Nguva yekusagadzikana kwezvikamu - matambudziko nemhinduro

1. Mabhora maviri akabatana netsvimbo, sezvakaratidzwa mumufananidzo uri pazasi. Usatarisa tsvimbo uremuHuremu hwebhora P magiramu mazana matanhatu uye huremu hwebhora Q magiramu mazana mana. Chii chinonzi nguva ye inertia yehurongwa nezve AB?

Zvinozivikanwa:

Chikamu chekutenderera chinonzi AB. Nguva yekusagadzikana kwezvikamu - matambudziko nemhinduro 1

m_p = magiramu mazana matanhatu = 0.6 kg, m_q = magiramu mazana mana = 0.4 kg

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

Zvaidiwa: Nguva yekusagadzikana kwehurongwa

Solution:

Ini = 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. Tsvimbo yeAB ine huremu hwe2-kg yakatenderera panzvimbo A, nguva yekusashanda kwetsvimbo ndeye 8 kg m²Kana yakatenderedzwa pamusoro penzvimbo O (AO = OB), chii chinonzi nguva yekusashanda kwetsvimbo.

Zvinozivikanwa: Nguva yekusagadzikana kwezvikamu - matambudziko nemhinduro 2

Huremu hwetsvimbo AB (m) = 2 kg

Kana ikatenderedzwa pamusoro penzvimbo A zvekuti radius yekutenderera (r) = kureba kweAB = r saka nguva yekusaita basa (I) = 8 kg m²

Kuda: Kana yakatenderedzwa pamusoro penzvimbo O zvekuti radius yekutenderera (r) = kureba kweAO = kureba kweOB = 1/2 r saka chii chinonzi nguva yekusashanda kwetsvimbo.

Solution:

Ini = Va.²

8 kg m² = (2 kg) r²

8 M² = (2) r²

r²= 8 XNUMX m² / 2

r²= 4 XNUMX m²

r = mamita maviri

Kana ikatenderedzwa pamusoro penzvimbo O saka ½ r = mita imwe, saka nguva yekusagadzikana:

Ini = Va.²= (2 kg)(1 m)² = (2 kg)(1 m²) = 2 kg m²

3. Mabhora maviri akabatana netsvimbo sezvakaratidzwa pamufananidzo uri pazasi. Usatarisa huremu hwetsvimbo. Chii chiri nguva yekusashanda zvakanaka kwehurongwa.

Zvinozivikanwa:

Huremu hwebhora A (m)_A) = magiramu mazana mashanu = 0.2 kg Nguva yekusagadzikana kwezvikamu - matambudziko nemhinduro 3

Huremu hwebhora B (m)_B) = magiramu mazana mashanu = 0.4 kg

Daro riri pakati pebhora A nechikamu chekutenderera (r)_A= = 0

onawo Sarudza nguva yekufamba kweprojectile

Daro riri pakati pebhora B nechikamu chekutenderera (r)_B) = 25 cm = 0.25 m

Zvaidiwa: Nguva yekusashanda zvakanaka kwehurongwa

Solution:

Nguva yekusaita basa kwebhora A:

I_A = (m_A)(r_A²) = (0.2)(0)² = 0

Nguva yekusagadzikana kwebhora B:

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

Nguva yekusagadzikana kwehurongwa:

Ini = ini_A+ Ini_B = 0 + 0.025 = 0.025 kg m² = 25 x gumi^-3 kg m²

4. Zvidimbu zvina zvine mass akasiyana, zvinoratidzwa mumufananidzo uri pazasi. Sarudza nguva yekusashanda kwesystem pamusoro pemutsetse wakatwasuka P.

mhinduro

Mutsetse wekutenderera unonzi P.

Zvinozivikanwa: Nguva yekusagadzikana kwezvikamu - matambudziko nemhinduro 4

Huremu hwechinhu A (m)_A) = m

Huremu hwechikamu B (m)_B) = 2m

Huremu hwechikamu C (m)_C) = 3m

Kupfuura kwechikamu D (m)_D) = 4m

Kureba pakati pechikamu A nechikamu chekutenderera (r)_A) = b

Kureba pakati pechikamu B nechikamu chekutenderera (r)_B) = b

Kureba pakati pechikamu C nechikamu chekutenderera (r)_C) = 2b

Kureba pakati pechikamu D nechikamu chekutenderera (r)_D) = 2b

Zvaidiwa: Nguva yekusagadzikana kwehurongwa pamusoro pemutsetse wakatwasuka P

Solution:

Ini = m_A r_A² +m_B r_B²+m_C r_C²+m_Dr_D²

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

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

Ini = mb²+ 2 mb² + 12 mb²+ 16 mb²

Ini = 31 mb²

5. Zvidimbu zvina zvakabatana netsvimbo. Usafuratira huremu hwetsvimbo. Sarudza nguva yekusashanda zvakanaka pamusoro pedenderedzwa rekutenderera kuburikidza netsvimbo m₁ uye m₂, sezvakaratidzwa mumufananidzo uri pazasi.

