{"id":1030,"date":"2021-09-09T13:33:11","date_gmt":"2021-09-09T13:33:11","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/eresmech\/?page_id=1030"},"modified":"2021-09-30T12:31:16","modified_gmt":"2021-09-30T12:31:16","slug":"4-1-2","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/eresmech\/mekanizma-teknigi\/ch4\/4-1-2\/","title":{"rendered":"4-1-2"},"content":{"rendered":"<div id=\"pl-gb1030-69d7910aebbd0\"  class=\"panel-layout\" ><div id=\"pg-gb1030-69d7910aebbd0-0\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-gb1030-69d7910aebbd0-0-0\"  class=\"panel-grid-cell\" ><div id=\"panel-gb1030-69d7910aebbd0-0-0-0\" class=\"so-panel widget widget_sow-editor panel-first-child panel-last-child widgetopts-SO\" data-index=\"0\" ><div\n\t\t\t\n\t\t\tclass=\"so-widget-sow-editor so-widget-sow-editor-base\"\n\t\t\t\n\t\t>\n<div class=\"siteorigin-widget-tinymce textwidget\">\n\t<h1><b>4.1<\/b> H\u0131z ve \u0130vme Analizi -2<\/h1>\n<p><strong><span style=\"color: #cc0000\"><u>Genel D\u00fczlemsel Hareket:<\/u><\/span><\/strong><\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1094\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-1.gif\" alt=\"\" width=\"470\" height=\"211\" \/><\/p>\n<p>D\u00fczlemde d\u00f6nme veya \u00f6teleme hareketi olarak tan\u0131mlanmayan hareket genel d\u00fczlemsel harekettir. Genel d\u00fczlemsel hareket d\u00f6nme ve \u00f6teleme hareketlerinin birle\u015fimi olan\u00a0<strong><span style=\"color: #cc0000\">ba\u011f\u0131l hareket<\/span>\u00a0<\/strong>kavram\u0131 kullan\u0131larak ele al\u0131nabilir.<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1095\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-2.gif\" alt=\"\" width=\"525\" height=\"234\" \/><\/p>\n<p style=\"text-align: center\" align=\"center\"><span style=\"color: #cc0000\">AB konumundan A\u2032B\u2033 konumuna \u00f6teleme, A\u2032B\u2032 konumuna A\u2032 merkezli d\u00f6nme<\/span><\/p>\n<p>AB noktalar\u0131 ile tan\u0131mlanan bir cismin d\u00fczlemsel hareketini ele alal\u0131m. Cismin birinci konumdan ikinci konuma belirli bir \u0394t zaman\u0131nda yer de\u011fi\u015fimi, cismin ilk olarak AB konumundan bir ara konum olan A\u2032B\u2033 konumuna \u00f6telemesi ve A\u2032 noktas\u0131ndan ge\u00e7en d\u00fczleme dik bir eksen etraf\u0131nda d\u00f6nerek A&#8217;B&#8217; konumuna gelmesi olarak ele al\u0131nabilir. Yani genel hareket d\u00f6nme ve \u00f6teleme hareketlerinin s\u00fcperpozisyonudur. AB konumu ile A\u2032B\u2032 konumu aras\u0131nda hareket sadece yukar\u0131da a\u00e7\u0131kland\u0131\u011f\u0131 \u015fekilde olmayabilir. \u00d6rne\u011fin istenir ise AB konumunu A\u2033B\u2032 gibi bir ara konuma getirip B\u2032 den ge\u00e7en bir eksen etraf\u0131nda d\u00f6nme yaparak son konuma eri\u015filebilir, veya ilk olarak A noktas\u0131ndan ge\u00e7en bir eksen etraf\u0131nda d\u00f6n\u00fclerek AB\u2033 A\u2032B\u2032 ne paralel konuma getirildikten sonra \u00f6teleme yap\u0131larak son konuma ge\u00e7ilebilir Noktalar\u0131n ger\u00e7ek y\u00f6r\u00fcngeleri sonlu yak\u0131n konumlarda bu hareketlerle ayn\u0131 olmayaca\u011f\u0131 tabiidir. Ancak bu iki konum birbirlerine sonsuz yak\u0131n duruma geldi\u011finde, bu hareketler aras\u0131nda fark kalmayacakt\u0131r.