Nthawi ya tinthu tating'onoting'ono topanda mphamvu komanso matupi olimba - mavuto ndi mayankho

Nthawi ya inertia ya tinthu tating'onoting'ono

1. Mpira wa magalamu 100 wolumikizidwa kumapeto kwa chingwe chokhala ndi kutalika kwa masentimita 30. Kodi nthawi ya kulephera kwa mpirawo ndi yotani pa mzere wozungulira wa AB? Musanyalanyaze kulemera kwa chingwe.

Zodziwika:

Mzere wozungulira pa AB

Misa mpira (m) = magalamu 100 = 100/1000 = 0.1 kg

Mtunda pakati pa mpira ndi mzere wozungulira (r) = 30 cm = 0.3 m

SE basi: Nthawi ya kutopa kwa mpira (I)

Yankho:

Ine = Mr.² = (0.1 kg)(0.3 m)²

I = (0.1 kg)(0.09 m²)

I = 0.009 kg m²

2. Mpira wa magalamu 100, m₁, ndi mpira wa magalamu 200, m₂, yolumikizidwa ndi ndodo yotalika masentimita 60. Kulemera kwa ndodo sikunyalanyazidwa. Mzere wozungulira uli pakati pa ndodo. Kodi nthawi ya inertia ya mpira ndi yotani pa mzere wozungulira?

Zodziwika:

Kulemera kwa mpira 1 (m₁) = Magalamu 100 = 100/1000 = 0.1 kg

Mtunda wa mpira 1 ndi mzere wozungulira (r)₁) = 30 cm = 30/100 = 0.3 m

Uzito wa mpira (m₂) = magalamu 200 = 200/1000 = 0.2 kg

The mtunda ya mpira 2 ndi mzere wozungulira (r)₂) = 30 cm = 30/100 = 0.3 m

Akufuna: mphindi ya inertia ya mipira

Yankho:

Ine = 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 mamita²) + (0.2 kg)(0.09 mamita²)

I = 0.009 kg m² + 0.018 kg m²

I = 0.027 kg m²

3. Mpira wa magalamu 200, m₁ ndi mpira wa gramu 100, m_2, yolumikizidwa ndi ndodo yotalika masentimita 60. Musanyalanyaze kulemera kwa ndodoyo. Mzere wozungulira uli pa mpira m₂Kodi nthawi ya kusagwira bwino ntchito kwa mipira ndi yotani? Musanyalanyaze kulemera kwa ndodo.

Zodziwika:

Kulemera kwa mpira 1 (m₁= = 2Magalamu 00 = 200/1000 = 0.2 kg

Mtunda pakati pa mpira 1 ndi mzere wozungulira (r)₁) = 60 cm = 60/100 = 0.6 m

Kulemera kwa mpira 2 (m₂) = magalamu 100 = 100/1000 = 0.1 kg

Mtunda pakati pa mpira 2 ndi mzere wozungulira (r)₂) = 0 m

Akufuna: Nthawi ya inertia ya mipira

Yankho:

Ine = m₁ r₁² +m₂ r₂²

I = (0.2 kg)(0,6 m)² + (0.2 kg)(0)²

I = (0.2 kg)(0.36 mamita²) + 0

I = 0.072 kg m²

4. Kulemera kwa mpira uliwonse ndi magalamu 100, olumikizidwa ndi chingwe. Kutalika kwa chingwe ndi 60 cm ndipo m'lifupi mwa chingwe ndi 30 cm. Kodi nthawi ya kusagwira bwino kwa mpira ndi yotani pa mzere wozungulira? Musanyalanyaze kulemera kwa chingwe.

