Nguva yekusagadzikana

3 Matambudziko nemhinduro nezve Moment of inertia equation

1. Sirinda yakasimba ine dhayamita ye8 cm nehuremu hwe2 kg. Panguva imwe chete, bhora rakasimba rine dhayamita ye5 cm nehuremu hwe4 kg. Kana zvinhu zviviri izvi zvikatenderera ne axis nepakati pazvo, sarudza chiyero chenguva yekusashanda kwesirinda nebhora.

Anozivikanwa:

Radiyo yesirinji yakasimba (r) = 8 cm = 0.08 m

Huremu hwesilinda yakasimba (m) = 2 kg

Radiyo yebhora rakasimba (r) = 5 cm = 0.05 m

Huremu hwebhora rakasimba (m) = 4 kg

Kuda: Kuenzanisa kwenguva yekusagadzikana kwe cylinder nebhora

mhinduro:

Fomura yenguva yekusagadzikana kwesimbi yakasimba:

Ini = ½ MR² = ½ (2)(0,08)² = 0,0064

Fomura yenguva yekusagadzikana kwebhora rakasimba:

Ini = 2/5 MR² = 1/5 (4)(0,05)² = (0,8)(0,0025) = 0,002

Kuenzanisa kwenguva yekusagadzikana kwe cylinder nebhora:

0,0064: 0,002

3,2: 1

2. Chirongo chakaiswa mabhisikiti chakashandiswa sechitoyi. Huremu hwechirongo i200 gramu uye dhayamita i15 cm. Chirongo chinomonerwa pasi rakati sandara. Kana chivharo nepasi pechirongo zvikasatariswa, tarisa nguva yekusashanda kwechirongo.

Anozivikanwa:

Kani iyi yakafanana nesirinda isina chinhu.

Huremu (m) = magiramu 200 = 0.2 kg

Nharaunda (r) = 15 cm = 0.15 m

Kuda:

Solution:

Fomura yenguva yekusagadzikana kwe silinda isina chinhu kuburikidza ne axis:

Ini = MR² = (0,2)(0,15)² = (0,2)(0,0225) = 0,0045 kg m²

3. Disiki yakasununguka kutenderera yakatenderedza divi rakamira inokwanisa kutenderera nekumhanya kwe80 revolutions paminiti. Kana chinhu chidiki chine huremu hwe4 x 10-2 kg chikabatanidzwa padhisiki iri 5 cm kubva padivi, zvinozoonekwa kuti kutenderera kwacho kuri 60 revolutions paminiti, wobva waona nguva yekusashanda kwedhisiki.

Anozivikanwa:

Kumhanya kwekutanga kwekona (ω)_o) = 80 put / 60 s = 4/3 put/s

Nguva yekutanga yekusagadzikana (I)_o) = Ini

Kumhanya kwekupedzisira kwekona (ω_t) = 60 put / 60 s = 1 put/s

Nguva yekupedzisira yekusagadzikana (I_t) = Ini + mr² = Ini + (0.04)(0.05)² = Ini + (0.04)(0.0025) = Ini + 0.0425

Kuda: nguva yekusagadzikana kwediski

Solution:

Mutemo wekuchengetedza angular momentum

Ini ω_o = Ini ω_t

Ini (4/3) = Ini + (0,0425 (1))

4 I / 3 = Ini + 0,0425

4 I = 3 I + 0,1275

4 I – 3 I = 0,1275

I = 0,1275 kg m²