Huwandu hwefizikisi mukufamba kwedenderedzwa

Huwandu hwefizikisi mukufamba kwedenderedzwa hunosanganisira kutama kwe angular, kumhanya kwe angular, uye kukurumidza kwe angular.

1. Kutama kwekona (θ)

Kufamba kwedenderedzwa kunonzi kufamba kwekona. Kufamba kwekona kusanganisira huwandu hwevector, saka, kune hukuru uye gwara. Kufamba kwekona kunowanzo ratidzwa nenzira yewachi (kutenderera kwewachi kana kurwisana newachi).

Kune mayuniti matatu ekuchinja kwekona. Chekutanga, dhigirii (o). Denderedzwa rimwe chete redenderedzwa rakaenzana ne360^oChechipiri, kutenderera. Denderedzwa rimwe chete redenderedzwa rakaenzana nedenderedzwa rimwe chete. Chechitatu, ma radians. Tarisa mufananidzo uri pazasi. Kana chinhu chichifamba mudenderedzwa, r = radius yedenderedzwa, x = kureba kwenzira yakatenderera iyo chinhu chinodarika = denderedzwa redenderedzwa.

Denderedzwa rimwe chete redenderedzwa rakaenzana ne2π radians.

Dambudziko remuenzaniso 1:

Chimurenga chimwe = 360 ^o . ½ chimurenga = …. Rad?

Solution:

1 revolution = 360 ^o = 2 π rad = 2(3.14) rad = 6.28 rad

1⁄2 revolution = 180 ^o = 1⁄2 (6.28 rad) = 3.14 rad

Dambudziko remuenzaniso 2:

1 rad = …… ^o ? 1 ^o = … rad ?

Solution:

180 ^o = π rad = 3.14 rad

2. Kumhanya kweAngular (ω)

a. Avhareji yekumhanya kwekona

Dambudziko remuenzaniso 3:

Vhiri rinotenderera newachi, rinotenderera kona ye180 ^o kwemasekonzi maviri uye 90 ^o kwesekondi imwe. Chii chiri kukura uye gwara reavhareji yekufamba kweavhareji?

Solution:

Kutungamira kweavhareji yekumhanya kwekona = kutungamira kwewachi.

9 ^o /s = … rad/s ?

Dambudziko remuenzaniso 4:

Vhiri rinotenderera newachi, rinotenderera nekona ye360 ^o kwemasekonzi mana. Vhiri rinotenderera newachi, richitenderera nekona ye180 ^o kwemasekonzi maviri. Ndeipi avhareji yekufamba kwekona?

Solution:

Kutungamira kweavhareji yekumhanya kwekona = kutungamira kwewachi.

3 ^o /s = … rad/s?

b. Kumhanya kwekona ipapo ipapo

Kumhanya kweinstant angular kunowanzonzi kumhanya kweiangle. Kana kungotaurwa chete kumhanya kweiangle, zvinoreva kumhanya kweinstant angular. Kukura kweinstant angular velocity = kukura kweinstant angular velocity munguva pfupi pfupi. Masvomhu:

Kana tiri mukufamba kwakatwasuka, tinogona kutsiva hukuru hwekukurumidza nekumhanya, kuitira kuti mukufamba kwedenderedzwa tigone kutsiva hukuru hwekukurumidza kweangle nekumhanya kweangle.

3. Kumhanyisa kwekona (α)

a. Avhareji yekumhanya kwekona

Dambudziko remuenzaniso 5:

Pakutanga hwindimiri yakanga yakamira, ichifuridzwa nemhepo, saka yakatenderera newachi. Mushure memasekonzi maviri, kumhanya kwekona kunosvika 90 ^o / s. Ndeipi avhareji yekumhanya kwekona?