<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1096\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-3.gif\" alt=\"\" width=\"518\" height=\"234\" \/><\/p>\n<p style=\"text-align: center\" align=\"center\"><span style=\"color: #cc0000\">AB konumundan A\u2033B\u2032 konumuna \u00f6teleme, A\u2032B\u2032 konumuna B\u2032 merkezli d\u00f6nme<\/span><\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1097\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-4.gif\" alt=\"\" width=\"559\" height=\"239\" \/><\/p>\n<p style=\"text-align: center\" align=\"center\"><span style=\"color: #cc0000\">AB konumundan AB\u2033 konumuna A merkezli d\u00f6nme, A\u2032B\u2032 konumuna \u00f6teleme<\/span><\/p>\n<p>Cisim \u00f6teleme yaparken her nokta cisim \u00fczerinde se\u00e7ilen bir noktan\u0131n h\u0131z ve ivmesi ile hareket edecektir. Cismin d\u00f6nme yapmas\u0131 s\u0131ras\u0131nda ise, cisim se\u00e7ilen noktadan ge\u00e7en d\u00fczleme dik bir eksen etraf\u0131nda d\u00f6nerken, se\u00e7ilen nokta konumunu de\u011fi\u015ftirmeyecek, di\u011fer noktalar bu noktaya g\u00f6re bir dairesel hareket yapacakt\u0131r. Se\u00e7ilmi\u015f olan nokta sabit bir nokta de\u011fildir ve bu nedenle cismin bu noktaya g\u00f6re hareketi\u00a0<span style=\"color: #000099\"><strong>ba\u011f\u0131l hareket<\/strong><\/span>tir.<\/p>\n<p>Hareketi incelemek i\u00e7in hareketli d\u00fczlem \u00fczerinde A noktas\u0131ndan ge\u00e7en, sabit koordinat eksenine paralel bir x-y koordinat eksenini yerle\u015ftirelim. \u00d6teleme s\u0131ras\u0131nda bu koordinat ekseni sabit koordinat eksenine (X-Y) paralel kal\u0131r.<\/p>\n<p style=\"text-align: center\"><div class=\"su-image-carousel  su-image-carousel-has-spacing su-image-carousel-has-lightbox su-image-carousel-has-outline su-image-carousel-adaptive su-image-carousel-slides-style-default su-image-carousel-controls-style-dark su-image-carousel-align-center\" style=\"max-width:350px\" data-flickity-options='{\"groupCells\":true,\"cellSelector\":\".su-image-carousel-item\",\"adaptiveHeight\":true,\"cellAlign\":\"left\",\"prevNextButtons\":true,\"pageDots\":false,\"autoPlay\":false,\"imagesLoaded\":true,\"contain\":false,\"selectedAttraction\":1,\"friction\":1}' id=\"su_image_carousel_69d7910aed88d\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/genmotion2_1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"350\" height=\"327\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/genmotion2_1.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/genmotion2_2.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"350\" height=\"290\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/genmotion2_2.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d7910aed88d_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d7910aed88d\"))}, 0);}var su_image_carousel_69d7910aed88d_script=document.getElementById(\"su_image_carousel_69d7910aed88d_script\");if(su_image_carousel_69d7910aed88d_script){su_image_carousel_69d7910aed88d_script.parentNode.removeChild(su_image_carousel_69d7910aed88d_script);}<\/script><\/p>\n<p>Cismin AB konumundan A\u2032B\u2032 konumuna ge\u00e7i\u015fi iki etapta oldu\u011fu kabul edilecektir. Birinci etapta hareket AB konumundan A&#8217;B&#8221; konumuna her noktan\u0131n \u0394<strong>r<sub>A<\/sub><\/strong> yer de\u011fi\u015fimi olacak \u015fekilde \u00f6telemesidir. \u00d6teleme A noktas\u0131n\u0131n toplam hareketi kadard\u0131r. Bu aynen (a) k\u0131sm\u0131nda ele alm\u0131\u015f