Nguva yekusagadzikana kwezvikamu uye miviri yakaoma - matambudziko nemhinduro

Nguva yekusagadzikana kwechikamu

1. Bhora remagiramu zana rakabatana kune rimwe divi retambo ine hurefu hwemasendimita makumi matatu. Ndeipi nguva yekusashanda kwebhora pamusoro pechikamu chekutenderera AB? Usafuratira huremu hwetambo.

Zvinozivikanwa:

Kutenderera kwe axis pa AB

Bhora rehuremu (m) = magiramu zana = 100/1000 = 0.1 kg

Daro riri pakati pebhora ne axis yekutenderera (r) = 30 cm = 0.3 m

Kudiwa: Nguva yekusaita basa kwebhora (I)

Solution:

Ini = mr ² = (0.1 kg)(0.3 m) ²

I = (0.1 kg)(0.09 ^m2 )

I = 0.009 kg m ²

2. Bhora remagiramu zana, m ₁ , nebhora remagiramu mazana maviri, m ₂ , zvakabatana netsvimbo ine hurefu hwemasendimita makumi matanhatu. Huremu hwetsvimbo hahuna hanya. Akisi yekutenderera iri pakati petsvimbo. Ndeipi nguva yekusagadzikana kwebhora pamusoro peakisi yekutenderera?

Zvinozivikanwa:

Huremu hwebhora 1 (m ₁ ) = 100 magiramu = 100/1000 = 0.1 kg

Daro rebhora 1 uye axis yekutenderera (r ₁ ) = 30 cm = 30/100 = 0.3 m

Huremu hwebhora (m ₂ ) = 200 magiramu = 200/1000 = 0.2 kg

Daro rebhora 2 uye axis yekutenderera (r _{2 ) = 30} cm = 30/100 = 0.3 m

Kudiwa: nguva yekusagadzikana kwemabhora

Mhinduro:

Ini = 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. Bhora remagiramu 200, m ₁ uye bhora remagiramu 100, m _2, rakabatanidzwa netsvimbo ine hurefu hwemasendimita 60. Usafuratira huremu hwetsvimbo. Mutsetse wekutenderera uri pabhora m _2. Chii chinonzi nguva yekusashanda kwemabhora? Usafuratira huremu hwetsvimbo.

Zvinozivikanwa:

Huremu hwebhora 1 (m ₁ ) = 2 00 magiramu = 200/1000 = 0.2 kg

Daro riri pakati pebhora 1 ne axis yekutenderera (r ₁ ) = 60 cm = 60/100 = 0.6 m

Huremu hwebhora 2 (m ₂ ) = 100 magiramu = 100/1000 = 0.1 kg

Daro riri pakati pebhora 2 ne axis yekutenderera (r2 ₎ = 0 m

Kudiwa: Nguva yekusagadzikana kwemabhora

Solution:

Ini = 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. Huremu hwebhora rega rega hunosvika magiramu zana, hwakabatana netambo. Kureba kwetambo ndeye 60 cm uye upamhi hwetambo ndeye 30 cm. Ndeipi nguva yekusashanda kwebhora pamusoro pechikamu chekutenderera. Usafuratira huremu hwetambo.

Zvinozivikanwa:

Huremu hwebhora = m ₁ = m ₂ = m ₃ = m ₄ = 1 00 magiramu = 100/1000 = 0.1 kg

Daro riri pakati pebhora nechikamu chekutenderera (r ₁ ) = 30 cm = 30/100 = 0.3 m

Daro riri pakati pebhora 2 ne axis yekutenderera (r ₂ ) = 30 cm = 30/100 = 0.3 m

Daro riri pakati pebhora 3 ne axis yekutenderera (r ₃ ) = 30 cm = 30/100 = 0.3 m

Daro riri pakati pebhora 4 ne axis yekutenderera (r ₄ ) = 30 cm = 30/100 = 0.3 m

Inozivikanwa: Nguva yekusagadzikana

Solution:

Ini = 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

Nguva yekusagadzikana kwechinhu chakasimba

5. Chii chinonzi nguva yekusashanda kwetsvimbo yakaenzana ine hurefu hwe2 kg ine hurefu hwe2 m. Chikamu chekutenderera chiri pakati petsvimbo.

Zvinozivikanwa:

Huremu hwetsvimbo (M) = 2 kg

Kureba kwetsvimbo (L) = 2 m

Zvinodiwa: Nguva yekusaita basa

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pakati petsvimbo refu yakafanana:

Ini = (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

6. Chii chinotora nguva yekusashanda kwetsvimbo yakaenzana ine hurefu hwe2 kg ine hurefu hwe2 m? Chikamu chekutenderera chiri pamucheto wetsvimbo.

Zvinozivikanwa:

Huremu hwetsvimbo (M) = 2 kg

Kureba kwetsvimbo yakasimba (L) = 2 m

Zvinodiwa: Nguva yekusaita basa

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pamugumo mumwe wetsvimbo:

Ini = (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

7. Sirinda yakasimba ye10-kg ine radius ye 0.1 m. Nzvimbo yekutenderera iri pakati pesirinda yakasimba, inoratidzwa mumufananidzo uri pazasi. Ndeipi nguva yekusashanda kwesirinda?

Zvinozivikanwa:

Huremu hwesirinda yakasimba (M) = 10 kg

Nharaunda yesirinji (L) = 0.1 m

Zvinodiwa: Nguva yekusaita basa

Zvinodiwa: Nguva yekusaita basa

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pakati pesilinda:

Ini = (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. Dura rakafanana rinorema 20 kg rine urefu hwe 0.1 m. Mutsetse wekutenderera uri pakati pedura unoratidzwa mumufananidzo uri pazasi.

Zvinozivikanwa:

Huremu hwebhora (M) = 20 kg

Nharaunda yebhora (L) = 0.1 m

Zvinodiwa: nguva yekusaita basa

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pakati pebhora:

Ini = (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. Ndiro yakatetepa ye 2 kg ine hurefu hwe 0.5 m uye upamhi hwe 0.2 m. Nzvimbo yekutenderera iri pakati pendiro yakatetepa inoratidzwa mumufananidzo uri pazasi. Ndeipi nguva yekusashanda kwendiro?

Zvinozivikanwa:

Huremu hweplate rectangular (M) = 2 kg

Kureba kweplate (a) = 0.5 m

Upamhi hweplate (b) = 0.2 m

Zvinodiwa: Nguva yeKusagadzikana

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pakati peplate:

I = (1/12 ) M (a ² + b ² )

Ini = (1/12)(2)(0.5 ² + 0.2 ² )

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

Ini = (1/6)(0.29)

I = 0.29/6 kg m ²