F = ma yana haɗa ƙarfi, nauyi, da gudun ƙaruwa. Ninka ƙarfi, ninka gudun ƙaruwa. Raba nauyi biyu, ninka gudun ƙaruwa.

• 1 N = 1 kg·m/s²
• Ƙarin ƙarfi → ƙarin gudun ƙaruwa
• Rage nauyi → ƙarin gudun ƙaruwa
• Yawan vector: yana da alkibla

Saurin motsi shine gudu tare da alkibla. Gudun ƙaruwa shine yadda saurin motsi yake canzawa — ƙara gudu, rage gudu, ko canza hanya.

• Mai kyau: ƙara gudu
• Mara kyau: rage gudu (raguwar gudu)
• Mota mai lanƙwasa: tana ƙara gudu (alkibla tana canzawa)
• Gudu marar canzawa ≠ gudun ƙaruwa na sifili idan tana lanƙwasa

Ƙarfin-G yana auna gudun ƙaruwa a matsayin ninki na nauyin duniya. 1g = 9.81 m/s². Matuƙa jirgin yaƙi suna jin 9g, 'yan sama jannati 3-4g a lokacin harba su.

• 1g = tsaye a duniya
• 0g = faɗuwa kyauta / kewaya
• G mara kyau = gudun ƙaruwa zuwa sama (jini zuwa kai)
• Dorewar 5g+ yana buƙatar horo

Matsayin duniya da ke amfani da m/s² a matsayin tushe tare da sikelin goma-goma. Tsarin CGS yana amfani da Gal don ilimin ƙasa.

• m/s² — raka'ar tushe ta SI, ta duniya baki ɗaya
• km/h/s — motoci (lokacin 0-100 km/h)
• Gal (cm/s²) — ilimin ƙasa, girgizar ƙasa
• milligal — neman nauyi, tasirin igiyar ruwa

Har yanzu ana amfani da raka'o'in al'ada na Amurka a fannin motoci da zirga-zirgar jiragen sama na Amurka tare da ma'auni na metric.

• ft/s² — matsayin injiniya
• mph/s — tseren ja, bayanan mota
• in/s² — gudun ƙaruwa a ƙaramin sikelin
• mi/h² — ba a cika amfani da shi ba (nazarin manyan hanyoyi)

Yanayin zirga-zirgar jiragen sama, sararin samaniya, da na likitanci suna bayyana gudun ƙaruwa a matsayin ninki na g don fahimtar juriyar ɗan adam cikin sauƙi.

• ƙarfin-g — rabo mara ma'auni ga nauyin duniya
• Nauyin duniya na yau da kullun — 9.80665 m/s² (daidai)
• Milligravity — binciken ƙarancin nauyi
• G na duniyoyi — Mars 0.38g, Jupiter 2.53g

Muhimman dabaru suna danganta gudun ƙaruwa, saurin motsi, nisa, da lokaci a ƙarƙashin gudun ƙaruwa marar canzawa.

• v₀ = saurin motsi na farko
• v = saurin motsi na ƙarshe
• a = gudun ƙaruwa
• t = lokaci
• s = nisa

Abubuwan da ke motsi a cikin da'ira suna ƙara gudu zuwa tsakiya koda a gudu marar canzawa. Dabara: a = v²/r

• Kewayar Duniya: ~0.006 m/s² zuwa Rana
• Mota mai lanƙwasa: ana jin ƙarfin g na gefe
• Zagayen abin hawa na nishaɗi: har zuwa 6g
• Satelit: gudun ƙaruwa na centripetal marar canzawa

Kusa da gudun haske, gudun ƙaruwa ya zama mai rikitarwa. Na'urorin ƙara saurin ƙwayoyin halitta suna kaiwa 10²⁰ g nan da nan a lokacin karo.

• Protons na LHC: miliyan 190 g
• Faɗaɗawar lokaci tana shafar gudun ƙaruwa da ake gani
• Nauyi yana ƙaruwa da saurin motsi
• Gudun haske: iyaka da ba za a iya kaiwa ba

Gudun ƙaruwa yana bayyana aikin mota. Lokacin 0-60 mph yana fassara kai tsaye zuwa matsakaicin gudun ƙaruwa.

• Mota mai tsere: 0-60 a 3s = 8.9 m/s² ≈ 0.91g
• Mota mai amfani: 0-60 a 10s = 2.7 m/s²
• Tesla Plaid: 1.99s = 13.4 m/s² ≈ 1.37g
• Taka birki: -1.2g mafi yawa (titi), -6g (F1)

Iyakokin zayyana jirgin sama sun dogara ne da juriyar g. Matuƙa jirgi suna horo don motsi mai yawan g.

