Mibvunzo yeMienzaniso yeRotational Dynamics

Mienzaniso gumi nerimwe yeMibvunzo yeRotational Dynamics

Nguva Yemaitiro

1. Tsvimbo yakareruka kwazvo, yakareba 140 cm. Masimba matatu anoshanda patsvimbo, F1 ₌ 20 Newton , _F2 = 10 N, uye F3 ₌ 40 N, imwe neimwe ine gwara nenzvimbo sezvakaratidzwa mumufananidzo. Hukuru hwenguva yesimba rinoita kuti tsvimbo itenderere pakati pehukuru hwayo nde...

A. 40 Nm

B. 39 Nm

C. 28 Nm

D. 14 Nm

E. 3 Nm

Kukurukurirana

Zvinozivikanwa kuti:

Pakati pehuremu hwetsvimbo iri pakati petsvimbo.

Kureba kwetsvimbo (l) = 140 cm = 1,4 metres

Simba 1 (F ₁ ) = 20 N, ruoko rwesimba 1 (l ₁ ) = 70 cm = 0,7 metres

Simba 2 (F ₂ ) = 10 N, ruoko rwesimba 2 (l ₂ ) = 100 cm – 70 cm = 30 cm = 0,3 mamita

Simba 3 (F ₃ ) = 40 N, ruoko rwesimba 3 (l ₃ ) = 70 cm = 0,7 metres

Mubvunzo: Hukuru hwenguva yesimba rinoita kuti tsvimbo itenderere pakati pehukuru hwayo

Mhinduro:

Nguva yesimba 1 inoita kuti tsvimbo itenderere newachi. Saka, nguva yesimba 1 haina kunaka.

τ ₁ = F ₁ l ₁ = (20 N)(0,7 m) = -14 N m

Nguva yesimba 2 inoita kuti tsvimbo itenderere ichipesana newachi. Saka, nguva yesimba 2 yakanaka.

τ ₂ = F ₂ l ₂ = (10 N)(0,3 m) = 3 N m

Nguva yesimba 3 inoita kuti tsvimbo itenderere newachi. Saka, nguva yesimba 3 haina kunaka.

τ ₃ = F ₃ l ₃ = (40 N)(0,7 m) = -28 N m

Nguva yesimba inobuda:

Στ = -14 Nm + 3 Nm – 28 Nm = – 42 Nm + 3 Nm = -39 Nm

Hukuru hwesimba renguva ino hunosvika mamita makumi matatu nemapfumbamwe (39 Newton metres). Chiratidzo chekuramba chinoreva kuti tsvimbo inotenderera ichipesana newachi.

Mhinduro chaiyo ndeiyi B.

2. Rod AB, ine huremu husingatariswe, inoiswa yakatwasuka uye inobatwa nemasimba matatu sezvakaratidzwa mumufananidzo. Nguva inobuda yesimba rinoshanda patsvimbo painotenderedzwa padivi paD ndeye… (sin 53 ^o = 0,8)

A. 2,4 N m

B. 2,6 N m

C. 3,0 N m

D. 3,2 N m

E. 3,4 N m

Kukurukurirana

Zvinozivikanwa kuti :

Nzvimbo yekutenderera kana kuti pivot iri panzvimbo D.

F ₁ = 10 N uye l ₁ = r ₁ chivi θ = (40 cm)(chivi 53 ^o ) = (0,4 m)(0,8) = 0,32 mita

F ₂ = 10√2 N uye l ₂ = r ₂ chivi θ = (20 cm)(chivi 45 ^o ) = (0,2 m)(0,5√2) = 0,1√2 mamita

F ₃ = 20 N uye l ₃ = r ₁ chivi θ = (10 cm)(chivi 90 ^o ) = (0,1 m)(1) = 0,1 mita

Akabvunzwa : Nguva yesimba inobuda

Mhinduro :

τ ₁ = F ₁ l ₁ = (10 N) (0,32 m) = 3,2 Nm

(zvakanaka nekuti nguva iyi yesimba inoita kuti bhokisi ritenderere risingaenderane newachi)

