Waqtiga inertia

1. Daqiiqada firfircoonida walaxda

Dib u eeg walax wareegaysa. Walaxda leh cuf m waxaa la siiyaa xoogga F si walaxdu ugu wareegto dhidibka O. Walaxda waa r marka laga reebo dhidibka wareegga. Marka hore, walaxdu waxay ku nasan tahay (v = 0). Ka dib marka ay ku dhaqaaqdo xoogga F, walaxdu waxay ku dhaqaaqdaa xawaare gaar ah si walaxyadu u yeeshaan dardargelin tangential ah. Xiriirka ka dhexeeya xoogga (F), cufnaanta (m), iyo dardargelinta tangential ee walaxyada waxaa lagu muujiyaa isle'egta 3:

F = ma _tan (Isleegta 3)

Walxaha ayaa wareegaya si ay walxuhu u yeeshaan dardargelin xagal ah. Xiriirka ka dhexeeya dardargelinta tangential iyo dardargelinta xagal waxaa lagu muujiyaa isle'egta 4:

tan = r α ₍ Isleeg 4)

Ku beddel a ee isla'egta 3 a ee isla'egta 4:

F = mr α

r F = mr ² α

τ = (mr ² ) α (Isleeg 5)

r F waa daqiiqadda xoogga, mr ^2- na waa daqiiqadda firfircoonida ee walaxda. Isla'egta 5 waxay sheegaysaa xiriirka ka dhexeeya daqiiqadda xoogga, daqiiqadda firfircoonida, iyo dardargelinta xagasha ee walaxda wareegaysa. Isla'egta 5 waa isla'egta sharciga labaad ee Newton ee walxaha wareegaya.

Daqiiqada firfircoonida walax waa natiijada cufka walaxda (m) iyo labajibbaaranaha masaafada u dhaxaysa walaxda leh dhidibka wareegga (r ² ).

I = mr ² (Isleeg 6)

I = daqiiqadda firfircoonida walaxda, m = cufka walaxda, r = masaafada u dhaxaysa walaxda iyo dhidibka wareegga. Isle'egta 6 waxaa loo isticmaalaa in lagu go'aamiyo daqiiqadda firfircoonida walaxda.

3.2 Tusaalooyin dhibaatooyin ah oo ku saabsan daqiiqadda firfircoonida ee walaxda

Muunad dhibaato 1.

Walax culeyskeedu yahay 2 kg ayaa lagu xidhay xarig dhererkiisu yahay 0.5 mitir ka dibna waa la wareegay. Waa maxay daqiiqadda firfircoonida walxaha marka la wareegayo?

Solution:

Aniga = Mudane ²

I = (2 kg) (0.5 m) ²

I = 0.5 kg m ²

Muunad dhibaato 2.

Laba qaybood, mid walba cufkiisu yahay 2 kg iyo 4 kg, waxaa isku xira silig khafiif ah, halkaas oo dhererka siliggu uu yahay 2 mitir. Iska ilow cufnaanta fiilooyinka. Go'aami daqiiqadda firfircoonida labada qaybood, haddii:

a) dhidibka wareegga wuxuu ku yaal labada qaybood ee u dhexeeya

Solution:

I = m ₁ r ₁ ² + m ₂ r ₂ ²

I = (2)(12) + (4)(12)

I = 2 + 4

I = 6 kg m ²

b) dhidibka wareegga wuxuu ku jiraa masaafad dhan 0.5 mitir u jirta walaxda oo miisaankeedu yahay 2 kg.

I = m ₁ r ₁ ² + m ₂ r ₂ ²

I = (2)(0.5 ² ) + (4)(1.5 ² )

I = (2)(0.25) + (4)(2.25)

I = 0.5 + 9

I = 9.5 kg m ²

c) dhidibka wareegga wuxuu ku jiraa masaafo dhan 0.5 mitir u jirta walaxda oo miisaankeedu yahay 4 kg.

I = m ₁ r ₁ ² + m ₂ r ₂ ²

I = (2)(1.52) + (4)(0.5 ² )

I = (2)(2.25) + (4)(0.25)

I = 4.5 + 1

I = 5.5 kg m ²

Iyada oo ku saleysan natiijooyinka xisaabinta kor ku xusan, daqiiqadda inertia waxaa si xooggan u saameeya goobta dhidibka wareegga. Inkasta oo qaabka iyo cabbirku isku mid yihiin sababtoo ah goobta dhidibka wareegga way kala duwan yihiin, daqiiqadda inertia sidoo kale way ka duwan tahay.