• Jirgin kasuwanci: iyakar ±2.5g
• Jirgin yaƙi: ikon +9g / -3g
• Jirgin sama mai zuwa sararin samaniya: 3g a lokacin harba shi, 1.7g a lokacin dawowa
• Fitarwa a 14g (iyakar rayuwar matuƙi)

Ƙananan canje-canje a gudun ƙaruwa suna bayyana tsarin ƙasa. Na'urorin Centrifuge suna raba abubuwa ta amfani da gudun ƙaruwa mai tsanani.

• Binciken nauyi: daidaiton ±50 microgal
• Girgizar ƙasa: 0.1-1g na yau da kullun, 2g+ mai tsanani
• Centrifuge na jini: 1,000-5,000g
• Ultracentrifuge: har zuwa 1,000,000g

Ninka darajar g da 10 don kimantawa da sauri (daidai: 9.81)

• 3g ≈ 30 m/s² (daidai: 29.43)
• 0.5g ≈ 5 m/s²
• Jirgin yaƙi a 9g = 88 m/s²

Raba 26.8 da sakan zuwa 60mph

• Sakan 3 → 26.8/3 = 8.9 m/s²
• Sakan 5 → 5.4 m/s²
• Sakan 10 → 2.7 m/s²

Raba da 2.237 don canza mph/s zuwa m/s²

• 1 mph/s = 0.447 m/s²
• 10 mph/s = 4.47 m/s²
• 20 mph/s = 8.94 m/s² ≈ 0.91g

Raba da 3.6 (kamar canjin gudu)

• 36 km/h/s = 10 m/s²
• 100 km/h/s = 27.8 m/s²
• Da sauri: raba da ~4

1 Gal = 0.01 m/s² (santimita zuwa mita)

• 100 Gal = 1 m/s²
• 1000 Gal ≈ 1g
• 1 milligal = 0.00001 m/s²

Mars ≈ 0.4g, Wata ≈ 0.17g, Jupiter ≈ 2.5g

• Mars: 3.7 m/s²
• Wata: 1.6 m/s²
• Jupiter: 25 m/s²
• Venus ≈ Duniya ≈ 0.9g

Tesla Plaid: 0-60 mph a cikin sakan 1.99. Menene gudun ƙaruwarsa?

60 mph = 26.82 m/s. a = Δv/Δt = 26.82/1.99 = 13.5 m/s² = 1.37g

F-16 yana jan 9g a ft/s²? Girgizar ƙasa a 250 Gal a m/s²?

Jirgi: 9 × 9.81 = 88.3 m/s² = 290 ft/s². Girgizar ƙasa: 250 × 0.01 = 2.5 m/s²

Tsalle da saurin 3 m/s a Wata (1.62 m/s²). Yaya tsawon?

v² = v₀² - 2as → 0 = 9 - 2(1.62)h → h = 9/3.24 = 2.78m (~9 ft)

Ƙuma tana ƙara gudu a 100g lokacin da ta yi tsalle — fiye da harba jirgin sama mai zuwa sararin samaniya. Ƙafafunta suna aiki kamar spring, suna fitar da kuzari a cikin millise seconds.

Yana ƙara saurin guduma a 10,000g, yana haifar da kumfa na cavitation da ke rushewa da haske da zafi. Gilashin akwatin kifi ba shi da dama.

Kwakwalwar ɗan adam na iya jure 100g na 10ms, amma 50g ne kawai na 50ms. Buga a wasan ƙwallon ƙafa na Amurka: 60-100g a kai a kai. Hulunan kwano suna rarraba lokacin bugun.

Babban Hadron Collider yana ƙara saurin protons zuwa 99.9999991% na gudun haske. Suna fuskantar miliyan 190 g, suna zagaye zoben kilomita 27 sau 11,000 a sakan.

Nauyin duniya ya bambanta da ±0.5% saboda tsawo, latitude, da yawan ƙasa. Hudson Bay yana da ƙarancin nauyi da 0.005% saboda dawowar bayan zamanin ƙanƙara.

Sled na Sojojin Sama na Amurka ya kai raguwar gudu na 1,017g a cikin sakan 0.65 ta amfani da birkin ruwa. Abin gwajin ya tsira (da kyar). Iyakar ɗan adam: ~45g tare da madaurin da ya dace.

Tsallen Felix Baumgartner na 2012 daga kilomita 39 ya kai Mach 1.25 a cikin faɗuwa kyauta. Gudun ƙaruwa ya kai 3.6g, raguwar gudu a lokacin buɗe laimar sauka: 8g.

Na'urorin auna nauyi na atomic suna gano 10⁻¹⁰ m/s² (0.01 microgal). Suna iya auna canjin tsawo na 1cm ko kogo a ƙarƙashin ƙasa daga sama.

Aristotle ya yi iƙirarin cewa abubuwa masu nauyi suna faɗuwa da sauri. Galileo ya tabbatar da kuskurensa ta hanyar mirgina ƙwallaye na tagulla a kan gangare (1590s). Ta hanyar rage tasirin nauyi, Galileo ya sami damar auna gudun ƙaruwa da agogon ruwa, inda ya gano cewa dukkan abubuwa suna ƙara gudu daidai ba tare da la'akari da nauyinsu ba.