τ ₁ = F ₂ l ₂ = (10√2 N)( 0,1√2 m) = -2 Nm

(hasi nekuti nguva iyi yesimba inoita kuti bhokisi ritenderere newachi)

τ ₁ = F ₂ l ₂ = (20 N) (0,1 m) = 2 Nm

(zvakanaka nekuti nguva iyi yesimba inoita kuti bhokisi ritenderere risingaenderane newachi)

Nguva yesimba inobuda:

Στ = τ ₁ – τ ₁ + τ ₃

Στ = 3,2 Nm – 2 Nm + 2 Nm

Στ = 3,2 Nm

Mhinduro chaiyo ndiD.

3. Rod AB, ine huremu husingatariswe, inoiswa yakatwasuka uye inobatwa nemasimba matatu sezvakaratidzwa mumufananidzo. Nguva inobuda yesimba rinoshanda patsvimbo kana richitenderedzwa padivi paD ndeye… (sin 53 ^o = 0,8)

A. 2,4 Nm

B. 2,6 Nm

C. 3,0 Nm

D. 3,2 Nm

E. 3,4 Nm

Kukurukurirana

Zvinozivikanwa kuti :

Chikamu chekutenderera chiri paD.

Daro riri pakati peF ₁ ne axis yekutenderera (r _AD ) = 40 cm = 0,4 m

Daro riri pakati peF2 _ne axis yekutenderera (r _BD ) = 20 cm = 0,2 m

Daro riri pakati peF3 _ne axis yekutenderera (r _CD ) = 10 cm = 0,1 m

F ₁ = 10 Newton

F ₂ = 10√2 Newton

F ₃ = 20 Newton

Chivi 53 ^o = 0,8

Mubvunzo : Nguva yesimba inobuda kana tsvimbo ikatenderedzwa padivi paD

Mhinduro :

Verenga nguva yesimba rinogadzirwa nesimba rega rega.

Nguva yesimba 1

Στ ₁ = (F ₁ )(r _AD chivi 53 ^o ) = (10 N)(0,4 m)(0,8) = 3,2 Nm

Nguva yesimba 1 yakanaka nekuti nzira yekutenderera kwetsvimbo inokonzerwa nenguva yesimba 1 inopokana newachi.

Nguva yesimba 2

Στ ₂ = (F ₂ )(r _BD chivi 45 ^o ) = (10√2 N)(0,2 m)(0,5√2) = -2 Nm

Nguva yesimba 2 haina kunaka nekuti nzira yekutenderera kwetsvimbo inokonzerwa nenguva yesimba 2 iri munzira imwecheteyo nekutenderera kwemaoko ewachi.

Nguva yesimba 3

Στ ₃ = (F ₃ )(r _CD chivi 90 ^o ) = (20 N)(0,1 m)(1) = 2 Nm

Nguva yesimba 3 yakanaka nekuti nzira yekutenderera kwetsvimbo inokonzerwa nenguva yesimba 3 inopokana newachi.

Nguva yesimba inoguma

Στ = Στ ₁ + Στ ₂ + Στ ₃

Στ = 3,2 – 2 + 2

Στ = 3,2 mamita eNewton

Mhinduro chaiyo ndiD.

Nguva yeInertia

4. Funga nezvemufananidzo wemabhora maviri akabatana newaya. Kureba kwewaya = 12 m, l ₁ = 4 m uye huremu hwewaya hazvitariswe, saka hukuru hwenguva yekusashanda kwehurongwa hwacho…

A. 52,6 kg m²

B. 41,6 kg m ²

C. 34,6 kg m ²

D. 22,4 kg m ²

E. 20,4 kg m ²

Kukurukurirana

Zvinozivikanwa kuti :

