Isikhathi sezinhlayiya ze-inertia kanye nemizimba eqinile - izinkinga nezixazululo

Isikhathi sokungabi namandla kwenhlayiya

1. Ibhola elingamagremu ayi-100 elixhunywe kolunye uhlangothi lwentambo enobude obungamasentimitha angama-30. Iyini isikhathi sokungapheleli kwebhola mayelana ne-axis yokujikeleza i-AB? Unganaki isisindo sentambo.

Kwaziwa:

I-axis yokujikeleza ku-AB

Ibhola eliyisisindo (m) = amagremu ayi-100 = 100/1000 = 0.1 kg

Ibanga phakathi kwebhola kanye ne-axis yokujikeleza (r) = 30 cm = 0.3 m

Okufunwayo: Isikhathi sokungakhathali kwebhola (I)

Isixazululo:

I = mr ² = (0.1 kg)(0.3 m) ²

I = (0.1 kg)(0.09 ^m2 )

I = 0.009 kg m ²

[irp]

2. Ibhola elingamagremu ayi-100, m ₁ , kanye nebhola elingamagremu angama-200, m ₂ , elixhunywe ngenduku enobude obungamasentimitha angama-60. Isisindo senduku asinakwa. I-axis yokujikeleza itholakala maphakathi nenduku. Iyini isikhathi sokungapheleli kwebhola mayelana ne-axis yokujikeleza?

Kwaziwa:

Isisindo sebhola 1 (m ₁ ) = 100 amagremu = 100/1000 = 0.1 kg

Ibanga lebhola 1 kanye ne-axis yokujikeleza (r ₁ ) = 30 cm = 30/100 = 0.3 m

Isisindo sebhola (m ₂ ) = 200 amagremu = 200/1000 = 0.2 kg

Ibanga lebhola 2 kanye ne-axis yokujikeleza (r ₂ ) = 30 cm = 30/100 = 0.3 m

Kufunwa: umzuzu wokungabi namandla kwamabhola

Impendulo:

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 m2 ⁾ + (0.2 kg)( 0.09 ^m2 )

I = 0.009 kg m ² + 0.018 kg m ²

I = 0.027 kg m ²

[irp]

3. Ibhola elingamagremu angu-200, m ₁ kanye nebhola elingamagremu angu-100, m _2, elixhunywe ngenduku enobude obungamasentimitha angu-60. Unganaki isisindo senduku. I-axis yokujikeleza itholakala ebholeni m _2. Iyini isikhathi sokungapheleli kwamabhola. Unganaki isisindo senduku.

Kwaziwa:

Isisindo sebhola 1 (m ₁ ) = 2 00 amagremu = 200/1000 = 0.2 kg

Ibanga eliphakathi kwebhola 1 kanye ne-axis yokujikeleza (r ₁ ) = 60 cm = 60/100 = 0.6 m

Isisindo sebhola 2 (m ₂ ) = 100 amagremu = 100/1000 = 0.1 kg

Ibanga eliphakathi kwebhola 2 kanye ne-axis yokujikeleza (r ₂ ) = 0 m

Okufunwayo: Isikhathi sokungakhathali kwamabhola

Isixazululo:

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 ^m2 ) + 0

I = 0.072 kg m ²

[irp]

4. Isisindo sebhola ngalinye singamagremu ayi-100, sixhunywe ngentambo. Ubude bentambo bungama-60 cm kanti ububanzi bentambo bungama-30 cm. Iyini isikhathi sokungapheleli kwebhola mayelana ne-axis yokujikeleza. Unganaki isisindo sentambo.

Kwaziwa:

Isisindo sebhola = m ₁ = m ₂ = m ₃ = m ₄ = 1 00 amagremu = 100/1000 = 0.1 kg

Ibanga eliphakathi kwebhola kanye ne-axis yokujikeleza (r ₁ ) = 30 cm = 30/100 = 0.3 m

Ibanga eliphakathi kwebhola 2 kanye ne-axis yokujikeleza (r ₂ ) = 30 cm = 30/100 = 0.3 m

Ibanga eliphakathi kwebhola 3 kanye ne-axis yokujikeleza (r ₃ ) = 30 cm = 30/100 = 0.3 m

Ibanga eliphakathi kwebhola 4 kanye ne-axis yokujikeleza (r ₄ ) = 30 cm = 30/100 = 0.3 m

Okudumile: Isikhathi sokungahlali kahle

Isixazululo:

Mina = 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 + (0.1 kg)(0.3 m) ²

I = (0.1 kg)( 0.09 m2 ⁾ + (0.1 kg)(0.09 m2 ⁾ + (0.1 kg)(0.09 m2 ⁾ + (0.1 kg)(0.09 ^m2 )

I = 0.036 kg m ²

[irp]

Isikhathi sokungahlali kahle kwento eqinile

5. Iyini isikhathi sokungakhathali kwenduku ende engu-2 kg enobude obungu-2 m. I-axis yokujikeleza itholakala maphakathi nenduku.