oldu\u011fumuz rijit cismin \u00f6telemesidir. \u0130kinci olarak cismin A&#8217; den ge\u00e7en d\u00fczleme dik bir eksen etraf\u0131nda \u0394\u03d5 a\u00e7\u0131s\u0131 kadar d\u00f6nmesidir. Cismin rijit olmas\u0131 nedeni ile cismin \u00fczerinde bulunan B noktas\u0131 B\u2033 konumundan B\u2032 konumuna giderken AB uzunlu\u011fu sabit olaca\u011f\u0131ndan B\u2032, A\u2032 merkezli BA yar\u0131\u00e7apl\u0131 bir daire yay\u0131 \u00fczerinde olacakt\u0131r ve B noktas\u0131 A noktas\u0131na g\u00f6re \u0394<strong>r<\/strong><sub>B\/A<\/sub>\u00a0kadar konumunu de\u011fi\u015ftirecektir. Bu hareket B noktas\u0131n\u0131n A noktas\u0131na g\u00f6re ba\u011f\u0131l hareketidir.<\/p>\n<p>B noktas\u0131n\u0131n toplam yer de\u011fi\u015fimi bu iki yer de\u011fi\u015fimin vekt\u00f6rel toplam\u0131d\u0131r:<\/p>\n<p style=\"text-align: center\">\u0394<strong>r<\/strong><sub>B<\/sub> = \u0394<strong>r<\/strong><sub>A<\/sub> +\u0394<strong>r<\/strong><sub>B\/A<\/sub><\/p>\n<p>B\u2033 den B\u2032 ne hareket bir d\u00f6nme hareketi oldu\u011fundan, \u0394<strong>r<\/strong><sub>B\/A<\/sub> = |BA|\u0394\u03d5 olacakt\u0131r. Bu ba\u011f\u0131l hareketin o andaki mutlak a\u00e7\u0131sal d\u00f6nmenin fonksiyonu oldu\u011funa dikkat edelim. Se\u00e7mi\u015f oldu\u011fumuz A, B noktalar\u0131 de\u011fi\u015fse bile \u0394\u03d5 ayn\u0131 kalacakt\u0131r ve bu a\u00e7\u0131 cismin birinci konumu ile ikinci konumu aras\u0131nda kalan d\u00f6nme a\u00e7\u0131s\u0131d\u0131r. Bu nedenle de\u011fi\u015fik A noktas\u0131 se\u00e7imi bu a\u00e7\u0131sal d\u00f6nmeyi etkilemeyecektir. Ayn\u0131 \u015fekilde, d\u00f6nme ve \u00f6teleme hareketlerinin s\u0131ras\u0131 de\u011fi\u015ftirilse, d\u00f6nme a\u00e7\u0131s\u0131 yine ayn\u0131d\u0131r. Yer de\u011fi\u015fim bir zaman i\u00e7inde oldu\u011fundan elde edilen denklemi bu zaman aral\u0131\u011f\u0131na b\u00f6ld\u00fc\u011f\u00fcm\u00fczde ve bu zaman aral\u0131\u011f\u0131n\u0131n limitte s\u0131f\u0131r oldu\u011funu d\u00fc\u015f\u00fcnd\u00fc\u011f\u00fcm\u00fczde:<\/p>\n<p style=\"text-align: center\"><strong>V<\/strong><sub>B<\/sub>\u00a0=\u00a0<strong>V<\/strong><sub>A<\/sub>+\u00a0<strong>V<\/strong><sub>B\/A<\/sub><\/p>\n<p>olur. Bu denklemde:<\/p>\n<p style=\"text-align: center\"><strong>V<sub>B\/A<\/sub><\/strong> = <strong>\u03c9<\/strong> \u00d7 <strong>r<sub>B\/A<\/sub><\/strong><\/p>\n<p><strong>\u03c9<\/strong> cismin a\u00e7\u0131sal h\u0131z\u0131 ve\u00a0<b><\/b><strong>r<\/strong><sub>B\/A<\/sub>\u00a0=\u00a0<strong>AB<\/strong>\u00a0=\u00a0<strong>r<\/strong><sub>B<\/sub> \u2212\u00a0<strong>r<\/strong><sub>A<\/sub> (B noktas\u0131n\u0131n A noktas\u0131na g\u00f6re ba\u011f\u0131l konumu)\u00a0d\u0131r. <strong>v<\/strong><sub>B\/A<\/sub>\u00a0cismin \u00fczerinde bulunan A ve B noktalar\u0131 aras\u0131nda\u00a0<strong><span style=\"color: #cc0000\">ba\u011f\u0131l h\u0131z<\/span><\/strong>d\u0131r.\u00a0<strong>v<\/strong><sub>B<\/sub>\u00a0ve\u00a0<strong>v<\/strong><sub>A<\/sub>, A ve B noktalar\u0131n\u0131n <strong><span style=\"color: #cc0000\">mutlak h\u0131z<\/span><\/strong>lar\u0131d\u0131r.