Mene ne kusurwa gudu da kuma yadda aka lasafta?

Yawancin lokaci, a lokacin da mutane magana game da motsi, muka kwatanta wani abu da yake motsi a cikin wani madaidaiciya line. Gudun da wannan yunkuri da aka kira mikakke, da kuma lissafi na ta talakawan darajar ne sauki: Ya isa ga samun rabo daga nesa tafiya da lokacin cikin abin da aka shawo kan ta cikin jiki. Idan abu ne koma tare da karkara, a cikin wannan yanayin ba m da mikakke kuma kusurwa gudu. Abin da irin darajar da kuma yadda aka lasafta? Wannan kawai zai yi magana a wannan labarin.

Kusurwa gudu: manufar da dabara

Lokacin da taro batu motsa a kan karkara gudun da motsi za a iya halin da kwana na juyawa daga radius cewa haɗu da dabba ba a kanta abu da cibiyar daga cikin da'irar. A fili yake cewa wannan adadi ne kullum canja dangane da lokaci. A rapidity tare da wannan tsari ya auku, da kuma a can ne ba wanin kusurwa gudu. A wasu kalmomin, da rabo daga cikin sabawa na radius vector daga cikin abu da tsawon lokaci ya dauki yin wannan abu juyawa. Kusurwa gudu Formula (1) za a iya rubuta a cikin hanyar:

w = φ / t, inda:

φ - juya kwana range,

t - lokaci lokaci na juyawa.

Unit na ji

A cikin kasa da kasa tsarin na al'ada raka'a (SI) ga faye hali na jũya sanya amfani radians. Saboda haka, 1 Rad / s - ainihin naúrar, wanda aka yi amfani da lissafi na kusurwa gudu. A daidai wannan lokaci, ba wanda ya haramta yin amfani da darajõji (lura cewa daya Rad ne daidai to 180 / pi, ko 57˚18 '). Har ila yau, mai kusurwa gudu za a iya bayyana a yawan juyin minti daya ko biyu da. Idan motsi faruwa gaba ɗaya a kusa da karkara, wannan darajar za a iya samu daga dabara (2):

w = 2π * n,

inda n - gudun.

In ba haka ba, kamar yadda aka yi ga al'ada gudun, lissafta wani talakawan ko instantaneous kusurwa gudun. Ya kamata a lura da cewa sama ne mai vector yawa. Don sanin ta shugabanci yawanci amfani da hannun daman mulki, wanda aka sau da yawa amfani da kimiyyar lissafi. A kusurwa gudu vector nuna a cikin shugabanci, a cikin abin da gaba motsi na dunƙule daga dama-hannu thread. A wasu kalmomin, shi ne directed tare da axis a kusa da jiki, a cikin shugabanci daga wanda juyawa da aka gani abin da ke faruwa anti-kewaye iri na agogo.

misalai na lissafi

Misali kana so ka sanin abin da yake cikin mikakke kuma kusurwa gudu da ƙafa, idan an san cewa da diamita ne daidai da daya mita, da kuma rotational kwana canje-canje a bisa ga dokar da φ = 7t. Mun yi amfani da mu farko dabara:

w = φ / t = 7t / t = 7 s ^-1.

Wannan ne ake bukata kusurwa gudu. Yanzu bari mu je sami saba gudun, muka matsa. Kamar yadda ka sani, v = s / t. Ganin cewa S a cikin yanayin - a karkara na cikin dabaran (l = 2π * r), kuma 2π - daya cikakken juyin juya hali, da wadannan da aka samu:

v = 2π * r / t = w * r = 7 * 0.5 = 3.5 m / s

A nan ne wani aiki a kan wannan batu. An sani cewa duniya ta radius a ekweita ne daidai da 6370 kilomita. Ake bukata domin sanin mikakke kuma kusurwa gudun motsi na da maki a kan wannan layi daya, wanda ya auku a sakamakon juyawa daga wannan duniya tamu a kan ta axis. A wannan yanayin, muna bukatar wani biyu dabara:

w = 2π * n = * 3.14 * 2 (1 / ( 24 * 3600)) = 7.268 * 10 -5 Rad / s.

Ya zauna domin sanin abin da yake cikin mikakke gudu: v = w * r = 7,268 * 10 ⁵ * 6370 * 1000 = 463 m / s.