Nguva yeinertia

1. Nguva yekusashanda zvakanaka kwechikamu

Ongorora chidimbu chinotenderera. Chidimbu chine huremu m chinopihwa simba F kuitira kuti chidimbu chitenderere kutenderedza axis O. Chidimbu chacho chakasiyana ne axis yekutenderera. Kutanga, chidimbu chacho chiri pa rest (v = 0). Mushure mekufamba nesimba ra F, zvidimbu zvinofamba nekumhanya kwakati kuti kuitira kuti zvidimbu zvive nekumhanya kwakati. Hukama huripo pakati pesimba (F), huremu (m), uye kukurumidza kwakati kwezvidimbu kunoratidzwa ne equation 3:

F = ma_kusviba (Equation 3)

Zvidimbu zvinotenderera kuitira kuti zvidimbu zvive nekumhanya kwe-angular. Hukama huripo pakati pekumhanya kwe-tangential nekumhanya kwe-angular hunoratidzwa ne equation 4:

a_kusviba =r α (Equation 4)

Isa a mu equation 3 ne a mu equation 4:

F = mr α

r F = mr² α

τ = (Va.²) α (Equation 5)

r F inguva yesimba uye mr.² ndiyo nguva yekusashanda kwechinhu chimwe chete. Equation 5 inotaura hukama huripo pakati penguva yesimba, nguva yekusashanda, uye kukurumidza kwemakona ezvikamu zvinotenderera. Equation 5 ndiyo equation yemutemo wechipiri waNewton wezvikamu zvinotenderera.

The nguva ye inertia chechikamu chimwe chete ndicho chigadzirwa chehukuru hwechikamu chimwe chete (m) uye sikweya yedaro riri pakati pezvikamu zvine axis of rotation (r).²).

Ini = Va.² (Equation 6)

I = nguva yekusashanda kwechikamu, m = huremu hwechikamu, r = daro riri pakati pechikamu ne axis yekutenderera. Equation 6 inoshandiswa kuona nguva yekusashanda kwechikamu.

3.2 Matambudziko emuenzaniso wenguva yekusashanda kwechikamu

Dambudziko remuenzaniso 1.

Chidimbu chine huremu hwe2 kg chakasungirirwa patambo yakareba mamita 0.5 ndokuzotenderedzwa. Ndeipi nguva yekusashanda kwezvidimbu pazvinotenderedzwa?

Solution:

Ini = Va.²

I = (2 kg) (0.5 m)²

I = 0.5 kg m²

Dambudziko remuenzaniso 2.

Zvidimbu zviviri, chimwe nechimwe chine huremu hwe2 kg uye 4 kg, zvakabatana newaya yakareruka, uko kureba kwewaya kuri mamita maviri. Usafuratira huremu hwewaya. Sarudza nguva yekusashanda kwezvidimbu zviviri, kana:

a) Chikamu chekutenderera chiri pakati pezvikamu zviviri

Solution:

Ini = m₁ r₁² +m₂ r₂²

Ini = (2)(12) + (4)(12)

Ini = 2 + 4

I = 6 kg m²

b) Mutsetse wekutenderera uri chinhambwe chemamita 0.5 kubva pachinhu chine huremu hwe2 kg

Ini = m₁ r₁² +m₂ r₂²

Ini = (2)(0.5²) + (4)(1.5²)

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

Ini = 0.5 + 9

I = 9.5 kg m²

c) Mutsetse wekutenderera uri chinhambwe chemamita 0.5 kubva pachinhu chine huremu hwe4 kg

Ini = m₁ r₁² +m₂ r₂²

Ini = (2)(1.52) + (4)(0.5²)

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

Ini = 4.5 + 1

I = 5.5 kg m²

Zvichibva pamhedzisiro yekuverenga pamusoro apa, nguva yekusagadzikana inokanganiswa zvakanyanya nenzvimbo ye axis yekutenderera. Kunyangwe chimiro nehukuru zvakafanana nekuti nzvimbo ye axis yekutenderera yakasiyana, nguva yekusagadzikana yakasiyanawo.