<\/p>\n<p>Ayn\u0131 sonucu karma\u015f\u0131k say\u0131larla elde etmemiz m\u00fcmk\u00fcnd\u00fcr. B noktas\u0131n\u0131n konumunu A noktas\u0131n\u0131n konum vekt\u00f6r\u00fc kullan\u0131larak yazd\u0131\u011f\u0131m\u0131zda:<\/p>\n<p style=\"text-align: center\"><b><\/b><b><\/b><b>r<\/b><sub>B<\/sub>\u00a0=\u00a0<b>r<\/b><sub>A<\/sub> + be<sup>i\u03d5<\/sup><\/p>\n<p>burada b = |AB| ve \u03d5 ise AB do\u011frusu ile referans eksenimizin reel pozitif y\u00f6n\u00fc ile yapt\u0131\u011f\u0131 a\u00e7\u0131d\u0131r (saat yelkovan\u0131na ters y\u00f6n pozitif kabul edilecektir). be<sup>i\u03d5<\/sup> terimi B noktas\u0131n\u0131n A noktas\u0131na g\u00f6re konumunu g\u00f6steren\u00a0<strong><span style=\"color: #cc0000\">ba\u011f\u0131l konum vekt\u00f6r\u00fc<\/span><\/strong>d\u00fcr. A ve B noktalar\u0131 ayn\u0131 cisimde olduklar\u0131ndan b uzunlu\u011fu sabittir. Ba\u011f\u0131l hareketle ilgilendi\u011fimizden; A noktas\u0131n\u0131n konumunu, h\u0131z\u0131n\u0131 ve ivmesini bildi\u011fimizi kabul edelim (<strong>v<\/strong><sub>A<\/sub>\u00a0ve\u00a0<strong>a<\/strong><sub>A<\/sub>\u00a0biliniyor).\u00a0<b><\/b><b><\/b><strong>r<\/strong><sub>B<\/sub>\u00a0konum vekt\u00f6r\u00fc denkleminin zamana g\u00f6re t\u00fcrevini ald\u0131\u011f\u0131m\u0131zda:<\/p>\n<p style=\"text-align: center\"><b><\/b><b><\/b><b><\/b><strong>v<\/strong><sub>B<\/sub>\u00a0=\u00a0<strong>v<\/strong><sub>A<\/sub> + ib\u03c9e<sup>i\u03d5<\/sup><\/p>\n<p>dir. Burada \u03c9 = d\u03d5\/dt dir. \u0130kinci terimin \u015fiddeti b\u03c9 d\u0131r ve y\u00f6n\u00fc ie<sup>i\u03d5<\/sup>\u00a0birim vekt\u00f6r\u00fc y\u00f6n\u00fcndedir. Bu birim vekt\u00f6r AB do\u011frusuna dik ve AB nin \u03c9\u00a0a\u00e7\u0131sal h\u0131z vekt\u00f6r\u00fcn\u00fcn y\u00f6n\u00fcne g\u00f6re 90\u00b0\u00a0saat yelkovan\u0131 y\u00f6n\u00fcnde veya ters y\u00f6n\u00fcnde d\u00f6nd\u00fcr\u00fclm\u00fc\u015f bir vekt\u00f6rd\u00fcr. Bu ikinci terim B noktas\u0131n\u0131n A noktas\u0131na g\u00f6re ba\u011f\u0131l h\u0131z\u0131d\u0131r. bu durumda:<\/p>\n<p style=\"text-align: center\"><b><\/b><b><\/b><b><\/b><b><\/b><strong>v<\/strong><sub>B\/A<\/sub> = ib\u03c9e<sup>i\u03d5<\/sup>\u00a0(B nin A ya g\u00f6re ba\u011f\u0131l h\u0131z\u0131)<\/p>\n<p>ve<\/p>\n<p style=\"text-align: center\"><strong>v<\/strong><sub>B<\/sub> =\u00a0<strong>v<\/strong><sub>A<\/sub>\u00a0+ <strong>v<\/strong><sub>B\/A<\/sub>\u00a0(B noktas\u0131n\u0131n mutlak h\u0131z\u0131)<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1098 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-6.gif\" alt=\"\" width=\"725\" height=\"318\" \/><\/p>\n<p>H\u0131z denkleminin zamana g\u00f6re t\u00fcrevi B noktas\u0131n\u0131n ivmesini verecektir:<\/p>\n<p style=\"text-align: center\"><strong>a<\/strong><sub>B<\/sub>\u00a0=\u00a0<strong>a<\/strong><sub>A<\/sub> + ib\u03b1e<sup>i\u03d5<\/sup> \u2212 b\u03c9<sup>2<\/sup>e<sup>i\u03d5<\/sup><\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1099 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-7.gif\" alt=\"\" width=\"677\" height=\"226\" \/><\/p>\n<p>Ba\u011f\u0131l h\u0131z\u0131n t\u00fcrevinden elde edilen birinci terimin \u015fiddeti ba ve y\u00f6n\u00fc ie<sup>i\u03d5<\/sup> dir. Bu y\u00f6n AB do\u011frusuna diktir. Bu ba\u011f\u0131l ivmeye\u00a0<strong><span style=\"color: #cc0000\">te\u011fetsel ba\u011f\u0131l ivme<\/span><\/strong>\u00a0diyece\u011fiz ve\u00a0<strong>a<sup>t<\/sup><\/strong><sub>B\/A<\/sub> olarak g\u00f6sterece\u011fiz. Ba\u011f\u0131l h\u0131z\u0131n t\u00fcrevinden elde edilen ikinci terimin ise \u015fiddeti b\u03c9<sup>2<\/sup> olup y\u00f6n\u00fc \u2212e<sup>i\u03d5<\/sup>\u00a0dir. Bu y\u00f6n AB y\u00f6n\u00fcnde olup d\u00f6nme ekseni \u00fczerinde olan A noktas\u0131na do\u011frudur. Bu y\u00f6n B noktas\u0131n\u0131n A ya g\u00f6re ba\u011f\u0131l y\u00f6r\u00fcngesine diktir ve\u00a0<strong><span style=\"color: #cc0000\">normal ba\u011f\u0131l ivme<\/span><\/strong>\u00a0olarak adland\u0131r\u0131larak\u00a0<strong>a<sup>n<\/sup><\/strong><sub>B\/A<\/sub>\u00a0\u015feklinde g\u00f6sterilecektir. B noktas\u0131n\u0131n ivmesi:<\/p>\n<p style=\"text-align: center\"><b><\/b><strong>a<\/strong><sub>B<\/sub>\u00a0=\u00a0<strong>a<\/strong><sub>A<\/sub>\u00a0+\u00a0<strong>a<sup>t<\/sup><\/strong><sub>B\/A<\/sub>\u00a0+\u00a0<strong>a<sup>n<\/sup><\/strong><sub>B\/A<\/sub><\/p>\n<p>ve<\/p>\n<p style=\"text-align: center\"><strong>a<\/strong><sub>B\/A<\/sub>=\u00a0<strong>a<sup>t<\/sup><\/strong><sub>B\/A<\/sub>\u00a0+\u00a0<strong>a<sup>n<\/sup><\/strong><sub>B\/A<\/sub><\/p>\n<p>Bu durumda, genel d\u00fczlemsel hareket durumunda bir cismin \u00fczerinde bulunan iki noktan\u0131n birbirlerine g\u00f6re ba\u011f\u0131l hareketi bu noktalardan birine g\u00f6re di\u011fer noktalar\u0131n d\u00f6nmesi olarak incelenebilece\u011fini ve ba\u011f\u0131l h\u0131z ve ivme terimlerinin bir nokta etraf\u0131nda d\u00f6nme gibi elde edilebilece\u011fini s\u00f6yleyebiliriz.<\/p>\n<p>\u0130kinci farkl\u0131 ba\u011f\u0131l hareket ise bir hareketli cismin di\u011fer bir hareketli cisme g\u00f6re \u00f6teleme yapmas\u0131d\u0131r. \u0130ki rijit cisim \u00fczerinde bulunan ve ani \u00e7ak\u0131\u015fan iki noktay\u0131 ele alal\u0131m. Bir cismin \u00fczerinde bulunan bir noktan\u0131n di\u011fer cisim \u00fczerinde y\u00f6r\u00fcngesini bildi\u011fimizi kabul edelim.<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1100 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-8.gif\" alt=\"\" width=\"548\" height=\"278\" \/><\/p>\n<p>2 numaral\u0131 d\u00fczlemin 1# konumundan hareket ederek 2# konuma geldi\u011fini ve bu s\u0131rada A<sub>2<\/sub>\u00a0noktas\u0131na 1# konumda \u00e7ak\u0131\u015f\u0131k olan A<sub>3<\/sub>\u00a0noktas\u0131n\u0131n 2 uzvuna g\u00f6re ba\u011f\u0131l hareket yaparak, A<sub>2<\/sub> noktas\u0131n\u0131n 2# konumuna (A\u2032<sub>2<\/sub>) gelmesi s\u0131ras\u0131nda A\u2032<sub>3<\/sub> noktas\u0131na geldi\u011fini d\u00fc\u015f\u00fcn\u00fcrsek; birinci konumda \u00e7ak\u0131\u015f\u0131k olan iki nokta ikinci konumda \u00e7ak\u0131\u015f\u0131k olmayacak (A\u2032<sub>2<\/sub> ve A\u2032<sub>3<\/sub>) , farkl\u0131 konumlarda bulunacaklard\u0131r. A<sub>3<\/sub>\u00a0noktas\u0131n\u0131n 2 uzvu \u00fczerinde y\u00f6r\u00fcngesi bilindi\u011fine g\u00f6re, bu noktan\u0131n hareketinin iki k\u0131s\u0131mdan olu\u015ftu\u011funu d\u00fc\u015f\u00fcnmemiz m\u00fcmk\u00fcnd\u00fcr. Bu hareketlerden birisi A<sub>3<\/sub>\u00a0noktas\u0131n\u0131n 2 uzvu ile birlikte hareketi, bu durumda A<sub>3<\/sub> ten A\u2033<sub>3<\/sub> ne hareket (A\u2033<sub>3<\/sub> ve A\u2032<sub>2<\/sub> \u00e7ak\u0131\u015f\u0131k) , ikincisi ise, 2 cismine g\u00f6re A\u2033<sub>3<\/sub> den A\u2032<sub>3<\/sub> e harekettir (bu s\u0131rada 2 cisminin hareketi yoktur). Bu iki hareketin s\u0131ras\u0131 \u00f6nemli de\u011fildir. \u015eekilde g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi, A<sub>3<\/sub>\u00a0noktas\u0131 ilk olarak A<sub>2<\/sub> ile ayn\u0131 hareketi yapacak, yani \u0394<strong>r<\/strong><sub>A<\/sub><sub>2<\/sub> kadar yer de\u011fi\u015ftirecek, daha sonra 2 cismine g\u00f6re \u0394<strong>r<\/strong><sub>A<\/sub><sub>3\/2<\/sub>\u00a0kadar yer de\u011fi\u015ftirecektir. A<sub>3<\/sub>\u00a0\u00fcn toplam yer de\u011fi\u015ftirmesi bu iki yer de\u011fi\u015ftirmenin toplam\u0131d\u0131r.