Nthawi ya kusakhazikika kwa tinthu tating'onoting'ono - mavuto ndi mayankho

Nthawi ya kusakhazikika kwa tinthu tating'onoting'ono - mavuto ndi mayankho

1. Mipira iwiri yolumikizidwa ndi ndodo, monga momwe zasonyezedwera pachithunzi chili pansipa. Musanyalanyaze ndodo UnyinjiKulemera kwa mpira P ndi magalamu 600 ndipo kulemera kwa mpira Q ndi magalamu 400. Kodi mphindi ya inertia za dongosolo lokhudza AB?

Zodziwika:

Mzere wozungulira ndi AB.

m_p = magalamu 600 = 0.6 kg, m_q = magalamu 400 = 0.4 kg

r_p = 20 cm = 0.2 m, r_q = 50 cm = 0.5 m

Akufuna: Nthawi ya inertia ya dongosolo

Yankho:

Ine = m_p r_p² +m_q r_q²

I = (0.6 kg)(0.2 m)² + (0.4 kg)(0.5 m)²

I = (0.6 kg)(0.04 m²) + (0.4 kg)(0.25 m²)

I = 0.024 kg m² + 0.1 kg m²

I = 0.124 kg m²

2. Ndodo ya AB yokhala ndi kulemera kwa 2-kg yozungulira pafupifupi mfundo A, nthawi ya inertia ya ndodo ndi 8 kg m²Ngati yazungulira mozungulira mfundo O (AO = OB), kodi nthawi ya inertia ya ndodo ndi chiyani?

Zodziwika:

Kulemera kwa ndodo AB (m) = 2 kg

Ngati yazungulira mozungulira mfundo A kotero kuti utali wa kuzungulira (r) = kutalika kwa AB = r ndiye kuti mphindi ya inertia (I) = 8 kg m²

SE basi: Ngati yazungulira mozungulira mfundo O kotero kuti utali wa kuzungulira (r) = kutalika kwa AO = kutalika kwa OB = 1/2 r ndiye kuti nthawi ya inertia ya ndodo ndi yotani?

Yankho:

Ine = Mr.²

8 kg m² = (2 kg) r²

8 mamita² = (2) r²

r² = 8 m² / 2

r² = 4 m²

r = mamita awiri

Ngati yazungulira mozungulira mfundo O kotero ½ r = mita imodzi, ndiye kuti nthawi ya inertia:

Ine = Mr.² = (2 kg)(1 m)² = (2 kg)(1 m²) = 2 kg m²

3. Mipira iwiri yolumikizidwa ndi ndodo monga momwe zasonyezedwera pachithunzi pansipa. Musanyalanyaze kulemera kwa ndodo. Kodi nthawi ya kusagwira ntchito bwino kwa dongosolo ndi chiyani?

Zodziwika:

Unyinji wa mpira A (m_A) = magalamu 200 = 0.2 kg

Kulemera kwa mpira B (m_B) = magalamu 400 = 0.4 kg

Mtunda pakati pa mpira A ndi mzere wozungulira (r)_A= = 0

Mtunda pakati pa mpira B ndi mzere wozungulira (r)_B) = 25 cm = 0.25 m

Akufuna: Nthawi ya kusakhazikika kwa dongosololi

Yankho:

Nthawi ya inertia ya mpira A:

I_A = (m_A)(r_A²) = (0.2)(0)² = 0

Nthawi ya kulephera kwa mpira B:

I_B = (m_B)(r_B²) = (0.4)(0.25)² = (0.4)(0.0625) = 0.025 kg m²

Nthawi ya inertia ya dongosolo:

Ine = ine_A + I_B = 0 + 0.025 = 0.025 kg m² = 25x10 pa^-3 makilogalamu m²

4. Tinthu tinayi tokhala ndi unyinji wosiyana, tawonetsedwa pachithunzi pansipa. Dziwani nthawi ya inertia ya dongosolo pafupi ndi mzere wopingasa P.

Anakonza

Mzere wozungulira ndi wopingasa P.

Zodziwika:

Kulemera kwa tinthu A (m_A) = m

Kulemera kwa tinthu tating'onoting'ono B (m_B) = 2m

Kulemera kwa tinthu C (m_C) = 3m

Kudutsa kwa tinthu D (m_D) = 4m

Mtunda pakati pa tinthu A ndi mzere wozungulira (r)_A) = b

Mtunda pakati pa tinthu B ndi mzere wozungulira (r)_B) = b

Mtunda pakati pa tinthu C ndi mzere wozungulira (r)_C) = 2b

Mtunda pakati pa tinthu tating'onoting'ono D ndi mzere wozungulira (r)_D) = 2b

Akufuna: Nthawi ya inertia ya dongosolo pafupi ndi mzere wopingasa P

Yankho:

Ine = m_A r_A² +m_B r_B² +m_C r_C² +m_D r_D²

Ine = (m)(b)² + (2m)(b)² + (3m)(2b)² + (4m)(2b)²

Ine = mb² + 2 mb² + (3m)(4b²) + (4m)(4b²)

Ine = mb² + 2 mb² + 12 mb² + 16 mb²

Ine = 31 mb²

5. Tinthu tinayi tolumikizidwa ndi ndodo. Musanyalanyaze kulemera kwa ndodo. Dziwani nthawi ya inertia yozungulira mzere wa kuzungulira kudzera mu tinthu m₁ ndi m₂, monga momwe chithunzi chili pansipa chikusonyezera.