Solution:

Paavhareji, kumhanya kwekona kwemhepo kunochinja ne45 o/sekondi yega yega sekondi = … rad / s sekondi yega yega?

b. Kukurumidza kwekona panguva imwe chete

Kukurumidza kwe-angular acceleration kunowanzo pfupikiswa se-angular acceleration. Kukurumidza kwe-angular acceleration kuchinja kwe-angular velocity munguva pfupi pfupi. Masvomhu:

Ukuru hwakatsetseka mukufamba kwedenderedzwa

Huwandu hwemutsara huwandu huri mukufamba kwakatwasuka, zvakaita sekutama (daro), kumhanya (kumhanya), uye kumhanyisa. Kune rumwe rutivi, huwandu hwekufamba kwakatwasuka hunogona kunzi huwandu hwekona.

1. Kutama

Tarisa chinhu chiri kutenderera, senge vhiri kana feni kana windmill kana wachi, nezvimwewo. Kana chinhu chakafanana nefeni chikatenderera, zvikamu zvese zvefeni zvinotenderera pamwe chete. Kana feni ikatenderera kamwe chete (360 ^o ), zvikamu zvese zvefeni, zviri pamucheto uye pedyo neaxis zvinotorawo kutenderera kamwe chete kana 360 ^o . Kutenderera kumwe chete kana 360 ^o hukuru hwekusanduka kwekona kunoitwa nezvikamu zvese zvefeni, zviri pamucheto uye pedyo neaxis.

Kana feni yaita kamwe chete, chikamu chefeni chiri pamucheto nechikamu chefeni chiri pedyo ne axis of rotation zvinofamba kusvika padenderedzwa rimwe chete (2). Kana radius yefeni iri 20 cm, daro riri pakati pemucheto wefeni ne axis of rotation i20 cm. Semuenzaniso, daro riri pakati pe axis nechikamu chimwe chefeni chiri pedyo ne axis = 1 cm. Kana feni yaita kamwe chete, divi refeni rinofamba rakatenderera kusvika pa (2)(3.14)(20 cm) = 125.6 cm,

nepo nzvimbo iri pedyo neakisi ichifamba yakatenderera kusvika pa (2)(3.14)(1 cm) = 6.28 cm. 125.6 cm ndiko kukura kwekufambiswa kunoitwa nemupendero wefeni,

nepo 6.28 cm iri hukuru hwekutama kunoitwa nenzvimbo iri pedyo ne axis yekutenderera. Kana r iri diki, kutatama kudiki. Hukama huripo pakati pekutama (d) nekutama kwe angular (θ) hunoratidzwa ne equation:

θ = d / r

d = r θ

d = kutama (mita), r = radius kana chinhambwe kubva pa axis yekutenderera (mita), θ = kutama kwekona (radians)

Dambudziko remuenzaniso 6:

CD ine 5 cm mu radius inotenderera nepakona ye90o. Chii chinonzi displacement ye point 2 cm kubva pa axis of rotation?

Solution:

r = daro kubva pa axis yekutenderera = 2 cm = 0.02 m

θ = 90 ^o = 1.57 rad (inofanira kutaurwa muma radians)

d = (0.02 m)(1.57 rad) = 0.03 m.

Kuchinjana kweAngular hakuna system unit yepasi rose uye hakuna dimension (dimension yayo i1), saka mukuverenga sezviri pamusoro apa, ingobvisa radians unit kubva mumhedzisiro yekuverenga.

2. Velocity

Kana ichitenderedzwa, feni kana chimwe chinhu chinotenderera, zvechokwadi, chinoda nguva yakatarwa. Kana feni ikatenderera newachi uye ikatora kutenderera kamwe chete (360 ^o ) kwesekondi imwe chete,

ipapo kumhanya kwekona kwezvikamu zvese zvefeni i1 rev/s = 360 ^o /s = 6.28 rad/s uye kutungamira kwekufamba kwekona kwakafanana nekutungamira kwetsono yeawa.