<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1101 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-9.gif\" alt=\"\" width=\"620\" height=\"429\" \/><\/p>\n<p>A<sub>3<\/sub>\u00a0noktas\u0131n\u0131n toplam yer de\u011fi\u015fimi:<\/p>\n<p style=\"text-align: center\">\u0394<strong>r<\/strong><sub>A<\/sub><sub>3<\/sub>\u00a0= \u0394<strong>r<\/strong><sub>A<\/sub><sub>2<\/sub> + \u0394<strong>r<\/strong><sub>A<\/sub><sub>3\/2<\/sub><\/p>\n<p>Birinci konumdan ikinci konuma ge\u00e7i\u015f belirli bir \u0394t zaman aral\u0131\u011f\u0131nda olaca\u011f\u0131ndan, yer de\u011fi\u015fim vekt\u00f6rlerini \u0394t ye b\u00f6ler ve limitte \u0394t s\u0131f\u0131r al\u0131n\u0131r ise:<\/p>\n<p style=\"text-align: center\"><strong>v<\/strong><sub>A<\/sub><sub>3<\/sub> = <strong>v<\/strong><sub>A<\/sub><sub>2<\/sub> + <strong>v<\/strong><sub>A<\/sub><sub>3\/2<\/sub><\/p>\n<p>H\u0131z denklemi elde edilecektir. Bu denklemde <strong>v<\/strong><sub>A<\/sub><sub>3\/2<\/sub>, A<sub>3<\/sub>\u00a0noktas\u0131n\u0131n 2 cismine g\u00f6re ba\u011f\u0131l h\u0131z vekt\u00f6r\u00fcd\u00fcr ve daima bu noktan\u0131n 2 cismine g\u00f6re ba\u011f\u0131l y\u00f6r\u00fcngesine te\u011fettir.<\/p>\n<p>Mekanizmalarda bu tip ba\u011f\u0131l hareket iki hareketli uzuv aras\u0131nda bir kayar mafsal, kamal\u0131 silindir mafsal\u0131 veya kam \u00e7ifti oldu\u011funda s\u00f6z konusudur. Kam \u00e7iftlerinin incelemesi e\u015fde\u011fer mekanizma kavram\u0131 ile yap\u0131l\u0131r. Kayar mafsalla birle\u015ftirilen iki uzuv aras\u0131nda ba\u011f\u0131l hareket s\u0131ras\u0131nda bir uzuv \u00fczerinde bulunan herhangi bir noktan\u0131n di\u011fer uzuv \u00fczerinde y\u00f6r\u00fcngesi, mafsal ekseni y\u00f6n\u00fcnde bir do\u011frudur. Kamal\u0131 silindirde ise, bir uzvun silindir ekseni \u00fczerinde al\u0131nan bir noktas\u0131n\u0131n di\u011fer uzva g\u00f6re y\u00f6r\u00fcngesi bir do\u011frudur.<\/p>\n<p>\u0130ki uzuv aras\u0131nda ba\u011f\u0131l hareketi a\u00e7\u0131klamak i\u00e7in birbirleri ile kayar mafsalla ba\u011fl\u0131 2 ve 3 uzuvlar\u0131n\u0131 ele alal\u0131m. Ayr\u0131ca (basit bir hareket olmas\u0131 i\u00e7in) 2 uzvu sabit uzva bir d\u00f6ner mafsalla ba\u011fl\u0131 olsun. B hem 2 ve hemde 3 uzvu \u00fczerinde bulunan iki ayr\u0131 \u00e7ak\u0131\u015fan B<sub>2<\/sub>\u00a0ve B<sub>3<\/sub>\u00a0noktalar\u0131d\u0131r. B noktas\u0131 i\u00e7in (B<sub>2<\/sub>\u00a0veya B<sub>3<\/sub>) karma\u015f\u0131k say\u0131lar ile konum vekt\u00f6r\u00fc yaz\u0131ld\u0131\u011f\u0131nda:<\/p>\n<p style=\"text-align: center\"><b><\/b><strong>R<\/strong><sub>B<\/sub> = re<sup>i\u03b8<\/sup><\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1102 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-10.gif\" alt=\"\" width=\"207\" height=\"265\" \/><\/p>\n<p><strong>R<\/strong><sub>B<\/sub>\u00a0hem B<sub>2<\/sub>\u00a0ve hemde B<sub>3<\/sub>\u00a0i\u00e7in konum vekt\u00f6r\u00fcd\u00fcr. Ancak B<sub>2<\/sub>\u00a0i\u00e7in r sabit olacakt\u0131r. B<sub>3<\/sub>\u00a0i\u00e7in ise