Motsotso oa likaroloana tse sa sebetseng le 'mele e tiileng - mathata le litharollo

Motsotso oa inertia ea karoloana

1. Bolo ea ligrama tse 100 e hokahaneng pheletsong e 'ngoe ea thapo e bolelele ba 30 cm. Nako ea ho se sebetse hantle ha bolo e mabapi le axis ea potoloho AB ke efe? Hlokomoloha boima ba thapo.

Tse tsejoang:

Mokhahlelo oa potoloho ho AB

Bolo e boima (m) = 100 grams = 100/1000 = 0.1 kg

Sebaka se pakeng tsa bolo le mothapo oa potoloho (r) = 30 cm = 0.3 m

Ho batloa: Motsotso oa ho se tsitse ha bolo (I)

Tharollo:

Ke = monghadi ² = (0.1 kg)(0.3 m) ²

I = (0.1 kg)(0.09 ^m2 )

I = 0.009 kg m ²

2. Bolo ea ligrama tse 100, m ₁ , le bolo ea ligrama tse 200, m ₂ , li hokahantsoe ke thupa e bolelele ba 60 cm. Boima ba thupa ha bo hlokomolohuoe. Mothapo oa potoloho o bohareng ba thupa. Nako ea ho se sebetse hantle ha bolo ke efe mabapi le mothapo oa potoloho?

Tse tsejoang:

Boima ba bolo 1 (m ₁ ) = 100 grams = 100/1000 = 0.1 kg

Sebaka sa bolo 1 le axis ea potoloho (r ₁ ) = 30 cm = 30/100 = 0.3 m

Boima ba bolo (m ₂ ) = 200 grams = 200/1000 = 0.2 kg

Sebaka sa bolo 2 le axis ea potoloho (r ₂ ) = 30 cm = 30/100 = 0.3 m

Ho batloa: motsotso oa ho hloka botsitso ha libolo

Karabo:

Ke = 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

3. Bolo ea ligrama tse 200, m ₁ le bolo ea ligrama tse 100, m _2, li hokahantsoe ke thupa e bolelele ba 60 cm. Hlokomoloha boima ba thupa. Mothapo oa potoloho o ho bolo ea m _2. Motsotso oa ho se sebetse hantle ha libolo ke ofe? Hlokomoloha boima ba thupa.

Tse tsejoang:

Boima ba bolo 1 (m ₁ ) = 2 00 grams = 200/1000 = 0.2 kg

Sebaka se pakeng tsa bolo ea 1 le axis ea potoloho (r ₁ ) = 60 cm = 60/100 = 0.6 m

Boima ba bolo 2 (m ₂ ) = 100 grams = 100/1000 = 0.1 kg

Sebaka se pakeng tsa bolo ea 2 le axis ea potoloho (r ₂ ) = 0 m

Ho batloa: Motsotso oa ho hloka botsitso ha libolo

Tharollo:

Ke = 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

4. Boima ba bolo ka 'ngoe ke ligrama tse 100, tse hokahaneng ka thapo. Bolelele ba thapo ke 60 cm 'me bophara ba thapo ke 30 cm. Nako ea ho se sebetse hantle ha bolo ke efe mabapi le axis ea potoloho? Hlokomoloha boima ba thapo.

Tse tsejoang:

Boima ba bolo = m ₁ = m ₂ = m ₃ = m ₄ = 1 00 grams = 100/1000 = 0.1 kg

Sebaka se pakeng tsa bolo le mothapo oa potoloho (r ₁ ) = 30 cm = 30/100 = 0.3 m

Sebaka se pakeng tsa bolo ea 2 le axis ea potoloho (r ₂ ) = 30 cm = 30/100 = 0.3 m

Sebaka se pakeng tsa bolo ea 3 le axis ea potoloho (r ₃ ) = 30 cm = 30/100 = 0.3 m

Sebaka se pakeng tsa bolo ea 4 le axis ea potoloho (r ₄ ) = 30 cm = 30/100 = 0.3 m

Tse tsejoang: Motsotso oa ho se inertia

Tharollo:

Ke = 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

Motsotso oa ho hloka botsitso ha ntho e thata

5. Nako ea ho se sebetse hantle ha thupa e telele ea 2 kg e lekanang e bolelele ba limithara tse 2 ke efe. Mothapo oa ho potoloha o bohareng ba thupa.

Tse tsejoang:

Boima ba thupa (M) = 2 kg

Bolelele ba thupa (L) = 2 m

Ho batloa: Motsotso oa ho se inertia

Tharollo:

Foromo ea motsotso oa inertia ha motsoako oa potoloho o le bohareng ba molamu o molelele o ts'oanang:

Ke = (1/12) ML ²

Ke = (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

6. Nako ea ho se sebetse hantle ha thupa e bolelele ba 2 kg e lekanang e bolelele ba limithara tse 2 ke efe? Mothapo oa potoloho o fumaneha pheletsong e 'ngoe ea thupa.

Tse tsejoang:

Boima ba thupa (M) = 2 kg

Bolelele ba thupa e thata (L) = 2 m

Ho batloa: Motsotso oa ho se inertia

Tharollo:

Foromo ea motsotso oa inertia ha motsoako oa potoloho o le pheletsong e 'ngoe ea molamu:

Ke = (1/3) ML ²

Ke = (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

7. Silindara e tiileng ea boima ba lik'hilograma tse 10 e nang le radius ea 0.1 m. Mothapo oa potoloho o bohareng ba silindara e tiileng, o bontšitsoeng setšoantšong se ka tlase. Nako ea ho se sebetse ha silindara ke efe?

Tse tsejoang:

Boima ba silindara e tiileng (M) = 10 kg

Radius ea silindara (L) = 0.1 m

Ho batloa: Motsotso oa ho se inertia

Ho batloa: Motsotso oa ho se inertia

Tharollo:

Foromo ea motsotso oa inertia ha motsoako oa potoloho o le bohareng ba silindara:

Ke = (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. Selikalikoe se lekanang sa 20 kg se bolelele ba 0.1 m. Mothapo oa potoloho o bohareng ba selikalikoe o bontšitsoe setšoantšong se ka tlase.

Tse tsejoang:

Boima ba selika-likoe (M) = 20 kg

Radius ea selika-likoe (L) = 0.1 m

Ho batloa: motsotso oa ho se inertia

Tharollo:

Foromo ea motsotso oa inertia ha motsoako oa potoloho o le bohareng ba lebala:

Ke = (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

9. Poleiti e tšesaane e khutlonnetsepa ea 2-kg e bolelele ba 0.5 m le bophara ba 0.2 m. Mothapo oa potoloho o bohareng ba poleiti e khutlonnetsepa e bontšitsoeng setšoantšong se ka tlase. Nako ea ho se sebetse hantle ha khutlonnetsepa ke efe?

Tse tsejoang:

Boima ba poleiti e khutlonnetsepa (M) = 2 kg

Bolelele ba poleiti (a) = 0.5 m

Bophara ba poleiti (b) = 0.2 m

Ho Batloa: Nako ea Boima

Tharollo:

Foromo ea motsotso oa inertia ha motsoako oa potoloho o le bohareng ba poleiti:

Ke = (1/12 ) M (a ² + b ² )

Ke = (1/12)(2)(0.5 ² + 0.2 ² )

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

Ke = (1/6)(0.29)

I = 0.29/6 kg m ²