Bir cismin veya sistemin a\u011f\u0131rl\u0131k merkezi,<\/strong> s\u00f6z konusu cismin veya sistemin k\u00fctlesine etki eden t\u00fcm yer\u00e7ekimi kuvvetinin etki etti\u011fi kabul edilen noktad\u0131r.<\/p>\n Ba\u015fka bir deyi\u015fle, bir cismin a\u011f\u0131rl\u0131k merkezi, D\u00fcnya’n\u0131n s\u00f6z konusu cisme uygulad\u0131\u011f\u0131 yer\u00e7ekimi kuvvetinin uygulama noktas\u0131d\u0131r.<\/p>\n \u00d6rne\u011fin bir k\u00fcrenin a\u011f\u0131rl\u0131k merkezi k\u00fcrenin merkezidir. Bir k\u00fcrenin k\u00fctlesi t\u00fcm v\u00fccuda e\u015fit olarak da\u011f\u0131t\u0131ld\u0131\u011f\u0131ndan bu, a\u011f\u0131rl\u0131k merkezinin basit bir \u00f6rne\u011fidir, ancak a\u015fa\u011f\u0131da g\u00f6rece\u011fimiz gibi bazen bir cismin a\u011f\u0131rl\u0131k merkezini belirlemek i\u00e7in bir hesaplama yap\u0131lmas\u0131 gerekir.<\/p>\n Fizikte a\u011f\u0131rl\u0131k merkezi genellikle cdg veya CDG olarak k\u0131salt\u0131l\u0131r. Benzer \u015fekilde a\u011f\u0131rl\u0131k merkezine de denge merkezi veya denge merkezi ad\u0131 verilir.<\/p>\n Tahmin edebilece\u011finiz gibi m\u00fchendislikte bir sistemin a\u011f\u0131rl\u0131k merkezinin nerede oldu\u011funu bilmek, \u00f6rne\u011fin bir yap\u0131n\u0131n dengesini ve stabilitesini do\u011fru bir \u015fekilde incelemenizi sa\u011flar. <\/p>\n Bir sistemin a\u011f\u0131rl\u0131k merkezinin koordinatlar\u0131n\u0131 hesaplamak i\u00e7in<\/strong> , sistemdeki her k\u00fctlenin \u00e7arp\u0131mlar\u0131n\u0131n toplam\u0131n\u0131 bir referans noktas\u0131na olan uzakl\u0131\u011f\u0131na g\u00f6re bulman\u0131z ve ard\u0131ndan sonucu t\u00fcm k\u00fctlelerin toplam\u0131na b\u00f6lmeniz gerekir.<\/p>\n Bu form\u00fcl\u00fc biri a\u011f\u0131rl\u0131k merkezinin X koordinat\u0131n\u0131 bulmak i\u00e7in, di\u011feri Y koordinat\u0131n\u0131 bulmak i\u00e7in olmak \u00fczere iki kez kullanman\u0131z gerekir. Yani a\u011f\u0131rl\u0131k merkezini hesaplamak i\u00e7in form\u00fcller \u015funlard\u0131r: <\/p>\n \n \n Mant\u0131ksal olarak e\u011fer \u00fc\u00e7 boyutta \u00e7al\u0131\u015f\u0131yorsan\u0131z ayn\u0131 form\u00fcl\u00fc benzer \u015fekilde z koordinat\u0131 i\u00e7in de uygulaman\u0131z gerekir. <\/p>\n A\u015fa\u011f\u0131da a\u011f\u0131rl\u0131k merkezinin tan\u0131m\u0131 ve form\u00fcl\u00fc dikkate al\u0131narak bir sistemin a\u011f\u0131rl\u0131k merkezinin nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rmeniz i\u00e7in ad\u0131m ad\u0131m bir al\u0131\u015ft\u0131rma yer almaktad\u0131r.<\/p>\n Bu durumda sistemin d\u00f6rt geometrik \u015fekli simetrik oldu\u011fundan, a\u011f\u0131rl\u0131k merkezini hesaplamak i\u00e7in her \u015feklin merkezinin koordinatlar\u0131n\u0131 almak gerekir.<\/p>\n \u00d6ncelikle a\u011f\u0131rl\u0131k merkezinin X koordinat\u0131n\u0131 hesapl\u0131yoruz:<\/p>\n \n Daha sonra a\u011f\u0131rl\u0131k merkezinin Y koordinat\u0131n\u0131 kar\u015f\u0131l\u0131k gelen form\u00fcl\u00fcyle buluyoruz:<\/p>\n \n Sonu\u00e7 olarak t\u00fcm sistemin a\u011f\u0131rl\u0131k merkezi \u015fu \u015fekildedir: <\/p>\n \n A\u011f\u0131rl\u0131k merkezi ile k\u00fctle merkezi aras\u0131ndaki fark,<\/strong> a\u011f\u0131rl\u0131k merkezinin yer\u00e7ekimi kuvvetinin uygulama noktas\u0131 olmas\u0131, k\u00fctle merkezinin ise t\u00fcm d\u0131\u015f kuvvetlerin uygulama noktas\u0131 olmas\u0131d\u0131r.