1. Inersiya momenti 2 kg m2 bo'lgan jism 1 rad/s tezlikda aylanadi . Jismning burchak momenti nima ?
Ma'lum:
Inersiya momenti (I) = 2 kg m 2
Burchak tezligi ( ω ) = 1 rad/s
Kerakli: Burchak momentum (L)
yechim:
Burchak momentumining formulasi:
L = I ω
L = burchak momentumi (kg m² / s), I = inersiya momenti (kg m² ) , ω = burchak tezligi (rad/s)
Burchak momentumi:
L = I ω = (2)(1) = 2 kg m2 /s
2. Radiusi 0.1 m bo'lgan 2 kg silindrli blok 2 rad/s o'zgarmas burchak tezligida aylanadi. Blokning burchak momentumi nima?
Ma'lum:
Kasnakning massasi (m) = 2 kg g
Kasnak radiusi (r) = 0.1 m
Burchak tezligi (ω) = 2 r ad/s
Kerakli: Burchak momentum
yechim:
Qattiq silindr uchun inersiya momentining formulasi:
I = 1/2 janob 2
I = inersiya momenti (kg m² ) , m = massa (kg), r = radius (m²)
Inersiya momenti:
I = 1/2 (2)(0.1) 2 = (1)(0.01) = 0.01 kg m2
Burchak tezligi:
L = I ω = ( 0.01 )( 2 ) = 0.02 kg m2 / s
3. Radiusi 0.2 m bo'lgan 2 kg og'irlikdagi bir xil shar 4 rad/s tezlikda aylanadi . Sharning burchak momentumi nima?
Ma'lum:
To'pning massasi (m) = 2 kg
Sharning radiusi (r) = 0.2 m
Burchak tezligi (ω) = 4 ra d/s
Kerakli: Burchak momentum
yechim:
Yagona shar uchun inersiya momentining formulasi:
I = (2/5) janob 2
I = inersiya momenti t (kg m² ) , m = massa (kg), r = radius (m)
Bir tekis shar uchun inersiya momenti:
I = (2/5)(2)(0.2) 2 = (4/5)(0.04) = 0.032 kg m2
Sferaning burchak momentumi:
L = I ω = ( 0.032 )( 4 ) = 0.128 kg m2 / s
4. 1 kg og'irlikdagi zarracha 2 rad/s doimiy burchak tezligida aylanadi . Agar aylana radiusi 10 sm bo'lsa, burchak tezligi qanday bo'ladi?
Ma'lum:
Ob'ektning massasi ( m) = 1 kg g
Aylana radiusi (r) = 10 sm = 10/100 = 0.1 m
Burchak tezligi (ω) = 2 rad/ s
Kerakli: Burchak momentum
yechim:
Zarrachalar uchun inersiya momentining formulasi:
I = janob 2 = (1)(0.1) 2 = (1)(0.01) = 0.01 kg m 2
Burchak momentumi:
L = I ω = (0.01)(2) = 0.02 kg m2 / s
