatsetseka kwerimu revhiri A
v_A =v_B =v_C = 0,8π m/s
Kumhanya kwevhiri A kwekona
v_A =r_A ω_A
ω_A =v_A /r_A = 0,8π / 0,25 = 3,2π rad/s
Mhinduro chaiyo ndiC.

11. Dombo rine huremu m rinosungirirwa kumagumo kwetambo ine hurefu hwe l uye rozotenderera nekumhanya kwe ω kusvika nzira yedombo yatenderera mudenga rakatwasuka uye tambo yoita kona ye θ kuenda kudivi rakatwasuka (ona mufananidzo). Kumhanya kwedombo kwe angled ndiko...

Kukurukurirana

Mhinduro chaiyo ndiC.