<\/p>\n Yani a\u011f\u0131rl\u0131k merkezi, bir sistemdeki t\u00fcm yer\u00e7ekimi kuvvetlerinin yerini almas\u0131yla ortaya \u00e7\u0131kan kuvvetin etki etti\u011fi kabul edilen noktad\u0131r; k\u00fctle merkezi ise bile\u015fke kuvvetin etki etti\u011fi kabul edilen noktad\u0131r. Sistem d\u0131\u015f\u0131ndaki t\u00fcm kuvvetler.<\/p>\n Ancak yer\u00e7ekimi alan\u0131 d\u00fczg\u00fcn oldu\u011funda a\u011f\u0131rl\u0131k merkezi k\u00fctle merkeziyle \u00e7ak\u0131\u015f\u0131r. Bu nedenle, D\u00fcnya’daki yer\u00e7ekimi neredeyse tekd\u00fcze oldu\u011fundan, pratik ama\u00e7lar i\u00e7in k\u00fctle merkezi ve a\u011f\u0131rl\u0131k merkezi ayn\u0131 nokta olarak kabul edilir. <\/p>\n Geometrik merkez,<\/strong> geometrik bir \u015feklin ortas\u0131ndaki noktad\u0131r. \u00d6rne\u011fin, bir dikd\u00f6rtgenin geometrik merkezi, simetri eksenlerinin kesi\u015fme noktas\u0131d\u0131r.<\/p>\n Bir cismin veya sistemin geometrik merkezi, cismin tekd\u00fcze bir yo\u011funlu\u011fa sahip oldu\u011fu veya sistemin k\u00fctle da\u011f\u0131l\u0131m\u0131n\u0131n simetrik oldu\u011fu durumlarda k\u00fctle merkeziyle ve dolay\u0131s\u0131yla a\u011f\u0131rl\u0131k merkeziyle \u00e7ak\u0131\u015f\u0131r.<\/p>\n Ayn\u0131 \u00f6rne\u011fi takip edersek, bir dikd\u00f6rtgenin geometrik merkezi onun a\u011f\u0131rl\u0131k merkezi ve k\u00fctle merkezidir. <\/p>\n Bir cismin a\u011f\u0131rl\u0131k merkezi a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/p>\n \n<\/span> A\u011f\u0131rl\u0131k merkezi nas\u0131l hesaplan\u0131r<\/span><\/h2>\n
![\"CDG_x=\\cfrac{\\sum](\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-881732a8a4b902f9d56d505b8b34e2eb_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/div>\n![\"CDG_y=\\cfrac{\\sum](\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-046d8b6e491e055221740d6a5d8c4a1f_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/div>\n<\/div>\n<\/span> A\u011f\u0131rl\u0131k merkezini hesaplama \u00f6rne\u011fi<\/span><\/h2>\n
\n
![\"\u00e7\u00f6z\u00fcmlenmi\u015f](\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/centre-de-gravite-centre-de-masse-exercice-resolu.png\")
<\/figure>\n<\/div>\n![\"\\begin{aligned}](\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-ab4ab958998ab401b3facce7064be29b_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\begin{aligned}](\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fe1cace8d53d430ec4e7cc550fc7ee74_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"CDG=(7,75\\](\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-14bae1047b3fa1dcff4e5c8be97514fa_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> A\u011f\u0131rl\u0131k merkezi ve k\u00fctle merkezi<\/span><\/h2>\n
<\/span> A\u011f\u0131rl\u0131k merkezi ve geometrik merkez<\/span><\/h2>\n
<\/span> A\u011f\u0131rl\u0131k Merkezi \u00d6zellikleri<\/span><\/h2>\n
\n
\n
![\"\\displaystyle](\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-b226b193f321aa3a4365556458d3c5a1_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n