Huremu hwebhora A (m _A ) = 0,2 kg

Huremu hwebhora B (m _B ) = 0,6 kg

Daro riri pakati pebhora A ne axis yekutenderera (r _A ) = mamita mana

Daro riri pakati pebhora B ne axis yekutenderera (r _B ) = 12 – 4 = 8 metres

Mubvunzo : Nguva yekusashanda zvakanaka (I) kwehurongwa

Mhinduro :

Nguva yekusagadzikana kwebhora A

I _A = (m _A )(r _A ² ) = (0,2)(4) ² = (0,2)(16) = 3,2 kg ^m2

Nguva yekusagadzikana kwebhora B

I _B = (m _B )(r _B ² ) = (0,6)(8) ² = (0,6)(64) = 38,4 kg m ²

Nguva yekusashanda kwehurongwa hwezvimedu :

I = I _A + I _B = 3,2 + 38,4 = 41,6 kg m ²

Mhinduro chaiyo ndeiyi B.

Mutemo wechipiri waNewton wekufamba kwekufamba

5. Tarisa mufananidzo wevhiri rakasimba rakafanana parutivi. Tambo inomonererwa kumucheto kwevhiri uye mugumo wetambo unodhonzwa nesimba F re6 N. Kana huremu hwevhiri huri 5 kg uye radius yaro iri 20 cm, kumhanyisa kwevhiri kwekona kuri…

A. 0,12 rad s^-2

B. 1,2 rad s ^–2

C. 3,0 rad s ^–2

D. 6,0 rad s ^–2

E. 12,0 rad s ^–2

Kukurukurirana

Zvinozivikanwa kuti:

Simba rekudhonza (F) = 6 Newton

Huremu hwevhiri (M) = 5 kg

Dunhu revhiri (R) = 20 cm = 20/100 m = 0,2 m

Mubvunzo: Kukurumidza kwevhiri (α) kwekona

Mhinduro:

Verenga nguva yesimba:

τ = FR = (6 Newton)(0,2 metres) = 1,2 Newton metres

Verenga nguva yekusaita basa:

Fomura yenguva yekusashanda kwevhiri rakasimba muchimiro chedhisiki kana ndiro ndeye 1/2 MR ² = 1/2 (5 kg)(0,2 m) ² = 1/2 (5 kg)(0,04 m ² ) = 1/2 (0,2) = 0,1 kg m ².

Verenga kumhanyisa kwe angular uchishandisa fomura ye rotational dynamics:

τ = ini α

α = τ / I = 1,2 / 0,1 = 12 rad s ^-2

Mhinduro chaiyo ndiE.

6. Pulley yedhisiki yakasimba ine huremu hwe8 kg uye radius ye10 cm inotenderedzwa kumucheto kwetambo ine mutoro we4 kg wakasungirirwa kumucheto mumwe (g = 10 ms ^-2 ). Kukurumidza kwekufamba kwemutoro pasi kuri...

A. 2,5 ms ^–2

B. 5,0 ms ^–2

C. 10,0 ms ^–2

D. 20,0 ms ^–2

E. 33,3 ms ^–2

Kukurukurirana

Zvinozivikanwa kuti:

Huremu hwepureti yedhisiki yakasimba (m) = 8 kg

Nharaunda yedhisiki pulley yakasimba (r) = 10 cm = 0,1 metres

Huremu hwemutoro (m) = 4 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ²

Kurema kwemutoro (w) = mg = (4 kg)(10 m/s ² ) = 40 kg m/s ² = 40 Newtons

Mubvunzo: Kukurumidza kwekufamba kwemutoro pasi

Mhinduro:

Verenga nguva yekusashanda kwediski yakasimba:

I = 1/2 MR ² = 1/2 (8 kg)(0,1 m) ² = (4 kg)(0,01 m ² ) = 0,04 kg m ²

Verenga nguva yesimba:

τ = F r = (40 N) (0,1 m) = 4 Nm

Verenga kumhanyisa kwekona uchishandisa fomura yechipiri yaNewton yekufamba kwese kwese:

Στ = I α

4 = 0,04 α

α = 4 / 0,04 = 100

Verenga kukurumidza kwekufamba kwemutoro pasi:

a = r α = (0,1)(100) = 10 m/s ²

Mhinduro chaiyo ndiC.