Zodziwika:

Unyinji wa mpira = m₁ = m₂ = m₃ = m₄ = 1Magalamu 00 = 100/1000 = 0.1 kg

Mtunda pakati pa mpira ndi mzere wozungulira (r)₁) = 30 cm = 30/100 = 0.3 m

Mtunda pakati pa mpira 2 ndi mzere wozungulira (r)₂) = 30 cm = 30/100 = 0.3 m

Mtunda pakati pa mpira 3 ndi mzere wozungulira (r)₃) = 30 cm = 30/100 = 0.3 m

Mtunda pakati pa mpira 4 ndi mzere wozungulira (r)₄) = 30 cm = 30/100 = 0.3 m

Zodziwika: Mphindi ya inertia

Yankho:

Ine = 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 mamita²) + (0.1 kg)(0.09 m²) + (0.1 kg)(0.09 m²) + (0.1 kg)(0.09 m²)

I = 0.036 kg m²

Nthawi ya inertia ya chinthu cholimba

5. Kodi ndodo yofanana yolemera makilogalamu awiri ndi kutalika kwa mamita awiri ndi chiyani? Mzere wozungulira uli pakati pa ndodo.

Zodziwika:

Kulemera kwa ndodo (M) = 2 kg

Kutalika kwa ndodo (L) = 2 m

SE basi: Mphindi ya inertia

Yankho:

Fomula ya mphindi ya inertia pamene mzere wozungulira uli pakati pa ndodo yayitali yofanana:

Ine = (1/12) ML²

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 m²

I = 2/3 kg m²

6. Kodi ndodo yofanana yolemera makilogalamu awiri ndi kutalika kwa mamita awiri imakhala ndi nthawi yotani? Mzere wozungulira uli kumapeto kwa ndodo.

Zodziwika:

Kulemera kwa ndodo (M) = 2 kg

Kutalika kwa ndodo yolimba (L) = 2 m

SE basi: Mphindi ya inertia

Yankho:

Fomula ya mphindi ya inertia pamene mzere wozungulira uli kumapeto kwa ndodo:

Ine = (1/3) ML²

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 m²

7. Silinda yolimba ya makilogalamu 10 yokhala ndi utali wa mamita 0.1. Mzere wozungulira uli pakati pa silinda yolimba, yomwe yawonetsedwa pachithunzi chili pansipa. Kodi nthawi ya inertia ya silinda ndi yotani?

Zodziwika:

Kulemera kwa silinda yolimba (M) = 10 kg

Utali wa silinda (L) = 0.1 m

SE basi: Nthawi ya inertia

SE basi: Nthawi ya inertia

Yankho:

Fomula ya mphindi ya inertia pamene mzere wozungulira uli pakati pa silinda:

Ine = (1/2) MR²

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 m²

8. Chipilala chofanana cha makilogalamu 20 chokhala ndi kutalika kwa 0.1 m. Mzere wozungulira womwe uli pakati pa chipilalacho wawonetsedwa pachithunzi chili pansipa.

Zodziwika:

Kulemera kwa mbulunga (M) = 20 kg

Utali wa mlengalenga (L) = 0.1 m

SE basi: mphindi ya kutopa

Yankho:

Fomula ya mphindi ya inertia pamene mzere wozungulira uli pakati pa bwalo:

Ine = (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. Mbale yopyapyala yolemera makilogalamu awiri yokhala ndi kutalika kwa mamita 0.5 ndi m'lifupi mwa mamita 0.2. Mzere wozungulira uli pakati pa mbale yopyapyala yomwe yawonetsedwa pachithunzi chili pansipa. Kodi nthawi ya kulephera kwa mzera ndi yotani?

Zodziwika:

Kulemera kwa mbale yozungulira (M) = 2 kg

Kutalika kwa mbale (a) = 0.5 m

M'lifupi mwa mbale (b) = 0.2 m

Akufuna: Mphindi ya inertia

Yankho:

Fomula ya mphindi ya inertia pamene mzere wozungulira uli pakati pa mbale:

Ine = (1/12M (a)² + b²)

Ine = (1/12)(2)(0.5² + 0.2²)

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

Ine = (1/6)(0.29)

I = 0.29/6 kg m²