Lokacin inertia ga barbashi - matsaloli da mafita

Lokacin inertia ga barbashi - matsaloli da mafita

1. Ƙwallo biyu da aka haɗa da sanda, kamar yadda aka nuna a cikin hoton da ke ƙasa. Yi watsi da nauyin sandar . Nauyin ƙwallon P shine gram 600 kuma nauyin ƙwallon Q shine gram 400. Menene lokacin inertia na tsarin game da AB?

An sani:

Axis na juyawa shine AB.

m _p = gram 600 = 0.6 kg, m _q = gram 400 = 0.4 kg

r _p = 20 cm = 0.2 m, r _q = 50 cm = 0.5 m

Ana so: Lokacin rashin ƙarfin tsarin

Magani:

I = m _p r _p ² + m _q r _q ²

I = (0.6 kg)(0.2 m) ² + (0.4 kg)(0.5 m) ²

I = (0.6 kg)(0.04 m ² ) + (0.4 kg)(0.25 m ² )

I = 0.024 kg m ² + 0.1 kg m ²

I = 0.124 kg m ²

2. Sandar AB mai nauyin kilogiram 2 tana juyawa a kusa da maki A, lokacin inertia na sandar shine kilogiram 8 m ^2. Idan aka juya a kusa da maki O (AO = OB), menene lokacin inertia na sandar.

An sani:

Nauyin sanda AB (m) = 2 kg

Idan aka juya a kusa da wurin A ta yadda radius na juyawa (r) = tsawon AB = r to lokacin inertia (I) = 8 kg m ²

Ana so: Idan an juya shi a kusa da wurin O ta yadda radius na juyawa (r) = tsawon AO = tsawon OB = 1/2 r to menene lokacin inertia na sandar.

Magani:

Ni = Mr. ²

8 kg m ² = (2 kg) r ²

8 m ² = (2) r ²

r ² = 8 m ^2/2

r ² = 4 m ²

r = mita 2

Idan aka juya a kusa da ma'ana O don haka ½ r = mita 1, to lokacin inertia:

I = mr ² = (2 kg)(1 m) ² = (2 kg)(1 m ² ) = 2 kg m ²

3. Ƙwallaye biyu da aka haɗa da sanda kamar yadda aka nuna a cikin hoton da ke ƙasa. Yi watsi da nauyin sandar. Menene lokacin rashin ƙarfin tsarin.

An sani:

Nauyin ƙwallon A (m)_A) = gram 200 = 0.2 kg

Nauyin ƙwallon B (m _B ) = gram 400 = 0.4 kg

Nisa tsakanin ƙwallon A da kuma axis na juyawa (rA ₎ = 0

Nisa tsakanin ƙwallon B da kuma axis na juyawa (r _B ) = 25 cm = 0.25 m

Ana so: Lokacin rashin ƙarfin tsarin

Magani:

Lokacin inertia na ball A:

I _A = (m _A )(r _A ² ) = (0.2)(0) ² = 0

Lokacin inertia na ball B:

I _B = (m _B )(r _B ² ) = (0.4)(0.25) ² = (0.4)(0.0625) = 0.025 kg m ²

Lokacin inertia na tsarin:

I = I _A + I _B = 0 + 0.025 = 0.025 kg m ² = 25 x 10 ^-3 kg m ²

4. Ƙwayoyin cuta guda huɗu masu tarin abubuwa daban-daban, waɗanda aka nuna a cikin hoton da ke ƙasa. Ƙayyade lokacin inertia na tsarin game da layin kwance P.

Magani

Axis na juyawa shine layin kwance P.

An sani:

Nauyin barbashi A (m _A ) = m

Nauyin barbashi B (m _B ) = 2m

Nauyin barbashi C (m _C ) = 3m

Guduwar ƙwayoyin D (m _D ) = 4m

Nisa tsakanin barbashi A da kuma axis na juyawa (rA ₎ = b

Nisa tsakanin barbashi B da kuma axis na juyawa (r _B ) = b

Nisa tsakanin barbashi C da kuma axis na juyawa (rC ₎ = 2b

Nisa tsakanin barbashi D da kuma axis na juyawa (r _D ) = 2b

Ana so: Lokacin inertia na tsarin game da layin kwance P

Magani:

I = m _A r _A ² + m _B r _B ² + m _C r _C ² + m _D r _D ²

I = (m) (b) ² + (2m) (b) ²⁺ (3m) (2b) ²⁺ (4m) (2b) ²

I = mb ² + 2 mb ² + (3m) (4b ² ) + (4m) (4b ² )

I = mb ² + 2 mb ² + 12 mb ² + 16 mb ²

I = 31 mb ²

5. Ƙwayoyin halitta guda huɗu da sanda ta haɗa. Yi watsi da nauyin sandar. Kayyade lokacin inertia game da axis na juyawa ta cikin ƙwayoyin halitta m ₁ da m ₂ , kamar yadda aka nuna a cikin hoton da ke ƙasa.