7. Pure yakasimba ine huremu (M) uye radius (R) sezvakaratidzwa mumufananidzo! Mugumo mumwe wetambo isina huremu wakaputirwa papure, mumwe mugumo wetambo wakaturikwa nemutoro we m kg, kumhanyisa kwepure (α) kwe angular kana mutoro ukasunungurwa. Kana chidimbu che plasticine A chine huremu hwe 1⁄2 M chakabatanidzwa papure, kuti chibudise kumhanyisa kwe angular kwakafanana mutoro unofanira kugadzirwa…. (I pure = 1/2 MR ² )

A. 3/4 m kg

B. 3/2 m kg

C. 2 m kg

D. 3 m kg

E. 4 m kg

Kukurukurirana

Zvinozivikanwa kuti :

uremu hwemutoro = m

Kurema kwemutoro = w = mg

Huremu hwepulley yakasimba = M

Nharaunda yepulley yakasimba = R

Kukurumidza kwepulley kwekona = α

Akabvunzwa :

Kana huremu hwepulley hukawedzera kusvika M + M/2 = 3M/2 uye kumhanyisa kwepulley kwekona = α, huremu hwemutoro chii?

Mhinduro :

Nguva yekusashanda kwepulley isina plasticine:

Ini = 1/2 MR ² = 0,5 MR ²

Nguva yekusashanda kwepulley + plasticine:

I = 1/2 (3M/2) R ² = (3M/4) R ² = 0,75M R ²

Nguva yesimba:

τ = FR

Mutemo wechipiri waNewton wekufamba kwese kwese:

Στ = I α

w R = I α

mg R = I α

α = mg R / I

Kuti pave nekumhanya kwakafanana kwekona, huremu hwemutoro hunofanira kugadzirwa….. Tsiva α mu equation 2 na α mu equation 1:

Mhinduro chaiyo ndeiyi B.

8.. Pulley yakagadzirwa nechinhu chakasimba chine tambo yakamonererwa kurutivi rwayo rwekunze inoratidzwa sezvakaratidzwa mumufananidzo. Kukweshana kwepulley netambo uye kukweshana pa axis yayo yekutenderera zvinoregeredzwa. Kana mutoro ukadzika nekukurumidzisa nguva dzose a ms ^-2 , saka kukosha kwemoment of inertia yepulley kwakaenzana na….

A. I = τ α R

B. I = τ α ^-1 R

C. I = τ a R

D. I = τ a ^-1 R ^-1

E. I = τ a R ^-1

Kukurukurirana

Zvinozivikanwa kuti:

Simba = w = mg

Ruoko rwesimba = R

Kukurumidza kwekona = α

Kukurumidza kwemutoro = a ms ^-2

Mubvunzo: Nguva yekusashanda zvakanaka kwepulley (I)

Mhinduro:

Hukama huripo pakati pekumhanya kwemutsara uye kumhanya kwekona:

a = R α

α = a / R

Nguva yekusagadzikana inoverengerwa uchishandisa fomula:

τ = ini α

I = τ : α = τ : a / R = τ (R / a) = τ R a ^-1

Hapana mhinduro chaiyo.

9. Pure yakagadzirwa nechinhu chakasimba chine tambo yakamonererwa kurutivi rwayo rwekunze inoratidzwa sezvakaratidzwa mumufananidzo. Kukweshana kwepure kusingatariswe. Kana nguva yekusashanda kwepure I = β uye tambo ikadhonzwa nesimba risingaperi F, ipapo kukosha kwaF kwakaenzana na….

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

Kukurukurirana

Zvinozivikanwa kuti:

Simba rekudhonza = F

Nguva yekusashanda kwepulley = β

Kukurumidza kwepulley kwekona = α

Radiyo yepulley = R

Mubvunzo: Kukosha kwaF kwakaenzana na….

