Daqiiqada walxaha inertia iyo jirka adag - dhibaatooyinka iyo xalalka

Daqiiqada firfircoonida walaxda

1. Kubbad 100-garaam ah oo ku xiran hal dhinac oo xarig ah oo dhererkeedu yahay 30 cm. Waa maxay daqiiqadda firfircoonida kubbadda ee ku saabsan dhidibka wareegga AB? Iska ilow cufka xarigga.

La yaqaan:

dhidibka wareegga ee AB

Kubbad cufnaan (m) = 100 garaam = 100/1000 = 0.1 kg

Masaafada u dhaxaysa kubadda iyo dhidibka wareegga (r) = 30 cm = 0.3 m

La Doonayo: Daqiiqada firfircoonida kubadda (I)

Xalka:

I = mr ² = (0.1 kg)(0.3 m) ²

I = (0.1 kg)(0.09 m ² )

I = 0.009 kg m ²

2. Kubbad 100-garaam ah, m ₁ , iyo kubad 200-garaam ah, m ₂ , oo ay ku xiran yihiin ul dhererkeedu yahay 60 cm. Cufka usha waa la iska indho tiray. Dhidibka wareegga wuxuu ku yaal bartamaha usha. Waa maxay daqiiqadda firfircoonida kubbadda ee ku saabsan dhidibka wareegga?

La yaqaan:

Cufka kubbadda 1 (m ₁ ) = 100 garaam = 100/1000 = 0.1 kg

Masaafada kubbadda 1 iyo dhidibka wareegga (r ₁ ) = 30 cm = 30/100 = 0.3 m

Cufka kubbadda (m2 ₎ = 200 garaam = 200/1000 = 0.2 kg

Masaafada kubbadda 2aad iyo dhidibka wareegga (r ₂ ) = 30 cm = 30/100 = 0.3 m

La doonayay: daqiiqad firfircoon oo kubadaha ah

Jawaab:

I = m ₁ r ₁ ² + m ₂ r ₂ ²

I = (0.1 kg)( 0.3 m) ² + (0.2 kg)( 0.3 m) ²

I = (0.1 kg)( 0.09 m ² ) + (0.2 kg)( 0.09 m ² )

I = 0.009 kg m ² + 0.018 kg m ²

I = 0.027 kg m ²

3. Kubbad 200-garaam ah, m ₁ iyo kubad 100-garaam ah, m _2, oo ay ku xiran yihiin ul dhererkeedu yahay 60 cm. Iska ilow cufka usha. Dhidibka wareegga wuxuu ku yaal kubbadda m _2. Waa maxay daqiiqadda firfircoonida kubbadaha. Iska ilow cufka usha.

La yaqaan:

Cufka kubbadda 1 (m ₁ ) = 2 00 garaam = 200/1000 = 0.2 kg

Masaafada u dhaxaysa kubbadda 1 iyo dhidibka wareegga (r ₁ ) = 60 cm = 60/100 = 0.6 m

Cufka kubbadda 2 (m2 ₎ = 100 garaam = 100/1000 = 0.1 kg

Masaafada u dhaxaysa kubbadda 2 iyo dhidibka wareegga (r ₂ ) = 0 m

La Doonayay: Daqiiqada firfircoonida kubadaha

Xalka:

I = m ₁ r ₁ ² + m ₂ r ₂ ²

I = (0.2 kg)( 0,6 m) ² + (0.2 kg)(0 ) ²

I = (0.2 kg)( 0.36 m ² ) + 0

I = 0.072 kg m ²

4. Cufnaanta kubbad kasta waa 100 garaam, oo lagu xiray xarig. Dhererka xariggu waa 60 cm, ballaca xarigguna waa 30 cm. Waa maxay daqiiqadda firfircoonida kubbadda ee ku saabsan dhidibka wareegga. Iska ilow cufka xarigga.

La yaqaan:

Cufka kubadda = m ₁ = m ₂ = m ₃ = m ₄ = 1 00 garaam = 100/1000 = 0.1 kg

Masaafada u dhaxaysa kubbadda iyo dhidibka wareegga (r ₁ ) = 30 cm = 30/100 = 0.3 m

Masaafada u dhaxaysa kubbadda 2 iyo dhidibka wareegga (r ₂ ) = 30 cm = 30/100 = 0.3 m

Masaafada u dhaxaysa kubbadda 3 iyo dhidibka wareegga (r ₃ ) = 30 cm = 30/100 = 0.3 m

Masaafada u dhaxaysa kubbadda 4 iyo dhidibka wareegga (r ₄ ) = 30 cm = 30/100 = 0.3 m

La yaqaan: Daqiiqada firfircoonida

Xalka:

