Kuzungulira kwa matupi olimba - mavuto ndi mayankho

Mphindi ya mphamvu

1. Mphamvu zitatu zimagwira ntchito pa mtanda wautali mamita 6, monga momwe chithunzi chili pansipa chikusonyezera. Kodi mphamvu ya ukonde yomwe imazungulira mtandawo mozungulira O ngati mzere wozungulira ndi chiyani?

Zodziwika: Kuzungulira kwa matupi olimba - mavuto ndi mayankho 1

Mzere wozungulira pa mfundo O.

Mphamvu 1 (F ₁ ) = F

Mtunda pakati pa mzere wa zochita wa F1 _ndi mzere wozungulira (r1 ₎ = mamita 3

Mphamvu 2 (F ₂ ) = 2F

Mtunda pakati pa mzere wa zochita wa F2 _ndi mzere wozungulira (r2 ₎ = mamita awiri

Mphamvu 3 (F ₃ ) = 2F

Mtunda pakati pa mzere wa zochita wa F3 _ndi mzere wozungulira (r3 ₎ = mamita awiri

Kufunidwa: Kukula kwa nthawi ya mphamvu

Yankho:

Nthawi ya mphamvu 1:

τ ₁ = F ₁ r ₁ = (F)(3) = -3F

Mphamvu ya 1 imazungulira mtanda mozungulira wotchi kotero timayika chizindikiro choyipa.

Nthawi ya mphamvu 2:

τ ₂ = F ₂ r ₂ = (2F)(2) = 4F

Mphamvu ya 2 imazungulira kuwala kotsutsana ndi wotchi kotero timayika chizindikiro chabwino.

Nthawi ya mphamvu 3:

τ ₃ = F ₃ r ₃ tchimo 30 ^o = (2F) (3) (0.5) = 3F

Mphamvu ya 2 imazungulira kuwala kotsutsana ndi wotchi kotero timayika chizindikiro chabwino.

Zotsatira za mphindi ya mphamvu:

Στ = τ ₁ + τ ₂ + τ ₃

Στ = -3F + 4F + 3F

Στ = 4F

Kukula kwa mphamvu ya mphindi ndi 4F Newton-meter. Zotsatira za mphamvu ya mphindiyo zimazungulira kuwala kotsutsana ndi wotchi kotero timayika chizindikiro chabwino.

2. α = 30 ^o , kutalika kwa AB = BC = mita 1. Kodi mphamvu ya nthawi yozungulira mzere wa kuzungulira pa mfundo A ndi yotani?

Zodziwika:

Mzere wozungulira pamalopo A.

Mphamvu 1 (F ₁ ) = 10 N

Mtunda pakati pa mzere wa zochita wa F1 _ndi mzere wozungulira (r1 ₎ = mita imodzi

Mphamvu 2 (F ₂ ) = 10 N

Mtunda pakati pa mzere wa zochita wa F2 _ndi mzere wozungulira (r2 ₎ = mita imodzi

Mphamvu 3 (F ₃ ) = 20 N

Mtunda pakati pa mzere wa zochita wa F3 _ndi mzere wozungulira (r3 ₎ = mamita awiri

Kufunidwa: Zotsatira za nthawi ya mphamvu

Yankho:

Nthawi ya mphamvu 1:

τ ₁ = F ₁ r ₁ tchimo 30 ^o = (10) (1) (0.5) = 5 N m

Mphamvu ya 1 imazungulira kuwala kozungulira motsatira wotchi kotero timaganiza kuti pali chizindikiro chabwino.

Nthawi ya mphamvu 2:

τ ₂ = F ₂ r ₂ sin 30 ^o = (10)(1)(0.5) = -5 Newton mita

Mphamvu ya mphindi 2 imazungulira beam m mozungulira wotchi kotero timayika chizindikiro chotsutsa.

Nthawi ya mphamvu 3:

τ ₃ = F ₃ r ₃ sin 60 ^o = (20)(2)(0.5√3) = -20√3 Newton mita

Mphamvu ya mphindi 3 imazungulira beam m mozungulira wotchi kotero timayika chizindikiro chotsutsa.

Zotsatira za mphindi ya mphamvu:

Στ = τ ₁ + τ ₂ + τ ₃

Στ = 5 – 5 – 20√3

Στ = – 20√3 N m

Kukula kwa mphamvu ya mphindi ndi 20√3 N m. Zotsatira za mphamvu ya mphindi zimazungulira kuwala kozungulira wotchi kotero timayika chizindikiro chotsutsa.