Walxaha u dhow dhidibka wareegga waxay leeyihiin daqiiqad yar oo firfircooni ah, halka walxaha ka fog dhidibka wareegga ay leeyihiin daqiiqad weyn oo firfircooni ah. Haddii aan u qaadanno in labada walxood ee kor ku xusan ay yihiin walxo adag, markaa walxo kastaa waxay ku dhow yihiin dhidibka wareegga.

waxay leedahay daqiiqad ka yar oo firfircooni ah marka loo eego daqiiqadda firfircooni ee walaxda oo ka fog dhidibka wareegga.

3.3 Daqiiqad firfircooni ah oo ah jir adag oo isku mid ah

Walxaha adag waxay ka kooban yihiin walxo badan. Daqiiqada firfircoonida jirka adag waa wadarta guud ee daqiiqadaha firfircoonida ee walax kasta oo dhista walaxda.

Aniga = Σ mr ²

Aniga = m₁ r₁² +m₂ r₂² +m₃ r₃² + ….. + m_n r_n²

Si loo go'aamiyo daqiiqadda inertia ee shay adag, waxaan u baahanahay inaan dib u eegno shayga marka uu wareego sababtoo ah goobta dhidibka wareegga wuxuu saameeyaa daqiiqadda inertia ee shayga. Daqiiqadda inertia (I) ee walax kasta waxay sidoo kale ku xiran tahay cufka (m) ee walaxda iyo labajibbaaranka masaafada (r ² ) ee walaxda ka timaadda dhidibka wareegga. Cufka dhammaan walxaha dhisa walaxda waa cufka walaxda.

Dhibaatadu waxay tahay, masaafada walax kasta u jirta dhidibka wareegga way kala duwan tahay.

Dib u eeg hoos u dhaca qaacidada daqiiqadda firfircoonida ee giraanta khafiifka ah oo leh faraha R iyo cufnaanta M.

Haddii dhidibka wareeggu uu ku yaal bartamaha giraanta, dhammaan walxaha giraanta khafiifka ah waxay ka yimaadaan dhidibka wareegga. Daqiiqadda firfircoonida giraanta khafiifka ah waxay la mid tahay daqiiqadda firfircoonida dhammaan walxaha:

Aniga = Σ mr²

Aniga = m₁ r₁² +m₂ r₂² +m₃ r₃² + ….. + m_n r_n²

Cufka dhammaan walxaha = cufka giraanta khafiifka ah (M)

I = M (r ₁ ² + r ₂ ² + r ₃ ² + ….. + r _n ² )

Walax kasta oo ka mid ah giraanta khafiifka ah waa r laga bilaabo dhidibka wareegga si r ₁ = r ₂ = r ₃ = rn = R

Isle'egta daqiiqadda firfircoonida ee giraanta khafiifka ah:

I = MR ²

I = daqiiqadda firfircoonida giraanta khafiifka ah, M = cufka giraanta khafiifka ah, R = gacanka giraanta khafiifka ah.

Ka waran haddii dhidibka wareeggu uusan ku oolin bartamaha giraanta? Haddii dhidibka wareeggu uusan ku oolin bartamaha giraanta, qaacidada daqiiqadda inertia ee giraanta khafiifka ah laguma soo saari karo habka kor ku xusan.

sababtoo ah masaafada walax kasta u jirta dhidibka wareegga way ka duwan tahay. Soo saarista qaacidada daqiiqadda inertia ee dhibaato sidan oo kale ah laguma soo hadal qaadin mowduucan.

Qaacidada daqiiqadda firfircoonida ee walxaha adag qaarkood

3.4 Muunad dhibaato ah oo ku saabsan daqiiqadda firfircoonida jirka adag ee isku midka ah

Muunad dhibaato 1aad:

Dhululubo usha AB waxay leedahay miisaan dhan 3 kg marka la dhex wareego B,

Daqiiqadda inertia waa 27 kg m ^2. Waa maxay daqiiqadda inertia haddii

lagu wareejiyay C?

Solution:

Solution:

Qaacidada daqiiqadda inertia ee usha adag ee isku midka ah (dhidibka wareegga waa bartamaha usha):

I = 1/12 ML ²

27 = (1/12) ML ²

(27)(12) = ML ²

324 = ML ²

Qaacidada daqiiqadda inertia ee ul adag oo isku mid ah (dhidibka wareegga ee geeska usha):

I = 1/3 ML ²

I = 1/3 (324)

I = 108 kg m ²