8 - § . Qattiq jismning qo‘zg ‘almas o ‘q atrofidagi aylanma

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K z = ■ (88.2) (74.1) form ulaga k o ‘ra: I z =

8 8 - § . Qattiq jismning qo‘zg ‘almas o ‘q atrofidagi aylanma
harakati differensial tenglamasi
Q attiq jism ning q o ‘zg‘alm as o ‘q atro fi
d a g i a y la n m a h a ra k a ti te x n ik a d a k o ‘p
u c h ra y d ig a n h a ra k a tla rd a n b iri. S hu nin g
u c h u n jism n in g a y la n ish o ‘qiga n isb a ta n
k in etik m o m en tin i aniqlash va differensial
tenglam asini keltirib chiqarish m uhim aha-
m iyatga ega.
Jism q o ‘z g ‘a lm a s Oz o ‘q a tr o f id a ю.
b u rc h a k tezlik b ila n a y la n m a h a ra k a t qi-
lay otg an b o ‘lsin (165-rasm ). Jism M v nuq-
ta sid a n aylanish o ‘q igacha b o ‘lgan m aso-
fani hv desak, (85.4) form ulaga asosan:
K 1
= Ъ т1 K K V) =
■ (88.1)
Biroq, Vv = /^,co- S huning u ch u n (88.1) quyidagicha yoziladi:
K z =
■
(88.2)
(74.1) form ulaga k o ‘ra: I z = X mv^v
2 ■
D em ak , (88.2) dan
K z = / гсо
(88.3)
hosil b o ‘ladi.
(88.3)
d an k o ‘ram izki, jism ning aylanish o ‘qiga nisbatan kinetik
m om enti uning m azkur о ‘qqa nisbatan inersiya m om enti bilan bur
chak tezligining ко ‘paytm asiga teng.
z
162

(88.3) ni (8 6 .4 ) n in g u c h in c h is ig a q o ‘y sak, q a ttiq jism n in g
q o ‘zg ‘almas o ‘q atrofidagi aylanma harakatining differensial tengla-
masi kelib chiqadi:
УоЫ
<88-4>
(88.4) differensial tenglam ani m o d d iy n u q ta h arak atin in g diffe
rensial tenglam asi (64.2) bilan taqqoslab, inersiya m om enti aylanm a
harakatdagi jism nin g inertlik oMchovini ifodalanishini ko‘ram iz.

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