Principia na Newton (1687) ya haɗa ra'ayin: F = ma. Ƙarfi yana haifar da gudun ƙaruwa wanda ya saba da nauyi. Wannan dabara ɗaya ta bayyana faɗuwar tuffa, kewayar wata, da hanyoyin harsasai. Gudun ƙaruwa ya zama haɗin kai tsakanin ƙarfi da motsi.

• 1590: Gwaje-gwajen Galileo a kan gangare suna auna gudun ƙaruwa marar canzawa
• 1638: Galileo ya buga Sabbin Kimiyoyi Biyu, yana tsara kinematics
• 1687: F = ma na Newton ya haɗa ƙarfi, nauyi, da gudun ƙaruwa
• An kafa g ≈ 9.8 m/s² ta hanyar gwaje-gwajen pendul

Masana kimiyya na ƙarni na 19 sun yi amfani da pendul masu juyawa don auna nauyin gida da daidaito na 0.01%, suna bayyana siffar duniya da bambancin yawa. An tsara raka'ar Gal (1 cm/s², wanda aka sanya wa Galileo suna) a 1901 don binciken ilimin ƙasa.

A 1954, ƙungiyar ƙasa da ƙasa ta karɓi 9.80665 m/s² a matsayin nauyin duniya na yau da kullun (1g)—an zaɓi a matsayin matakin teku a latitude 45°. Wannan darajar ta zama abin tunani ga iyakokin zirga-zirgar jiragen sama, lissafin ƙarfin-g, da ma'aunin injiniya a duk duniya.

• 1817: Pendul mai juyawa na Kater ya kai daidaiton nauyi na ±0.01%
• 1901: An daidaita raka'ar Gal (cm/s²) don ilimin ƙasa
• 1940s: Na'urar auna nauyi ta LaCoste ta ba da damar binciken fili na 0.01 milligal
• 1954: ISO ta karɓi 9.80665 m/s² a matsayin nauyin duniya na yau da kullun (1g)

Matuƙan jirgin yaƙi na Yaƙin Duniya na II sun fuskanci suma a lokacin lanƙwasa masu kaifi—jini ya taru daga kwakwalwa a ƙarƙashin 5-7g mai dorewa. Bayan yaƙin, Col. John Stapp ya hau sled na roka don gwada juriyar ɗan adam, inda ya tsira daga 46.2g a 1954 (raguwar gudu daga 632 mph zuwa sifili a cikin sakan 1.4).

Tseren sararin samaniya (1960s) ya buƙaci fahimtar yawan g mai dorewa. Yuri Gagarin (1961) ya jure 8g a lokacin harba shi da 10g a lokacin dawowa. 'Yan sama jannatin Apollo sun fuskanci 4g. Waɗannan gwaje-gwajen sun tabbatar da: mutane suna jure 5g har abada, 9g na ɗan lokaci (tare da rigunan g), amma 15g+ na haifar da haɗarin rauni.

• 1946-1958: Gwajin sled na roka na John Stapp (tsira a 46.2g)
• 1954: An saita ma'aunin kujerar fitarwa a 12-14g na sakan 0.1
• 1961: Jirgin Gagarin ya tabbatar da yiwuwar tafiye-tafiyen ɗan adam zuwa sararin samaniya (8-10g)
• 1960s: An haɓaka rigunan anti-g da ke ba da damar motsin jirgin yaƙi na 9g

Babban Hadron Collider (2009) yana ƙara saurin protons zuwa 99.9999991% na gudun haske, yana kaiwa 1.9×10²⁰ m/s² (miliyan 190 g) a cikin gudun ƙaruwa na da'ira. A waɗannan gudun, tasirin relativistic ya fi rinjaye—nauyi yana ƙaruwa, lokaci yana faɗaɗa, kuma gudun ƙaruwa ya zama asymptotic.

A halin yanzu, na'urorin auna nauyi na atomic interferometer (2000s+) suna gano 10 nanogal (10⁻¹¹ m/s²)—suna da hankali sosai har suna auna canjin tsawo na 1cm ko kwararar ruwa a ƙarƙashin ƙasa. Aikace-aikace sun haɗa da neman mai zuwa hasashen girgizar ƙasa da sa ido kan dutsen mai fitar da wuta.

• 2000s: Na'urorin auna nauyi na atomic sun kai hankalin 10 nanogal
• 2009: LHC ya fara aiki (protons a miliyan 190 g)
• 2012: Satelit na taswirar nauyi suna auna filin duniya da daidaito na microgal
• 2020s: Na'urorin auna quantum suna gano raƙuman nauyi ta hanyar ƙananan gudun ƙaruwa