Kwaziwa:

Isisindo senduku (M) = 2 kg

Ubude benduku (L) = 2 m

Okufunwayo: Isikhathi sokungahlaliseki

Isixazululo:

Ifomula yomzuzu we-inertia lapho i-axis yokujikeleza itholakala enkabeni yenduku ende efanayo:

I = (1/12) ML ²

I = (1/12) (2 kg)( 2 m) ²

I = (1/12) (2 kg)(4 ^m2 )

I = (1/12)(8 kg ^m2 )

I = 8/12 kg m ²

I = 2/3 kg m ²

[irp]

6. Iyini isikhathi sokungakhathali kwenduku ende engu-2 kg enobude obungu-2 m? I-axis yokujikeleza itholakala ekugcineni kwenduku.

Kwaziwa:

Isisindo senduku (M) = 2 kg

Ubude benduku eqinile (L) = 2 m

Okufunwayo: Isikhathi sokungahlaliseki

Isixazululo:

Ifomula yomzuzu we-inertia lapho i-axis yokujikeleza itholakala ekugcineni kwenduku:

I = (1/3) ML ²

I = (1/3) (2 kg)( 2 m) ²

I = (1/3) (2 kg)(4 ^m2 )

I = (1/3)(8 kg ^m2 )

I = 8/3 kg m ²

[irp]

7. Isilinda esiqinile esingamakhilogremu ayi-10 esine-radius engu-0.1 m. I-axis yokujikeleza itholakala maphakathi nesilinda esiqinile, eboniswe esithombeni esingezansi. Iyini isikhathi sokungapheleli kwesilinda?

Kwaziwa:

Isisindo sesilinda esiqinile (M) = 10 kg

Irediyasi yesilinda (L) = 0.1 m

Okufunwayo: Isikhathi sokungakhathali

Okufunwayo: Isikhathi sokungakhathali

Isixazululo:

Ifomula yesikhathi se-inertia lapho i-axis yokujikeleza itholakala enkabeni yesilinda:

I = (1/2) MR ²

I = (1/2) (10 kg)(0.1 m) ²

I = (1/2) (10 kg)(0.01 ^m2 )

I = (1/2)(0.1 kg ^m2 )

I = 0.05 kg m ²

8. Imbulunga efanayo engamakhilogremu angu-20 enobude obungu-0.1 m. I-axis yokujikeleza etholakala maphakathi nembulunga iboniswe esithombeni esingezansi.

Kwaziwa:

Isisindo sembulunga (M) = 20 kg

Irediyasi yesiyingi (L) = 0.1 m

Kufunwa: umzuzu wokungabi naso isikhathi

Isixazululo:

Ifomula yomzuzu we-inertia lapho i-axis yokujikeleza itholakala enkabeni yesphere:

I = (2/5) MR ²

I = (2/5)(20 kg)(0.1 m) ²

I = (2/5)(20 kg)(0.01 ^m2 )

I = (2/5)(0.2 kg ^m2 )

I = 0.4/5 kg m ²

I = 0.08 kg m ²

[irp]

9. Ipuleti elincane elingunxande elingamakhilogremu angu-2 elinobude obungu-0.5 m kanye nobubanzi obungu-0.2 m. I-axis yokujikeleza itholakala maphakathi nepuleti elingunxande eliboniswe esithombeni esingezansi. Iyini isikhathi sokungapheleli konxande?

Kwaziwa:

Isisindo sepuleti elingunxande (M) = 2 kg

Ubude bepuleti (a) = 0.5 m

Ububanzi bepuleti (b) = 0.2 m

Okufunwayo: Isikhathi Sokungabi Naso Isikhathi

Isixazululo:

Ifomula yesikhathi se-inertia lapho i-axis yokujikeleza itholakala maphakathi nepuleti:

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