Kodi thupi lolimba n’chiyani, ndipo limasiyana bwanji ndi thupi losalimba?
- Yankho: Thupi lolimba ndi chinthu chopangidwa bwino chomwe mtunda pakati pa mfundo ziwiri zilizonse mkati mwa thupi umakhalabe wofanana, mosasamala kanthu za mphamvu zakunja kapena mphamvu. Mosiyana ndi zimenezi, thupi losalimba limatha kusintha, zomwe zimapangitsa kuti mtunda pakati pa mfundo mkati mwa thupi usinthe.
Kodi nthawi ya inertia ya thupi lolimba imakhudzana bwanji ndi kufalikira kwake kwa misa?
- Yankho: Nthawi ya kulephera kwa thupi lolimba ndi muyeso wa kukana kwake ku kayendedwe kozungulira mozungulira mzere wina ndipo zimadalira kulemera kwa thupi ndi kufalikira kwake poyerekeza ndi mzere wozungulira. Zimawerengedwa ndi kuchuluka kwa zinthu zomwe zimapangidwa ndi kulemera kwa chinthu chilichonse komanso sikweya ya mtunda wake kuchokera ku mzere wozungulira.
Kodi kufunika kwa mphamvu yozungulira ya thupi lozungulira lolimba n'chiyani?
- Yankho: Mphamvu ya kayendedwe ka ... $I ω^{2}$ , kumene $I$ ndi nthawi ya inertia, ndipo $ω$ ndi liwiro la angular.
Kodi chimachitika ndi chiyani ndi angular momentum ya dongosolo la tinthu ngati palibe ma torque akunja omwe agwira ntchito pa iyo?
- Yankho: Ngati palibe ma torque akunja omwe agwira ntchito pa dongosolo la tinthu tating'onoting'ono, mphamvu yonse ya angular ya dongosololi imasungidwa. Iyi ndi mfundo yosungira mphamvu ya angular.
Kodi chiphunzitso cha parallel-axis chimathandiza bwanji kupeza nthawi ya inertia ya thupi lolimba?
- Yankho: Chiphunzitso cha parallel-axis chimalola munthu kuwerengera nthawi ya inertia ya thupi lolimba pafupi ndi mzere uliwonse wofanana ndi ndi mtunda $d$ kutali ndi mzere kudzera pakati pa kulemera kwake. Ilo limati $I = I_{c m} + m d^{2}$ , kumene $I_{c m}$ ndi nthawi ya inertia pakati pa misa, $m$ ndi kulemera konse, ndipo $d$ ndi mtunda pakati pa nkhwangwa ziwiri.
Kodi kusiyana pakati pa kugubuduzika popanda kutsetsereka ndi kugubuduzika ndi kutsetsereka ndi chiyani?
- Yankho: Kugubuduzika popanda kutsetsereka kumachitika pamene thupi lolimba limazungulira mozungulira mzere wokhazikika pomwe likutembenuzikanso, popanda kuyenda kulikonse pakati pa thupi ndi pamwamba. Kugubuduzika ndi kutsetsereka kumatanthauza kuti pali kuyenda kapena kutsetsereka pakati pa thupi ndi pamwamba.
Kodi kutalika kwa gyration kumakhudzana bwanji ndi nthawi ya inertia?
- Yankho: Chiyerekezo cha gyration ndi muyeso womwe umafotokoza momwe kulemera kwa thupi kumagawidwira mozungulira mzere wake wozungulira. Chimatanthauzidwa ngati muzu wa sikweya wa chiŵerengero cha mphindi ya inertia ndi kulemera ndipo chimapereka mtunda wofanana kuchokera ku mzere komwe kulemera konse kungakhazikitsidwe popanda kusintha mphindi ya inertia.
Kodi kuonjezera nthawi ya inertia kumakhudza bwanji kuthamanga kwa angular kwa thupi lolimba pa torque yopatsidwa?
- Yankho: Pa torque inayake, kuwonjezera nthawi ya inertia kumachepetsa kuthamanga kwa angular, monga $α = τ/I$ , kumene $α$ ndi kuthamanga kwa angular, $τ$ ndi mphamvu, ndipo $I$ ndi nthawi ya inertia.
Kodi mphamvu yogwiritsidwa ntchito pa thupi lolimba ingayambitse kuyenda kosinthasintha komanso kozungulira? Fotokozani momwe zimakhalira.
- Yankho: Inde, mphamvu yogwiritsidwa ntchito pa thupi lolimba ingayambitse kuyenda kosinthasintha komanso kozungulira. Ngati mphamvuyo ikugwiritsidwa ntchito pamalo omwe sagwirizana ndi pakati pa misa, ingayambitse thupi kusinthasintha (kusuntha molunjika) ndikuzungulira. Kusuntha kosinthasintha kumatsimikiziridwa ndi mphamvu yeniyeni, pomwe kuyenda kozungulira kumadalira mphamvu yopangidwa ndi mphamvu yozungulira pakati pa misa.
N’chifukwa chiyani munthu wochita maseŵera otsetsereka amazungulira mofulumira akamakoka manja ake pafupi ndi thupi lake?

Yankho: Mwa kukoka manja awo pafupi ndi thupi lawo, wochita maseŵera otsetsereka amachepetsa nthawi yawo ya kulephera kuchita zinthu mopitirira muyeso. Malinga ndi kusunga mphamvu ya angular, ngati nthawi ya kulephera kuchita zinthu mopitirira muyeso yachepa ndipo palibe mphamvu yakunja yomwe yagwiritsidwa ntchito, liwiro la angular liyenera kuwonjezeka. Motero, wochita maseŵera otsetsereka amazungulira mofulumira.

Mafunso ndi mayankho awa amapereka kumvetsetsa mfundo zazikulu zokhudzana ndi kuzungulira kwa matupi olimba.