r de\u011fi\u015fken bir uzunluktur. Bu nedenle, \u00e7ak\u0131\u015fan noktalar oldu\u011fundan B<sub>2<\/sub>\u00a0ve B<sub>3<\/sub> noktalar\u0131n\u0131n konum vekt\u00f6rleri ayn\u0131 ise de, t\u00fcrev al\u0131nd\u0131\u011f\u0131nda h\u0131z vekt\u00f6rleri ayn\u0131 olmayacakt\u0131r. T\u00fcrev al\u0131n\u0131rken hangi noktan\u0131n h\u0131z\u0131n\u0131 bulmak istiyorsak ona g\u00f6re r uzunlu\u011funun zamana g\u00f6re de\u011fi\u015fimi vard\u0131r veya yoktur. \u00d6rne\u011fin B<sub>2<\/sub>\u00a0noktas\u0131n\u0131n zamana g\u00f6re de\u011fi\u015fimi incelenecek ise:<\/p>\n<p style=\"text-align: center\"><strong>v<\/strong><sub>B2<\/sub>\u00a0= ir\u03c9e<sup>i\u03b8<\/sup><\/p>\n<p>burada \u03c9= d\u03b8\/ dt, 2 uzvunun a\u00e7\u0131sal h\u0131z\u0131d\u0131r. E\u011fer B<sub>3<\/sub>\u00a0noktas\u0131n\u0131n zamana g\u00f6re de\u011fi\u015fimi incelenecek ise:<\/p>\n<p style=\"text-align: center\"><strong>v<\/strong><sub>B2<\/sub>\u00a0= ir\u03c9e<sup>i\u03b8<\/sup> + (dr\/dt)e<sup>i\u03b8<\/sup><\/p>\n<p>Birinci terim\u00a0<strong>v<\/strong><sub>B2<\/sub>\u00a0yani B<sub>2<\/sub>\u00a0noktas\u0131n\u0131n h\u0131z\u0131d\u0131r. \u0130kinci terim ise B<sub>3<\/sub>\u00a0noktas\u0131n\u0131n 2 uzvuna g\u00f6re ba\u011f\u0131l h\u0131z\u0131d\u0131r. Bu h\u0131z ba\u011f\u0131l y\u00f6r\u00fcnge y\u00f6n\u00fcndedir. Bu durumda:<\/p>\n<p style=\"text-align: center\"><b><\/b><strong>v<\/strong><sub>B<\/sub><sub>3<\/sub>\u00a0=\u00a0<strong>v<\/strong><sub>B<\/sub><sub>2<\/sub> +\u00a0<strong>v<\/strong><sub>B<\/sub><sub>3\/2<\/sub><\/p>\n<p>B<sub>2<\/sub>\u00a0ve B<sub>3<\/sub>\u00a0noktalar\u0131n\u0131n h\u0131zlar\u0131n\u0131n farkl\u0131 olmas\u0131ndan dolay\u0131 B<sub>3<\/sub> bir an sonra 2 uzvu \u00fczerinde farkl\u0131 bir B\u2032<sub>2<\/sub>\u00a0noktas\u0131 ile \u00e7ak\u0131\u015facakt\u0131r.<\/p>\n<p><strong>r<\/strong><sub>B<\/sub><sub>3<\/sub>\u00a0konum vekt\u00f6r\u00fcn\u00fcn zamana g\u00f6re ikinci t\u00fcrevi al\u0131nd\u0131\u011f\u0131nda:<\/p>\n<p style=\"text-align: center\"><strong>a<\/strong><sub>B<\/sub><sub>3<\/sub> = d<strong>v<\/strong><sub>B<\/sub><sub>3<\/sub>\/dt = [ir\u03b1e<sup>i\u03b8<\/sup> \u2212 r\u03c9<sup>2<\/sup>e<sup>i\u03b8<\/sup> + i(dr\/dt)\u03c9e<sup>i\u03b8<\/sup>] + [(dr<sup>2<\/sup>\/dt<sup>2<\/sup>)e<sup>i\u03b8<\/sup> + i(dr\/dt)\u03c9e<sup>i\u03b8<\/sup>]\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1103\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-11.gif\" alt=\"\" width=\"502\" height=\"409\" \/><\/p>\n<p>Birinci parantez i\u00e7inde bulunan terimler\u00a0<strong>v<\/strong><sub>B<\/sub><sub>2<\/sub>\u00a0h\u0131z vekt\u00f6r\u00fcn\u00fcn t\u00fcrevi, ikinci parantezdeki terimler ise ba\u011f\u0131l h\u0131z vekt\u00f6r\u00fc\u00a0<b>v<\/b><sub>B<\/sub><sub>3\/2<\/sub> nin t\u00fcrevidir. Dikkat edilir ise, birinci parantezdeki ilk iki terim (ir\u03b1e<sup>i\u03b8<\/sup> \u2212 r\u03c9<sup>2<\/sup>e<sup>i\u03b8<\/sup>) r sabit olarak al\u0131nd\u0131\u011f\u0131nda elde edilecek olan terimlerdir. Bu iki terim r&#8217;nin sabit oldu\u011fu durumda ikinci t\u00fcrev i\u00e7in elde edilecek terimlerdir, B<sub>2<\/sub>\u00a0noktas\u0131n\u0131n te\u011fetsel ve normal ivmeleri olup toplam\u0131 B<sub>2<\/sub>\u00a0noktas\u0131n\u0131n ivmesini (<strong>a<\/strong><sub>B<\/sub><sub>2<\/sub>) verir. Birinci parantezdeki son terim