Amadziwika

Kulemera kwa tinthu 1 (m₁) = 1/4 kg

Kulemera kwa tinthu 2 (m₂) = 1/2 kg

Kulemera kwa tinthu 3 (m₃) = 1/4 kg

Kulemera kwa tinthu 4 (m₄) = 1/4 kg

Mtunda pakati pa tinthu 1 ndi mzere wozungulira (r)₁= = 0

Mtunda pakati pa tinthu 2 ndi mzere wozungulira (r)₂= = 0

Mtunda pakati pa tinthu 3 ndi mzere wozungulira (r)₃) = 10 cm = 10/100 m = 1/10 m

Mtunda pakati pa tinthu 4 ndi mzere wozungulira (r)₄) = 10 cm = 10/100 m = 1/10 m

Akufuna: Nthawi ya inertia

Yankho:

Ine = m₁ r₁² +m₂ r₂² +m₃ r₃² +m₄ r₄²

Ine = (1/4)(0)² + (1/2)(0)² + (1/4)(1/10)² + (1/4)(1/10)²

Ine = 0 + 0 + (1/4)(1/100) + (1/4)(1/100)

Ine = 1/400 + 1/400

Ine = 2/400

I = 1/200 kg.m²

1. Kodi nthawi ya inertia ya tinthu tating'onoting'ono ndi yotani?
   • yankho: Kwa tinthu tating'onoting'ono ta kulemera $m$ patali $r$ kuchokera ku mzere wozungulira, mphindi yake ya inertia $I$ waperekedwa ndi I=m×r².
2. Nchifukwa chiyani nthawi ya inertia nthawi zambiri imatchedwa "analogue yozungulira" ya misa?
   • yankho: Monga momwe kulemera kulili muyeso wa kukana kwa chinthu kusintha kwa kayendedwe kake komasulira (chifukwa cha lamulo lachiwiri la Newton), mphindi ya inertia ndi muyeso wa kukana kwa chinthu kusintha kwa kayendedwe kake kozungulira.
3. Kodi kusintha mtunda wa tinthu kuchokera ku mzere wake wozungulira kumakhudza bwanji nthawi yake ya inertia?
   • yankho: Nthawi ya inertia imagwirizana ndi sikweya ya mtunda kuchokera ku mzere wozungulira. Ngati muwonjezera mtunda kawiri, nthawi ya inertia idzawonjezeka ndi chinthu china.
4. Chifukwa chiyani sikweya ya mtunda (r) ndi²) imagwiritsidwa ntchito mu fomula ya mphindi ya inertia m'malo mwa mtunda wokha?
   • yankho: Sikweya ya mtunda imagwiritsidwa ntchito chifukwa cha momwe mphamvu ya kinetic imagwirira ntchito pozungulira. Pakuyenda kozungulira, tinthu tating'onoting'ono ta chinthu timathandizira ku mphamvu ya kinetic yozungulira kutengera kulemera kwake komanso mtunda wake kuchokera ku axis squared.
5. Kodi nthawi ya inertia ya tinthu imasintha bwanji ngati kulemera kwake kwachulukitsidwa katatu pamene mtunda kuchokera ku axis constant ukupitirizabe?
   • yankhoNgati kulemera kwachulukitsidwa katatu ndipo mtunda umakhala wosasinthasintha, nthawi ya inertia nayonso idzachulukitsa katatu chifukwa imagwirizana mwachindunji ndi kulemera.
6. Kodi tinthu tating'onoting'ono tingathe kukhala ndi nthawi yochepa ya zero? Ngati ndi choncho, kodi ndi pa mkhalidwe wotani?
   • yankhoInde, tinthu timeneti timakhala ndi mphindi ya zero ngati tili molunjika pa mzere wozungulira, zomwe zimapangitsa kuti tipeze mtunda wake. $r$ kuchokera ku mzere wofanana ndi zero.
7. Nchifukwa chiyani zinthu zosiyanasiyana zomwe zimakhala ndi kulemera kofanana ndi kukula kofanana zimakhala ndi nthawi zosiyana za inertia zikamazungulira mozungulira nkhwangwa zosiyanasiyana?
   • yankho: Kugawa kwa kulemera mozungulira mzere wozungulira kumatsimikiza nthawi ya inertia. Ngakhale zinthu ziwiri zili ndi kulemera ndi kukula kofanana, kugawa kwawo kulemera kofanana ndi mzere wozungulira kumatha kusiyana, zomwe zimapangitsa kuti pakhale nthawi zosiyanasiyana za inertia.
8. Kodi nthawi ya inertia ndi kuchuluka kwa scalar kapena vekitala?
   • yankho: Nthawi ya inertia ndi kuchuluka kwa scalar. Komabe, pa matupi olimba okhala ndi mawonekedwe ovuta komanso ma axes angapo ozungulira, imaimiridwa ndi tensor.
9. Ngati tinthu tiwiri, chilichonse cha misa $m$, zili patali r_1​ ndi r₂​ Kuchokera ku mzere wozungulira, kodi nthawi yophatikizana ya inertia ndi chiyani?
   • yankho: Nthawi ya inertia ndi yowonjezera pa tinthu tating'onoting'ono tosiyana. Motero, nthawi yophatikizana ya inertia I=m×r₁^{2 ​}+ m×r₂^2​.

10. Kodi nthawi ya inertia ikugwirizana bwanji ndi kusunga mphamvu ya angular?

    • yankho: Mphamvu ya angular $L$ ndi zotsatira za nthawi ya inertia $I$ ndi liwiro la angular $\omega$, yoimiridwa ndi equation $L=I\times \omega$Ngati palibe ma torque akunja omwe agwira ntchito pa dongosolo, mphamvu ya angular idzakhalabe yokhazikika. Izi zikutanthauza kuti ngati nthawi ya inertia isintha (monga momwe zimakhalira ndi munthu wokwera m'manja mwake), liwiro la angular liyenera kusintha kuti chinthucho chikhale chokhazikika.