Aylanish kinetik energiyasi – muammolar va yechimlar

1. Inersiya momenti 1 kg m2 bo'lgan jism 2 rad/s doimiy burchak tezligida aylanadi . Jismning aylanish kinetik energiyasi ^nima?

Ma'lum:

Inersiya momenti (I) = 1 kg m ²

Burchak tezligi ( ω) = 2 rad/s

Kerakli: Aylanish kinetik energiyasi (K E )

yechim:

Aylanish kinetik energiyasining formulasi:

KE = 1/2 I ω ²

KE = aylanish kinetik energiyasi (kg/m²/s²), Men = inersiya momenti (kg/m²), ω = burchak tezligi (rad/s)

Aylanish kinetik energiyasi:

KE = 1/2 I ō ² = 1/2 (1)(2) ² = 1/2 (1)(4) = 2 Joul

[irp]

2. Radiusi 0.2 m bo'lgan 20 kg silindrli blok 4 rad/s o'zgarmas burchak tezligida aylanadi. Blokning aylanish kinetik energiyasi qancha?

Ma'lum:

Silindr kasnagining massasi (m) = 20 kg

Silindr radiusi (r) = 0.2 m

Burchak tezligi (ω) = 4 ra d/s

Izlash: Aylanish kinetik energiyasi nima?

Yechim;

Silindrning inersiya momenti formulasi:

I = 1/2 janob ²

I = inersiya momenti ( kg m ² ), m = massa ( kg ), r = radius ( metr )

Silindr kasnagining inersiya momenti:

I = 1/2 (20)(0.2) ² = (10)(0.04) = 0.4 kg ^m2

Kasnakning aylanish kinetik energiyasi:

KE = 1/2 I ō ² = 1/2 (0.4)(4) ² = (0.2)(16) = 3.2 Joul

[irp]

3. Radiusi 0.1 m bo'lgan 10 kg og'irlikdagi shar 10 rad/s doimiy tezlikda aylanadi . Sharning kinetik energiyasi nima?

Ma'lum:

To'pning massasi (m) = 10 kg

Sharning radiusi (r) = 0.1 m

Burchak tezligi (ω) = 10 r ad/s

Kerakli: Aylanish kinetik energiyasi

yechim:

Inersiya momentining formulasi:

I = (2/5) janob ²

I = inersiya momenti (kg m² ⁾ , m = massa (kg), r = radius (m²)

To'pning inersiya momenti:

I = (2/5)(10)(0.1) ² = (4)(0.01) = 0.04 kg ^m2

To'pning aylanish kinetik energiyasi:

K E = 1/2 I ō ² = 1/2 (0.04)(10) ² = (0.02)(100) = 2 Joul

[irp]

4. 0.5 kg og'irlikdagi zarracha 2 rad/s doimiy burchak tezligida aylanadi . Agar aylana radiusi 10 sm bo'lsa, zarrachaning aylanish kinetik energiyasi qanday bo'ladi?

Ma'lum:

Zarrachaning massasi (m) = 0.5 kg

Sharning radiusi (r) = 10 sm = 10/100 = 0.1 m

Burchak tezligi (ω) = 2 rad/ s

Kerakli: Aylanish kinetik energiyasi

yechim:

Zarrachalar uchun inersiya momenti:

I = janob ² = (0.5)(0.1) ² = (0.5)(0.01) = 0.005 kg m ²

Aylanish kinetik energiyasi:

K E = 1/2 I ō ² = 1/2 (0.005)(2) ² = 1/2 (0.005)(4) = (0.005)(2) = 0.01 Joul