Mhinduro:

Fomura yechipiri yaNewton yekufamba kwese kwese:

Στ = β α ———- Equation 1

Tsananguro yefomura:

Στ = Inogadzirisa nguva yesimba (torque)

β = Nguva yekusaita basa

α = Kukurumidza kwekona

Nguva yesimba rinobuda papulley:

Στ = FR ———-> Equation 2

Tsananguro yefomura:

F = simba rekumanikidza

R = Kureba kubva panzvimbo yesimba F kusvika ku axis yekutenderera = radius yepulley

Tsiva Στ muequation 1 ne Στ muequation 2:

Στ = β . α

F. R = β. α

F = (β . α) / R

F = β . α . (R ^-1 )

Mhinduro chaiyo ndiD.

Kufamba Kwemakona

10. Chidimbu chine huremu hwe 0,2 gramu chinofamba mudenderedzwa chine kumhanya kwakafanana kwe 10 rad s ^-1 . Kana radius yenzira yechidimbu iri 3 cm, saka angled momentum yechidimbu iri...

A. 3 × 10 ^–7 kg m ² s ^-1

B. 9 × 10 ^–7 kg m ² s ^-1

C. 1,6 × 10 ^–6 kg m ² s ^-1

D. 1,8 × 10 ^–4 kg m ² s ^-1

E. 4,5 × 10 ^–3 kg m ² s ^-1

Kukurukurirana

Zvinozivikanwa kuti:

Huremu hwezvikamu (m) = 0,2 gramu = 2 x 10 ^-4 kg

Kumhanya kwekona (ω) = 10 rad s ^-1

Nharaunda yenzira yezvikamu (r) = 3 cm = 3 x 10 ^-2 mamita

Akabvunzwa: Kufamba kwechinhu chimwe nechimwe mukona

Mhinduro:

Fomura yeAngular momentum:

L = I ω

Tsananguro: I = angular momentum, I = moment of inertia, ω = angular velocity

Nguva yekusashanda kwechinhu chimwe nechimwe:

Ini = mr ² = (2 x 10 ^-4 )(3 x 10 ^-2 ) ² = (2 x 10 ^-4 )(9 x 10 ^-4 ) = 18 x 10 ^-8

Momentum yekona ndiyo:

L = I ω = (18 x 10 ^-8 )(10 rad s ^-1 ) = 18 x 10 ^-7 kg m ² s ^-1

Hapana mhinduro chaiyo.

11. Mutambi anotenderera maoko ake akatambanudzwa kusvika pakureba kwe160 cm. Zvadaro, maoko ake anopetwa kusvika pakureba kwe80 cm pamagokora. Kana kumhanya kwemutambi kukaramba kuripo, saka kumhanya kwake kwakatwasuka...

A. achiri

B. inova 1/2 yehukuru hwepakutanga

C. inova 3/4 yehukuru hwepakutanga

D. inova kaviri kupfuura yekutanga

E. inova yakapetwa ka4 kupfuura yekutanga

Kukurukurirana

Zvinozivikanwa kuti:

Nharaunda 1 (r ₁ ) = 160 cm

Nharaunda 2 (r ₂ ) = 80 cm

Kumhanya kwekona 1 (ω ₁ ) = ω

Kumhanya kwekona 1 (ω ₂ ) = ω

Akabvunzwa: Linear momentum

Mhinduro:

Kumhanya kwakatsetseka 1:

v ₁ = r ₁ ω ₁ = (160 cm) ω

Kumhanya kwakatsetseka 2:

v ₂ = r ₂ ω ₂ = (80 cm) ω

Mwero wemutsara 1:

p = mv ₁ = m (160 cm) ω

Mwero wemutsara 2:

p = mv ₂ = m (80 cm) ω

Saka linear momentum inova nehafu yekaviri yepakutanga.

Mhinduro chaiyo ndeiyi B.

Kwakabva mubvunzo:

Mibvunzo yeNational Examination Physics yeChikoro Chesekondari/Chikoro Chepamusoro Chebasa