An sani

Nauyin barbashi 1 (m₁) = 1/4 kg

Nauyin barbashi 2 (m ₂ ) = 1/2 kg

Nauyin barbashi 3 (m ₃ ) = 1/4 kg

Nauyin barbashi 4 (m ₄ ) = 1/4 kg

Nisa tsakanin barbashi 1 da kuma axis na juyawa (r1 ₎ = 0

Nisa tsakanin barbashi 2 da kuma axis na juyawa (r2 ₎ = 0

Nisa tsakanin barbashi 3 da kuma axis na juyawa (r ₃ ) = 10 cm = 10/100 m = 1/10 m

Nisa tsakanin barbashi 4 da kuma axis na juyawa (r ₄ ) = 10 cm = 10/100 m = 1/10 m

Ana so: Lokacin rashin kuzari

Magani:

I = m ₁ r ₁ ² + m ₂ r ₂ ² + m ₃ r ₃ ² + m ₄ r ₄ ²

I = (1/4)(0) ² + (1/2)(0) ² + (1/4)(1/10) ² + (1/4)(1/10) ²

I = 0 + 0 + (1/4)(1/100) + (1/4)(1/100)

I = 1/400 + 1/400

I = 2/400

I = 1/200 kg.m ²

1. Menene lokacin inertia ga ƙwayar cuta?
   • Amsa: Ga ƙwayar cuta guda ɗaya ta taro $m$ a nesa $r$ daga wani yanki na juyawa, lokacin inertia $I$ aka ba ta I=m×r².
2. Me yasa ake yawan kiran lokacin inertia a matsayin "juyawa analog" na taro?
   • Amsa: Kamar yadda taro yake auna juriyar abu ga canje-canje a cikin motsin fassara (saboda dokar Newton ta biyu), lokacin inertia shine ma'aunin juriyar abu ga canje-canje a cikin motsin juyawarsa.
3. Ta yaya sauya nisan kwayar halitta daga tsakiyar juyawarta ke shafar lokacin inertia ɗinsa?
   • Amsa: Lokacin inertia yana daidai da murabba'in nisan daga axis na juyawa. Idan ka ninka nisan, lokacin inertia zai ƙaru da kashi huɗu.
4. Me yasa murabba'in nisa yake (r)²) an yi amfani da shi a cikin dabarar lokacin inertia maimakon kawai nisa?
   • Amsa: Ana amfani da murabba'in nisan ne saboda yadda kuzarin motsi ke aiki a juyawa. A cikin motsi na juyawa, kowane barbashi na wani abu yana ba da gudummawa ga kuzarin motsi na juyawa bisa ga nauyinsa da kuma nisansa daga axis mai murabba'i.
5. Ta yaya lokacin inertia na barbashi ke canzawa idan nauyinsa ya ninka sau uku yayin da yake kiyaye nisan daga madaidaicin axis?
   • Amsa: Idan an ninka nauyin sau uku kuma an kiyaye nisan da ke tsakanin, lokacin inertia shi ma zai ninka saboda yana daidai da nauyin kai tsaye.
6. Shin ƙwayar cuta za ta iya samun lokacin rashin ƙarfi na sifili? Idan haka ne, a wane yanayi?
   • Amsa: Eh, ƙwayar cuta za ta sami lokacin inertia na sifili idan ta kasance kai tsaye a kan axis na juyawa, tana yin nisanta $r$ daga axis daidai yake da sifili.
7. Me yasa abubuwa daban-daban masu girma da girma iri ɗaya suke da lokutan inertia daban-daban lokacin da suke juyawa a kusa da gatari daban-daban?
   • Amsa: Rarraba taro a kusa da axis na juyawa yana ƙayyade lokacin inertia. Ko da abubuwa biyu suna da nauyi da girma iri ɗaya, rarraba taro dangane da axis na juyawa na iya bambanta, wanda ke haifar da lokutan inertia daban-daban.
8. Shin lokacin inertia adadi ne na scalar ko vector?
   • Amsa: Moment of inertia adadi ne na scalar. Duk da haka, ga jikin da ke da tauri masu siffofi masu rikitarwa da gatari da yawa na juyawa, ana wakilta shi da tensor.
9. Idan ƙwayoyin cuta guda biyu ne, kowanne daga cikinsu yana da nauyi $m$, suna nan a nesa r_1​ da kuma r₂​ daga axis na juyawa, menene haɗin lokacin inertia?
   • Amsa: Lokacin inertia ƙari ne ga ƙwayoyin cuta daban-daban. Don haka, lokacin inertia da aka haɗa I=m×r₁^{2 ​}+ m×r₂^2​.

10. Ta yaya lokacin inertia yake da alaƙa da kiyaye ƙarfin kusurwa?

    • Amsa: Motsin kusurwa $L$ samfurin lokacin inertia ne $I$ da kuma saurin kusurwa $\omega$, wanda aka wakilta ta hanyar lissafi $L=I\times \omega$Idan babu wani ƙarfin juyi na waje da ke aiki akan tsarin, ƙarfin juyi zai kasance mai dorewa. Wannan yana nufin idan lokacin inertia ya canza (kamar a cikin mai yin tsere a kan skater yana jan hannuwansa), saurin kusurwa dole ne ya daidaita don kiyaye samfurin ya kasance mai dorewa.