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Öğretmen, Arda ve Eren adlı öğrencilerle birlikte dersi sunmaktadır.","Video, kütle ve ağırlık merkezi kavramlarının tanımıyla başlayıp, bu kavramların arasındaki farkları açıklamaktadır. Ardından farklı cisim türleri (ahşap masa, telden yapılmış cisimler, levha şeklindeki cisimler, üç boyutlu cisimler) için ağırlık merkezi hesaplamaları, dengede kalma durumları ve parça ekleme/çıkarma durumlarında ağırlık merkezinin nasıl değiştiği detaylı olarak anlatılmaktadır.","Videoda ayrıca tork hesaplamaları, eğik düzlem üzerinde devrilme riski, iple asıldığında dengede kalan cisimler ve günlük hayattaki ağırlık merkezi örnekleri (erkeklerin ve kadınların fiziksel yeteneklerindeki farklar) gibi konular da ele alınmaktadır. Öğretmen, konuyu geometrik bir yapıda ve çeşitli örnek sorular üzerinden pekiştirmektedir."]},"endTime":2781,"title":"Fizik Dersi: Kütle ve Ağırlık Merkezi","beginTime":0}],"fullResult":[{"index":0,"title":"Kütle ve Ağırlık Merkezi Kavramları","list":{"type":"unordered","items":["Kütle ve ağırlık merkezi konusu, 11. sınıfta yer alan, geometrik bilgi ve tork bilgisiyle birleştirilen önemli bir konudur.","Ağırlık büyük G sembolü ile gösterilir ve vektördür, kütle ise m sembolü ile gösterilir ve vektör değildir.","Kütle, değişmeyen madde miktarıdır ve her yerde aynı kalır; kütle merkezi ise cismin tüm kütlesinin toplandığı varsayılan merkez noktasıdır."]},"beginTime":7,"endTime":100,"href":"/video/preview/15866361810308013124?parent-reqid=1765462615165890-6029985380247354058-balancer-l7leveler-kubr-yp-vla-229-BAL&text=%E2%84%A2Bukidz%E2%84%A2&t=7&ask_summarization=1"},{"index":1,"title":"Kütle Merkezi ve Ağırlık Merkezi Arasındaki Farklar","list":{"type":"unordered","items":["Ağırlık, bir 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noktalarda olduğunda, ağırlık merkezi her zaman yere yakın olur.","Kütle merkezinin koordinatlarını bulmak için tork ilkesi kullanılabilir, ancak her zaman bu yöntem işe yaramaz."]},"beginTime":336,"endTime":636,"href":"/video/preview/15866361810308013124?parent-reqid=1765462615165890-6029985380247354058-balancer-l7leveler-kubr-yp-vla-229-BAL&text=%E2%84%A2Bukidz%E2%84%A2&t=336&ask_summarization=1"},{"index":5,"title":"Ağırlık Merkezi Problemi Çözümü","list":{"type":"unordered","items":["Farklı ahşaplardan yapılan 60 kilogram kütleli ahşap masanın kütle merkezi O noktasında bulunuyor ve dördüncü ayağa gelen kuvvet 50 Newton olarak hesaplanıyor.","Ağırlık merkezi problemlerinde, cismin ağırlığını (kütlesi × yerçekimi ivmesi) bulup, bu ağırlığı cismin farklı noktalarına dağıtarak çözüm yapılır."]},"beginTime":639,"endTime":743,"href":"/video/preview/15866361810308013124?parent-reqid=1765462615165890-6029985380247354058-balancer-l7leveler-kubr-yp-vla-229-BAL&text=%E2%84%A2Bukidz%E2%84%A2&t=639&ask_summarization=1"},{"index":6,"title":"Telden Yapılmış Cisimlerin Ağırlık Merkezi","list":{"type":"unordered","items":["Telden yapılmış cisimlerin ağırlık merkezini bulmak için uzunluk kullanılır, aynı maddeden yapıldıysa uzunlukların karşılaştırılması yeterlidir.","Kare çerçeve, dikdörtgen, üçgen ve çember şeklindeki telden yapılmış cisimlerin ağırlık merkezleri sırasıyla ortadadır, çevresi 4L, 2(a+b), 3L ve 2πr'dir."]