Inozivikanwa

Huremu hwechinhu 1 (m₁) = 1/4 kg Nguva yekusagadzikana kwezvikamu - matambudziko nemhinduro 5

Huremu hwechinhu 2 (m₂) = 1/2 kg

Huremu hwechinhu 3 (m₃) = 1/4 kg

Huremu hwechinhu 4 (m₄) = 1/4 kg

Kureba pakati pechikamu 1 nechikamu chekutenderera (r)₁= = 0

Kureba pakati pechikamu 2 nechikamu chekutenderera (r)₂= = 0

Kureba pakati pechikamu 3 nechikamu chekutenderera (r)₃) = 10 cm = 10/100 m = 1/10 m

Kureba pakati pechikamu 4 nechikamu chekutenderera (r)₄) = 10 cm = 10/100 m = 1/10 m

onawo Kutungamira kwe magnetic induction - matambudziko nemhinduro

Zvaidiwa: Nguva yekusagadzikana

Solution:

Ini = m₁ r₁² +m₂ r₂²+m₃ r₃²+m₄r₄²

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

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

Ini = 1/400 + 1/400

Ini = 2/400

I = 1/200 kg.m²

Ndeipi nguva yekusagadzikana kwechinhu chimwe chete?
- mhinduro: Kune chidimbu chimwe chete chehuremu $m$ kure $r$ kubva pachikamu chekutenderera, nguva yacho yekusagadzikana $I$ inopiwa ne $I = m \times r^{2}$ .
Sei nguva yekusagadzikana ichiwanzonzi "anorongeka yekutenderera" yehukuru?
- mhinduro: Kungofanana nehuremu hunoratidza kuramba kwechinhu kuchichinja mukufamba kwacho kwekushandura (nekuda kwemutemo wechipiri waNewton), nguva yekusaita chinhu inoongorora kuramba kwechinhu kuchichinja mukufamba kwacho kwese.
Kuchinja daro rechinhu kubva pa axis yacho yekutenderera kunokanganisa sei nguva yacho yekusaita basa?
- mhinduro: Nguva yekusaita chinhu inoenderana ne sikweya yedaro kubva pa axis yekutenderera. Kana ukawedzera daro kaviri, nguva yekusaita chinhu ichawedzera nechina.
Sei sikweya yedaro iri (r)²) inoshandiswa mufomura yenguva yekusaita chinhu pachinzvimbo chekungotarisa daro chete?
- mhinduro: Chidimbu chedaro chinoshandiswa nekuda kwekushanda kwesimba rekinetic mukutenderera. Mukufamba kwekutenderera, chidimbu chimwe nechimwe chechinhu chinobatsira kusimba rekinetic rinotenderera zvichibva pahukuru hwaro uye daro rayo kubva ku axis squared.
Nguva yekusagadzikana kwechinhu chinoshanduka sei kana huremu hwacho hukapetwa katatu ukuwo daro kubva pa axis constant richiramba riripo?
- mhinduro: Kana huremu hwakapetwa katatu uye daro rikachengetwa rakafanana, nguva yekusaita chinhu ichawedzerawo katatu nekuti inoenderana nehuremu.
Chidimbu chimwe chinogona kuva nenguva yekusaita zero here? Kana zvakadaro, mumamiriro api ezvinhu?
- mhinduro: Ehe, chidimbu chinenge chine nguva yekusagadzikana kwe zero kana chiri panzvimbo yakananga pa axis yekutenderera, zvichiita kuti chive kure. $r$ kubva pa axis yakaenzana ne zero.
Sei zvinhu zvakasiyana zvine huremu hwakafanana nehukuru hwakafanana zvine nguva dzakasiyana dzekusaita chinhu kana zvichitenderera nemaaxes akasiyana?
- mhinduro: Kugoverwa kwehukuru pamusoro pe axis yekutenderera kunosarudza nguva yekusagadzikana. Kunyangwe kana zvinhu zviviri zvine huremu nehukuru hwakafanana, kugoverwa kwehukuru hwazvo maererano ne axis yekutenderera kunogona kusiyana, zvichikonzera nguva dzakasiyana dzekusagadzikana.
Ko nguva yekusagadzikana inguva ye scalar kana kuti vhector quantity here?
- mhinduro: Nguva yekusagadzikana ihuwandu hwe scalar. Zvisinei, kune miviri yakasimba ine maumbirwo akaomarara uye akawanda ma axes ekutenderera, inomiririrwa ne tensor.
Kana zvikamu zviviri, chimwe nechimwe chehukuru $m$ , dziri kure $r_{1}$ uye $r_{2}$ Kubva pa axis yekutenderera, chii chinonzi nguva yakabatana yekusagadzikana?
- mhinduro: Nguva yekusagadzikana inowedzerwa kune zvikamu zvakasiyana. Saka, nguva yakabatana yekusagadzikana $I = m \times r_{12} + m \times r_{22}$ .
Nguva yekusaita chinhu inobatana sei nekuchengetedzwa kwe angular momentum?
- mhinduro: Mwero wekona $L$ chibereko chenguva yekusaita basa $I$ uye kumhanya kwekona $ω$ , inomiririrwa ne equation $L = I \times ω$ Kana pasina ma torque ekunze anoshanda pane imwe system, angular momentum icharamba yakadaro. Izvi zvinoreva kuti kana nguva yekusaita chinhu ikachinja (semutambi anodhonza maoko ake), angular velocity inofanira kugadziriswa kuti chigadzirwa chirambe chakafanana.