Lokacin barbashi na inertia da jikin da ke da tauri - matsaloli da mafita

Lokacin inertia na barbashi

1. Kwallo mai nauyin gram 100 da aka haɗa da ƙarshen igiya mai tsawon santimita 30. Menene lokacin inertia na ƙwallon a kusa da axis na juyawa AB? Yi watsi da nauyin igiya.

An sani:

Axis na juyawa a AB

Mass ƙwallon (m) = gram 100 = 100/1000 = 0.1 kg

Nisa tsakanin ƙwallon da kuma axis na juyawa (r) = 30 cm = 0.3 m

SE busca: Lokacin rashin kuzari na ƙwallo (I)

Magani:

Ni = Mr.² = (0.1 kg)(0.3 m)²

I = (0.1 kg)(0.09 m²)

I = 0.009 kg m²

2. Kwallo mai nauyin gram 100, m₁, da kuma ƙwallon gram 200, m₂, wanda aka haɗa ta da sanda mai tsawon santimita 60. Ba a yi la'akari da nauyin sandar ba. Axis na juyawa yana tsakiyar sandar. Menene lokacin inertia na ƙwallon game da axis na juyawa?

An sani:

Nauyin ƙwallon 1 (m)₁) = gram 100 = 100/1000 = 0.1 kg

Nisa tsakanin ball 1 da kuma axis na juyawa (r)₁) = 30 cm = 30/100 = 0.3 m

Nauyin ƙwallon (m)₂) = gram 200 = 200/1000 = 0.2 kg

The distance na ball 2 da kuma axis na juyawa (r₂) = 30 cm = 30/100 = 0.3 m

Ana so: lokacin rashin ƙarfin ƙwallo

Amsa:

Ni = m₁ r₁² +m₂ r₂²

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)

Ni = 0.009 kg m² + 0.018 kg m²

Ni = 0.027 kg m²

3. Kwallo mai nauyin gram 200, m₁ da kuma ƙwallon gram 100, m_2, An haɗa shi da sanda mai tsawon santimita 60. Yi watsi da nauyin sandar. Axis na juyawa yana wurin ƙwallon m₂Menene lokacin rashin ƙarfin ƙwallo. Yi watsi da nauyin sandar.

An sani:

Nauyin ƙwallon 1 (m)₁) = 2gram 00 = 200/1000 = 0.2 kg

Nisa tsakanin ball 1 da kuma axis na juyawa (r)₁) = 60 cm = 60/100 = 0.6 m

Nauyin ƙwallon 2 (m)₂) = gram 100 = 100/1000 = 0.1 kg

Nisa tsakanin ball 2 da kuma axis na juyawa (r)₂= 0m

Ana so: Lokacin rashin kuzari na ƙwallo

Magani:

Ni = m₁ r₁² +m₂ r₂²

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 m²

4. Nauyin kowanne ƙwallon gram 100 ne, wanda aka haɗa ta hanyar igiya. Tsawon igiyar shine cm 60 kuma faɗin igiyar shine cm 30. Menene lokacin inertia na ƙwallon a kusa da axis na juyawa. Yi watsi da nauyin igiya.

An sani:

Nauyin ƙwallon = m₁ = m₂ = m₃ = m₄ = 1gram 00 = 100/1000 = 0.1 kg

Nisa tsakanin ƙwallon da kuma axis na juyawa (r)₁) = 30 cm = 30/100 = 0.3 m

Nisa tsakanin ball 2 da kuma axis na juyawa (r)₂) = 30 cm = 30/100 = 0.3 m

Nisa tsakanin ball 3 da kuma axis na juyawa (r)₃) = 30 cm = 30/100 = 0.3 m

Nisa tsakanin ball 4 da kuma axis na juyawa (r)₄) = 30 cm = 30/100 = 0.3 m

An sani: Lokacin inertia

Magani:

Ni = 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 m²) + (0.1 kg)(0.09 m²) + (0.1 kg)(0.09 m²) + (0.1 kg)(0.09 m²)

I = 0.036 kg m²

Lokacin inertia na abu mai tauri

5. Menene lokacin rashin ƙarfin sanda mai tsayin kilogiram 2 mai tsawon mita 2. Axis na juyawa yana tsakiyar sandar.

An sani:

Nauyin sanda (M) = 2 kg

Tsawon sandar (L) = 2 m

SE busca: Lokacin inertia

Magani:

Tsarin lokacin inertia lokacin da axis na juyawa yake a tsakiyar dogon sandar iri ɗaya:

I = (1/12) ML²

I = (1/12) (2 kg)(2 m)²

I = (1/12) (2 kg)(4 m)²)

I = (1/12)(8 kg m²)

I = 8/12 kg m²

I = 2/3 kg m²

6. Menene lokacin rashin ƙarfin sanda mai tsayin kilogiram 2 mai tsawon mita 2? Axis na juyawa yana nan a ƙarshen sandar.

An sani:

Nauyin sanda (M) = 2 kg

Tsawon sanda mai tauri (L) = 2 m

SE busca: Lokacin inertia

Magani:

Tsarin lokacin inertia lokacin da axis na juyawa yake a ƙarshen sandar:

I = (1/3) ML²

I = (1/3) (2 kg)(2 m)²

I = (1/3) (2 kg)(4 m)²)

I = (1/3)(8 kg m²)

I = 8/3 kg m²

7. Silinda mai ƙarfi mai nauyin kilogiram 10 tare da radius na mita 0.1. Axis na juyawa yana tsakiyar silinda mai ƙarfi, wanda aka nuna a cikin hoton da ke ƙasa. Menene lokacin inertia na silinda?

An sani:

Nauyin silinda mai ƙarfi (M) = 10 kg

Radius na silinda (L) = 0.1 m

SE busca: Lokacin inertia

SE busca: Lokacin inertia

Magani:

Tsarin lokacin inertia lokacin da axis na juyawa yake a tsakiyar silinda:

I = (1/2) MR²

I = (1/2) (10 kg)(0.1 m)²

I = (1/2) (10 kg)(0.01 m)²)

I = (1/2)(0.1 kg m²)

I = 0.05 kg m²

8. Wani yanki mai nauyin kilogiram 20 mai tsawon mita 0.1. An nuna axis na juyawa da ke tsakiyar yankin a cikin hoton da ke ƙasa.

An sani:

Nauyin ƙwallo (M) = 20 kg

Radius na ƙwallo (L) = 0.1 m

SE busca: wani lokaci na rashin kuzari

Magani:

Tsarin lokacin inertia lokacin da axis na juyawa yake a tsakiyar ƙwallo:

I = (2/5) MR²

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 m²

I = 0.08 kg m²

9. Faranti mai sirara mai nauyin kilogiram 2, mai tsawon mita 0.5 da faɗin mita 0.2. Axis na juyawa yana tsakiyar farantin mai kusurwa huɗu da aka nuna a cikin hoton da ke ƙasa. Menene lokacin inertia na murabba'in?

An sani:

Nauyin farantin murabba'i mai kusurwa huɗu (M) = 2 kg

Tsawon farantin (a) = 0.5 m

Faɗin farantin (b) = 0.2 m

Ana so: Lokacin inertia

Magani:

Tsarin lokacin inertia lokacin da axis na juyawa yake a tsakiyar farantin:

I = (1/12) M (a² + b²)

I = (1/12)(2)(0.5)² + 0.2²)

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

I = (1/6)(0.29)

I = 0.29/6 kg m²