Aniga = m₁ r₁² +m₂ r₂² +m₃ r₃² +m₄ r₄²

I = (0.1 kg)( 0.3 m) ² + (0.1 kg)( 0.3 m) ² + (0.1 kg)(0.3 m) ² + (0.1 kg)(0.3 m) ²

I = (0.1 kg)( 0.09 m ² ) + (0.1 kg)(0.09 m ^{2 )} + (0.1 kg)(0.09 m ² )

I = 0.036 kg m ²

Daqiiqadda firfircoonida shay adag

5. Waa maxay daqiiqadda firfircoonida usha isku midka ah ee 2-kg ah oo dhererkeedu yahay 2 m. Dhidibka wareegga wuxuu ku yaal bartamaha usha.

La yaqaan:

Cufka usha (M) = 2 kg

Dhererka usha (L) = 2 m

La Doonayo: Daqiiqada firfircoonida

Xalka:

Qaacidada daqiiqadda inertia marka dhidibka wareegga uu ku yaal bartamaha usha dheer ee isku midka ah:

I = (1/12) ML ²

I = (1/12) (2 kg)( 2 m) ²

I = (1/12) (2 kg)(4 m ² )

I = (1/12)(8 kg m ² )

I = 8/12 kg m ²

I = 2/3 kg m ²

6. Waa maxay daqiiqadda firfircoonida usha isku midka ah ee 2-kg ah oo dhererkeedu yahay 2 m? Dhidibka wareegga wuxuu ku yaal hal dhinac oo usha ah.

La yaqaan:

Cufka usha (M) = 2 kg

Dhererka usha adag (L) = 2 m

La Doonayo: Daqiiqada firfircoonida

Xalka:

Qaacidada daqiiqadda inertia marka dhidibka wareegga uu ku yaal hal dhammaad oo usha ah:

I = (1/3) ML ²

I = (1/3) (2 kg)( 2 m) ²

I = (1/3) (2 kg)(4 m ² )

I = (1/3)(8 kg m ² )

I = 8/3 kg m ²

7. Dhululubo adag oo 10-kg ah oo leh gacan 0.1 m. Dhidibka wareegga wuxuu ku yaal bartamaha dhululubada adag, oo lagu muujiyey sawirka hoose. Waa maxay daqiiqadda firfircoonida dhululubada?

La yaqaan:

Cufka dhululubo adag (M) = 10 kg

Radius-ka dhululubada (L) = 0.1 m

La Doonayo: Daqiiqada firfircoonida

La Doonayo: Daqiiqada firfircoonida

Xalka:

Qaacidada daqiiqadda inertia marka dhidibka wareeggu uu ku yaal bartamaha dhululubada:

I = (1/2) MR ²

I = (1/2) (10 kg)(0.1 m) ²

I = (1/2) (10 kg)(0.01 m ² )

I = (1/2)(0.1 kg m ² )

I = 0.05 kg m ²

8. Goob wareegsan oo isku mid ah oo 20-kg ah oo dhererkeedu yahay 0.1 m. Dhidibka wareegga ee ku yaal bartamaha wareegga waxaa lagu muujiyay sawirka hoose.

La yaqaan:

Cufka wareegga (M) = 20 kg

Gacanka kubbadda (L) = 0.1 m

La rabay: daqiiqad firfircooni ah

Xalka:

Qaacidada daqiiqadda inertia marka dhidibka wareegga uu ku yaal bartamaha wareegga:

I = (2/5) MR ²

I = (2/5)(20 kg)(0.1 m) ²

I = (2/5)(20 kg)(0.01 m ² )

I = (2/5)(0.2 kg m ² )

I = 0.4/5 kg m ²

I = 0.08 kg m ²

9. Saxan khafiif ah oo leydi ah oo 2-kg ah oo dhererkiisu yahay 0.5 m iyo ballaciisuna yahay 0.2 m. Dhidibka wareegga wuxuu ku yaal bartamaha saxanka leydi ee lagu muujiyay sawirka hoose. Waa maxay daqiiqadda firfircoonida leydiga?

La yaqaan:

Cufka saxanka leydi ah (M) = 2 kg

Dhererka saxanka (a) = 0.5 m

Ballaca saxanka (b) = 0.2 m

La Doonayo: Daqiiqada Inertia

Xalka:

Qaaciddada daqiiqadda inertia marka dhidibka wareegga uu ku yaal bartamaha saxanka:

I = (1/ 12 ) M (a ² + b ² )

I = (1/12)(2)(0.5 ² + 0.2 ² )

I = (2/12)(0.25 + 0.04)

I = (1/6)(0.29)

I = 0.29/6 kg m ²