Zvidimbu zviri pedyo ne axis of rotation zvine nguva diki yekusaita zvakanaka, nepo zvidimbu zviri kure ne axis of rotation zvine nguva yakakura yekusaita zvakanaka. Kana tikafunga kuti zvidimbu zviviri zviri pamusoro zvinhu zvakasimba, saka chidimbu chimwe nechimwe chiri pedyo ne axis of rotation.

ine nguva diki yekusaita chinhu pane nguva yekusaita chinhu yechinhu chiri kure ne axis yekutenderera.

3.3 Nguva yekusagadzikana kwemuviri wakasimba wakafanana

Zvinhu zvakaoma zvinoumbwa nezvidimbu zvakawanda. Nguva yekusagadzikana kwemuviri wakasimba ndiyo huwandu hwenguva dzekusagadzikana kwezvikamu chimwe nechimwe zvinovaka chinhu chacho.

Ini = Σ mr²

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

Kuti tione nguva yekusagadzikana kwechinhu chakasimba, tinofanira kuongorora chinhu chacho pachinotenderera nekuti nzvimbo ye axis yekutenderera inokanganisa nguva yekusagadzikana kwechinhu chacho. Nguva yekusagadzikana (I) yechikamu chimwe nechimwe inoenderanawo nehuremu (m) hwechikamu uye sikweya yedaro (r).²) yechinhu chinobva pa axis yekutenderera. Huremu hwezvinhu zvese zvinovaka chinhu ndicho huremu hwechinhu chacho.

Dambudziko nderekuti, daro rechinhu chimwe nechimwe kubva padenderedzwa rinotenderera rinosiyana.

Ongorora kudzikira kwefomura yenguva yekusagadzikana kwemhete yakatetepa ine minwe R uye uremu M.

Kana axis of rotation iri pakati pering, zvidimbu zvese zvering yakatetepa zvinowanikwa kubva paaxis of rotation. Nguva yekusagadzikana kwering yakatetepa yakaenzana nenguva yekusagadzikana kwezvikamu zvese:

Ini = Σ mr²

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

Huremu hwezvimedu zvese = huremu hwedenderedzwa rakatetepa (M)

Ini = M (r)₁² +r₂² +r₃² + ….. + r_n²)

Chikamu chimwe nechimwe chemhete yakatetepa chiri r kubva ku axis yekutenderera kuitira kuti r₁ =r₂ =r₃ = rn = R

Kuenzanisa kwenguva yekusagadzikana kwemhete yakatetepa:

Ini = MR²

I = nguva yekusashanda kwemhete yakatetepa, M = huremu hwemhete yakatetepa, R = radius yemhete yakatetepa.

Ko kana axis of rotation isiri pakati pering? Kana axis of rotation isiri pakati pering, fomura yenguva yekusagadzikana kwering yakatetepa haigone kuwanikwa uchishandisa nzira iri pamusoro apa,

nekuti daro rechikamu chimwe nechimwe kubva pa axis of rotation rakasiyana. Kuwana fomura yenguva yekusagadzikana kwedambudziko rakadai hakukurukurwi munyaya iyi.

Fomura yenguva yekusagadzikana kwezvinhu zvakaoma

3.4 Muenzaniso wedambudziko renguva yekusagadzikana kwemuviri wakasimba wakafanana

Dambudziko remuenzaniso 1:

Silinda yesimbi AB ine huremu hwe3 kg kana ichitenderedzwa kuburikidza neB,

nguva yekusagadzikana ndeye 27 kg m²Chii chiri nguva yekusaita basa kana

yakatenderedzwa kuburikidza neC?

Solution:

Solution:

Fomura yenguva yekusagadzikana kwetsvimbo yakasimba yakafanana (axis yekutenderera iri pakati petsvimbo):

I = 1/12 ML²

27 = (1/12) ML²

(27)(12) = ML²

324 = ML²

Fomura yenguva yekusagadzikana kwetsvimbo yakasimba yakafanana (axis yekutenderera pamucheto wetsvimbo):

I = 1/3 ML²

Ini = 1/3 (324)

I = 108 kg m²