},"beginTime":743,"endTime":857,"href":"/video/preview/15866361810308013124?parent-reqid=1765462615165890-6029985380247354058-balancer-l7leveler-kubr-yp-vla-229-BAL&text=%E2%84%A2Bukidz%E2%84%A2&t=743&ask_summarization=1"},{"index":7,"title":"Levha ve Üç Boyutlu Cisimlerin Ağırlık Merkezi","list":{"type":"unordered","items":["Levha şeklindeki cisimlerin ağırlık merkezi, içi dolu olduğu için alanı kullanılarak hesaplanır; dikdörtgenin alanı a×b, üçgenin alanı taban×yükseklik/2, dairenin alanı πr²'dir.","Üç boyutlu cisimlerin ağırlık merkezi, hacmi kullanılarak hesaplanır; küpün hacmi a³, dikdörtgenler prizmasının hacmi abc, kürenin hacmi 4/3πr³'dür."]},"beginTime":857,"endTime":1003,"href":"/video/preview/15866361810308013124?parent-reqid=1765462615165890-6029985380247354058-balancer-l7leveler-kubr-yp-vla-229-BAL&text=%E2%84%A2Bukidz%E2%84%A2&t=857&ask_summarization=1"},{"index":8,"title":"Telden Yapılmış Cisimlerin Dengesi","list":{"type":"unordered","items":["Telden yapılmış cisimlerin dengede kalması için, ağırlık merkezi (x koordinatı) hesaplanarak, cismin hangi noktadan asılması gerektiği belirlenir.","Dengede kalma için, ağırlık merkezinin ipin üzerindeki bir noktada olması yeterlidir.","Telden yapılmış cisimlerde, ağırlık merkezi hesaplanırken sadece uzunluklara değil, dik uzaklıklara da dikkat edilmelidir, özellikle üçgenlerde otomatik cevap verilmemelidir."]},"beginTime":1003,"endTime":1265,"href":"/video/preview/15866361810308013124?parent-reqid=1765462615165890-6029985380247354058-balancer-l7leveler-kubr-yp-vla-229-BAL&text=%E2%84%A2Bukidz%E2%84%A2&t=1003&ask_summarization=1"},{"index":9,"title":"Ağırlık Merkezi Hesaplama","list":{"type":"unordered","items":["İki soru inceleniyor: tel ve levha şeklindeki cisimlerin ağırlık merkezlerinin uzaklıkları hesaplanıyor.","Tel şeklindeki cisimlerde ağırlık merkezi, telin uzunluğuna bağlı olarak hesaplanıyor; telin çevresi 2πr, 2π2r ve 2π3r olan cisimlerin ağırlık merkezleri sırasıyla 3r, 2r ve 3r uzaklıktadır.","Levha şeklindeki cisimlerde ağırlık merkezi, levhanın alanına bağlı olarak hesaplanıyor; alanı πr², 4πr² ve 9πr² olan levhaların ağırlık merkezleri sırasıyla 2r, 4r ve 6r uzaklıktadır."]},"beginTime":1272,"endTime":1466,"href":"/video/preview/15866361810308013124?parent-reqid=1765462615165890-6029985380247354058-balancer-l7leveler-kubr-yp-vla-229-BAL&text=%E2%84%A2Bukidz%E2%84%A2&t=1272&ask_summarization=1"},{"index":10,"title":"Eğik Düzlem Üzerindeki Cisimlerin Devrilme Riski","list":{"type":"unordered","items":["Boyutları a ve b olan türdeş bir cismin ağırlık merkezi oturma düzleminin içinde kalıyorsa o cisim devrilmez.","Eğik düzlem üzerinde bulunan bir cismin devrilmemesi için, cismin ağırlık merkezinin oturma düzleminin içinde olması gerekir.","Eğik düzlem üzerindeki bir cismin devrilme riski, cismin boyutlarına ve eğik düzlemin açısına bağlıdır; en fazla 4/3 oranında olabilir, aksi takdirde devrilir."]},"beginTime":1466,"endTime":1622,"href":"/video/preview/15866361810308013124?parent-reqid=1765462615165890-6029985380247354058-balancer-l7leveler-kubr-yp-vla-229-BAL&text=%E2%84%A2Bukidz%E2%84%A2&t=1466&ask_summarization=1"},{"index":11,"title":"Dengede Kalan Cisimler","list":{"type":"unordered","items":["Türdeş r, k ve r yarıçaplı cisimler iple asıldığında dengede kalıyorsa, tork hesaplaması yapılabilir.","Dengede kalan cisimlerde, soldaki torkların toplamı sağdaki torkların toplamına eşittir.","Aynı maddeden yapılmış cisimlerde, kat sayısını arttırarak veya aynı kalınlıkta ise maddenin özkütlesini değiştirerek ağırlık farkı oluşturulabilir."]