Kana nharaunda yefeni iri 20 cm, ipapo mupendero wefeni unofamba wakatenderera nekumhanya kwe2(3.14)(20 cm) / 1 second = 125.6 cm/s = 1.256 m/s. Poindi iri 1 cm (0.01 m) kubva pa axis yekutenderera nekumhanya kwe2 (3.14) (1 cm)/1 second = 6.28 cm/s = 0.0628 m/s. R diki, kumhanya kudiki. Mukufamba kwedenderedzwa, kumhanya kunowanzonzi kumhanya kwetangential.

Hukama huripo pakati pevelocity (v) uye angular velocity (ω) hunoratidzwa ne equation:

v = kumhanya (m/s), r = radius kana daro kubva pa axis yekutenderera (m), ω = angular velocity (rad/s)

Dambudziko remuenzaniso 7:

Kumhanya kwetsono yechipiri i6.28 rad/minute = 6.28 rad / 60 second = 0.1 rad/s. Ndeipi kumhanya kwepoindi iri 2 cm (0.02 m) kubva pa axis yekutenderera?

Solution:

ω = 0.1 rad/s, r = 0.02 m

v = r

ω = (0.02 m)(0.1 rad/s) = 0.002 m/s

Bvisa ma radians kubva pamhedzisiro yekuverenga.

3. Kukurumidzisa

Nzvimbo yekufamba yakatenderera inokurumidza kana hukuru negwara rekufamba kwemhepo zvikachinja. Nokudaro, kune mhando mbiri dzekumhanya mukufamba kwedenderedzwa. Chekutanga, kukurumidza kwepakati (a _c ) kana kunonziwo radial acceleration (a _r ). Kumhanya kwepakati kunoitika nekuda kwekuchinja kwegwara rekufamba kwemhepo. Kutungamira kwekukurumidza kwepakati kunogara kuchienda pakati pedenderedzwa.

Kukura kwekumhanya kwepakati pesimba ndekwekuti:

a _c = kukurumidza kwepakati (m/s ² ), r = radius kana daro kubva pa axis yekutenderera (m), v = kumhanya (m/s), ω = angular velocity (rad/s)

Chechipiri, kukurumidza kwetangential (a _t ). Kukurumidza kwetangential kunoitika nekuda kwekuchinja kwehukuru hwespeed. Ongorora poindi iri pamucheto wefeni inotenderera. Kana, pakutanga, feni yakagara, ipapo poindi iri pamucheto wefeni yakagarawo (v = 0). Kana sekondi imwe gare gare, feni inotenderera nekumhanya kweangular kwe1 rev/s = 360 ^o /s = 6.28 rad/s kuitira kuti poindi iri pamucheto wefeni ifambe yakatenderera nekumhanya kwe1.2 m/s

ipapo nzvimbo iri pamucheto wemhepo yefeni inowana kukurumidza kwe1.2 m/s pasekondi = 1.2 m/s ².

Hukama huripo pakati pekuwedzera simba (a _t ) uye kuwedzera simba ( α ) hunoratidzwa ne equation:

a _t = kukurumidza kwetangential (m/s ² ), r = radius kana daro kubva pa axis yekutenderera (m), α = kukurumidza kwekona (rad/s ² )

Hukama huripo pakati penguva (T) nefrequency (f) nekumhanya uye kumhanya kwekona

Nguva yacho inotaura nguva yekuti chinhu chiite revolution imwe chete, ukuwo frequency yacho ichireva huwandu hwerevolutions kwesekondi imwe chete. Hukama huripo pakati peperiod nerefrequency hunoratidzwa kuburikidza ne equation: f = 1/T

Chikamu cheInternational System chenguva iyoyo ndechechipiri, chikamu cheInternational System chefrequency i1 / sekondi (= hertz). Kumhanya (v) uye angular velocity (ω) yezvikamu zvinofamba zvakatenderera zvinogona kuratidzwa mumapeji kana mafrequencies.

Kumhanya (v) kwechikamu chinofamba chakatenderera kunoratidzwa ne equation:

Hukuru hwe angular velocity (ω) yezvikamu zvinofamba zvakatenderera hunoratidzwa ne equation: