Maitiro ekufamba kwese kwese - matambudziko nemhinduro

1. Pulley ine nguva yekusashanda I = 2/5 MR ² ine huremu hwe2-kg. Kana nguva yesimba papulley iri 4 Nm saka chii chinonzi linear acceleration yepulley. Kukurumidza kunokonzerwa negravity g = 10 ms ^-2.

Inozivikanwa : Maitiro ekufamba kwese kwese - matambudziko nemhinduro 1

Nguva yekusashanda kwepulley (I) = 2/5 MR ²

Huremu hwepulley (M) = 2 kg

Nguva yesimba (τ) = 4 Nm

Kukurumidza kunokonzerwa negiravhiti (g) = 10 ms ^-2

Nharaunda yepulley (R) = 20 cm = 0.2 m

Zvinodiwa: Kukurumidza kwakanangana (a)

Solution:

Nguva yekusagadzikana kwepulley (I):

I = 2/5 MR ² = 2/5 (2)(0.2) ² = 2/5 (2)(0.04) = 2/5 (0.08) = 0.16 / 5 = 0.032 kg m ²

Kukurumidza kwekona ( α):

τ = ini α

α = τ/I = 4 / 0.032 = 125 rad.s ^-2

Kukurumidza kwemutsara (a):

a = R α = (0.2)(125) = 25 ms ^-2

Kukurumidza kwakanangana kwemucheto wepulley ndeye 25 ms ^-2.

2. Kukurumidza kwepulley kuri 2 ms ^-2 . Kukurumidza kunokonzerwa negiravhiti g = 10 ms ^-2 . Ndeipi nguva yekusashanda kwepulley.

Zvinozivikanwa:

Kukurumidza kwemutsetse kwemucheto wepulley (a) = 2 ms^-2

Kukurumidza kunokonzerwa negiravhiti (g) = 10 ms ^-2

Nharaunda yepulley (R) = 10 cm = 0.1 m

Kurema kwechinhu (w) = mg = (4)(10) = 40 N

Zvinodiwa: Nguva yekusagadzikana kwepulley

Solution:

Nguva yesimba (τ):

τ = FR = w R = (40)(0.1) = 4 Nm

Kukurumidza kwekona kwepulley (α) :

a = R α

α = a/R = 2 / 0.1 = 20 rad.s ^-2

Nguva yekusagadzikana kwepulley (I):

τ = ini α

I = τ/α = 4/20 = 0.2 kg m ²

3. Pulley yakawedzera simba pa 1 ms ^-2 . Kana radius yepulley iri 10 cm, chii chinonzi nguva yekusashanda kwepulley.

Zvinozivikanwa:

Kukurumidza kwemutsetse kwemucheto wepulley (a) = 1 ms^-2

Kukurumidza kunokonzerwa negiravhiti (g) = 10 ms ^-2

Nharaunda yepulley (R) = 10 cm = 0.1 m

Simba (F) = 4 N

Zvinodiwa: Nguva yekusashanda zvakanaka kwepulley

Solution:

Nguva yesimba (τ):

τ = FR = (4)(0.1) = 0.4 Nm

Kukurumidza kwepulley (α) kwekona:

a = R α

α = a/R = 1 / 0.1 = 10 rad.s ^-2

Nguva yekusagadzikana kwepulley (I):

τ = ini α

I = τ/α = 0.4 / 10 = 0.04 kg ^m2

Chii chinoenzana nekutenderera kwehukuru mukufamba kwakatwasuka?
- Pindura: Kutenderera kwakaenzana nehuremu mukufamba kwakatwasuka ndiyo nguva yekusaita chinhu, inowanzo ratidzwa se $I$ .
Torque inobatana sei nekufamba kwese kwese, uye inoenzaniswa sei nekushanda nesimba mukufamba kwemutsara?
- Pindura: Torque inofanana nesimba rinotenderera. Kunyange hazvo simba richikonzera kukurumidza kwakanangana muzvinhu, torque inokonzera kukurumidza kwekona mumiviri inotenderera. Torque inoverengwa sechibereko chesimba rinoshandiswa uye daro rakamira kubva pa axis yekutenderera kusvika pakushandiswa kwesimba.
Chii chiri hukama huripo pakati pekumhanya kwe angular, torque, uye nguva yekusagadzikana?
- Pindura: Hukama hwacho hunopiwa nemutemo wechipiri waNewton wekutenderera: $τ = I α$ , apo $τ$ ndiyo torque, $I$ inguva yekusagadzikana, uye $α$ ndiyo kona yekukurumidzira.
Kana nguva yekusagadzikana kwechinhu chinotenderera ikawedzera nepo torque yekunze ichiramba yakadaro, chii chinoitika kukukurumidza kwekona?
- Pindura: Kana nguva yekusagadzikana ikawedzera uye torque yekunze ikaramba iripo, kukurumidza kwekona kuchaderera.
Pfungwa dze "linear momentum" ne "angular momentum" dzakafanana sei mukufamba kwe "linear" ne "rotational motion"?
- Pindura: Mwero wemutsara (wakapihwa na $p = m v$ , apo $m$ yakakura uye $v$ ispeed) chibereko chekumhanya kwehukuru nemutsara, nepo angular momentum (yakapihwa na $L = I ω$ , apo $I$ inguva yekusagadzikana uye $ω$ ndiyo angular velocity) chibereko chenguva yekusashanda nesimba uye angular velocity.
Chii chinorehwa nekuchengetedzwa kwe angular momentum?
- Pindura: Kuchengetedzwa kwe angular momentum kunotaura kuti kana pasina ma torque ekunze, angular momentum yese ye closed system inoramba yakadaro.
Sei vanhu vanotsvedza vachimhanya nekukurumidza pavanopinza maoko avo mukati panguva yekutenderera?
- Pindura: Kana vakwikwidzi vema "figure skaters" vakapinza maoko avo mukati, vanoderedza nguva yavo yekusagadzikana. Nekuda kwekuchengetedzwa kwe "angular momentum", kana nguva yekusagadzikana yadzikira, "angular velocity" (kana kuti "rate of spin") inofanira kuwedzera kuti "angular momentum" irambe iripo.
Simba rekinetic rinotenderera rechinhu rinoenzaniswa sei nesimba rayo rekinetic rakatsetseka?
- Pindura: Simba rekinetic rinotenderera (rinopiwa ne 1/2 $I ω^{2}$ ) yakafanana ne linear kinetic energy (yakapihwa ne 1/2 $m v^{2}$ Yekutanga inobatanidzwa nekutenderera kwechinhu, uye yechipiri inobatanidzwa nekufamba kwayo kwakatwasuka.
Chinhu chinogona kuva nesimba rekutenderera uye rakatsetseka rekinetic panguva imwe chete here?
- Pindura: Ehe, chinhu chinogona kuva nesimba rekutenderera uye rekutenderera. Semuenzaniso, vhiri rinotenderera rine simba rekutenderera nekuda kwekutenderera kwaro uye simba rekutenderera nekuda kwekufamba kwaro mberi.
Kana radius yevhiri rinotenderera ikawedzera kaviri uku ichiramba ichichinja, nguva yayo yekusagadzikana inochinja sei?

Pindura: Nguva yekusashanda kwediski yakasimba inopiwa ne 1/2 $m r^{2}$ , apo $m$ ndiyo misa uye $r$ ndiyo radius. Kana radius ikawedzera kaviri uye huremu hukaramba hwakafanana, nguva yekusaita chinhu ichawedzera nechikamu chechina.