},"beginTime":1622,"endTime":1749,"href":"/video/preview/15866361810308013124?parent-reqid=1765462615165890-6029985380247354058-balancer-l7leveler-kubr-yp-vla-229-BAL&text=%E2%84%A2Bukidz%E2%84%A2&t=1622&ask_summarization=1"},{"index":12,"title":"Levhaların Dengede Kalma Koşulları","list":{"type":"unordered","items":["Kütleleri 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eder."]},"beginTime":1965,"endTime":2047,"href":"/video/preview/15866361810308013124?parent-reqid=1765462615165890-6029985380247354058-balancer-l7leveler-kubr-yp-vla-229-BAL&text=%E2%84%A2Bukidz%E2%84%A2&t=1965&ask_summarization=1"},{"index":15,"title":"Ağırlık Merkezi Soruları","list":{"type":"unordered","items":["Türdeş bir levhadan boyalı parçalar çıkarıldığında, ağırlık merkezinin yerinin değişmemesi için parçaların simetriğini alıp, bu simetriğin buluştuğu yerde parçalar yerleştirilmelidir.","İple dengede olan türdeş levhadan boyalı parçalar çıkarıldığında, dengenin bozulmaması için ağırlık merkezinin ipin altında kaldığı sürece sorun çıkmaz.","Ağırlık merkezinin belirli bir yönde hareket etmesi istendiğinde, parçaların çıkarma veya yapıştırma işlemleri bu yönde hareket etmesini 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yarıçaplı parçayı kesip atarken, Eren bu parçayı kendi levhasına yapıştırıyor.","Levhada yarıçapı 2r olan bir parçanın ağırlık merkezi 4r²'dir ve toplam ağırlığı 4g'dir.","R yarıçaplı parça çıkarıldığında ağırlık 3g olur ve ağırlık merkezi eksik yönünde kayar."]},"beginTime":2571,"endTime":2662,"href":"/video/preview/15866361810308013124?parent-reqid=1765462615165890-6029985380247354058-balancer-l7leveler-kubr-yp-vla-229-BAL&text=%E2%84%A2Bukidz%E2%84%A2&t=2571&ask_summarization=1"},{"index":18,"title":"Ağırlık Merkezi Değişiminin Matematiksel Analizi","list":{"type":"unordered","items":["Arda'nın levhasının ağırlık merkezi, Eren'inkine göre daha çok yer değiştirir.","Arda'nın sisteminde ağırlık merkezi r/3 kadar yer değiştirirken, Eren'in sisteminde ağırlık merkezi r/5 kadar yer değiştirir.","Aynı işi yapsalar bile toplam ağırlıklar farklı olduğundan, ağırlık merkezi değişimi de farklı olur."]},"beginTime":2662,"endTime":2705,"href":"/video/preview/15866361810308013124?parent-reqid=1765462615165890-6029985380247354058-balancer-l7leveler-kubr-yp-vla-229-BAL&text=%E2%84%A2Bukidz%E2%84%A2&t=2662&ask_summarization=1"},{"index":19,"title":"Ağırlık Merkezi ve Fiziksel Hareketler","list":{"type":"unordered","items":["Ağırlık merkezi farklılığı, fiziksel hareketlerde önemli bir rol oynar.","Erkekler ve kadınlar arasında bazı hareketlerin farklı olması, ağırlık merkezi farklılığından kaynaklanabilir.","Konu kütle ve ağırlık merkezi olarak tamamlanmış olup, dördüncü konu olarak 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Eğlenceli Çocuk Şarkılarımız: Sebzeler Şarkısı | • Sebzeler Şarkısı | Sebzeleri Öğreniyorum |... Hadi Hareket! 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