ise, B<sub>3<\/sub>\u00a0ile \u00e7ak\u0131\u015fan B<sub>2<\/sub> noktas\u0131n\u0131n art\u0131k \u00e7ak\u0131\u015fm\u0131yor olmas\u0131 ve ayr\u0131 bir B\u2032<sub>2<\/sub> noktas\u0131 ile \u00e7ak\u0131\u015f\u0131yor olmas\u0131d\u0131r. \u0394t zaman aral\u0131\u011f\u0131 i\u00e7inde B<sub>3<\/sub>\u00a0noktas\u0131 B<sub>2<\/sub> noktas\u0131ndan \u0394r kadar kayar \u00e7ift ekseni y\u00f6n\u00fcnde uzakla\u015facak ve B\u2032<sub>2<\/sub>\u00a0noktas\u0131 ile \u00e7ak\u0131\u015facakt\u0131r. B<sub>2<\/sub> noktas\u0131n\u0131n h\u0131z\u0131 ir\u03c9e<sup>i\u03b8<\/sup> iken B\u2032<sub>2<\/sub> noktas\u0131n\u0131n h\u0131z\u0131 i(r + \u0394r)\u03c9e<sup>i\u03b8<\/sup> d\u0131r. Bu \u0394t zaman aral\u0131\u011f\u0131nda h\u0131z de\u011fi\u015fimi fark\u0131 ise i\u0394r\u03c9e<sup>i\u03b8<\/sup> d\u0131r. Bu terim \u0394t ye b\u00f6l\u00fcn\u00fcr ve limitte \u0394t s\u0131f\u0131r olur ise kayar \u00e7ift eksenine dik ve \u015fiddeti (dr\/dt)\u03c9 olan ivme bile\u015fkesi bulunur.<\/p>\n<p>Ba\u011f\u0131l h\u0131z vekt\u00f6r\u00fcn\u00fc g\u00f6steren terimin t\u00fcrevini al\u0131nca elde etti\u011fimiz terimleri inceleyelim. \u0130kinci parantezde birinci terim ((dr<sup>2<\/sup>\/dt<sup>2<\/sup>)e<sup>i\u03b8<\/sup>) ba\u011f\u0131l h\u0131z\u0131n \u015fiddetinin de\u011fi\u015fimi ile ilgilidir ve y\u00f6n\u00fc ba\u011f\u0131l y\u00f6r\u00fcngeye te\u011fettir. \u0130kinci terim (i(dr\/dt)\u03c9e<sup>i\u03b8<\/sup>) ise ba\u011f\u0131l h\u0131z vekt\u00f6r\u00fcn\u00fcn y\u00f6n\u00fcn\u00fcn de\u011fi\u015fmesinden dolay\u0131d\u0131r. Bunu a\u00e7\u0131klamak i\u00e7in ba\u011f\u0131l h\u0131z\u0131n sabit oldu\u011funu d\u00fc\u015f\u00fcnelim. Bir \u0394t zaman aral\u0131\u011f\u0131nda 2 uzvu \u0394\u03b8 kadar A<sub>0<\/sub> etraf\u0131nda d\u00f6necektir. Ba\u011f\u0131l h\u0131z\u0131n y\u00f6n\u00fc bu d\u00f6nme ile e<sup>i\u03b8<\/sup> birim vekt\u00f6r y\u00f6n\u00fcnde iken e<sup>i(\u03b8<sub>\u00a0<\/sub>+<sub>\u00a0<\/sub>\u0394\u03b8)<\/sup>\u00a0birim vekt\u00f6r y\u00f6n\u00fcnde olacakt\u0131r. \u015eekilde g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi, ba\u011f\u0131l h\u0131z vekt\u00f6r\u00fcn\u00fcn i(dr\/dt)\u0394\u03b8e<sup>i\u03b8<\/sup>\u00a0kadar de\u011fi\u015fimi ile sonu\u00e7lan\u0131r ve bu terimin \u0394t zaman aral\u0131\u011f\u0131na b\u00f6l\u00fcn\u00fcp \u0394t s\u0131f\u0131ra giderken limiti al\u0131nd\u0131\u011f\u0131nda, i(dr\/dt)\u03c9e<sup>i\u03b8<\/sup> ivme vekt\u00f6r\u00fc bile\u015feni elde edilir. Bu terim ba\u011f\u0131l y\u00f6r\u00fcnge eksenine dik olup \u015fiddeti ise ba\u011f\u0131l h\u0131z ile a\u00e7\u0131sal h\u0131z\u0131n \u00e7arp\u0131m\u0131na e\u015fittir. Dikkat edilir ise, <b>a<\/b><sub>B3<\/sub> ivme denkleminde bulunan iki parantezde son terimler farkl\u0131 nedenlerle elde edilmi\u015f olmalar\u0131na ra\u011fmen, gerek y\u00f6n ve gerek \u015fiddet a\u00e7\u0131s\u0131ndan ayn\u0131 terimlerdir. Bu durumda bu iki terim i(dr\/dt)\u03c9e<sup>i\u03b8<\/sup> olarak birle\u015ftirilebilir. Bu terim\u00a0<strong><span style=\"color: #cc0000\">Coriolis ivme bile\u015feni<\/span><\/strong>\u00a0olarak adland\u0131r\u0131lmaktad\u0131r ve\u00a0<strong>a<sup>c<\/sup><\/strong><sub>B<\/sub><sub>3\/2<\/sub>\u00a0olarak g\u00f6sterilir. Coriolis ivme bile\u015feni bir ba\u011f\u0131l ivme bile\u015fenidir. \u015eiddeti a\u00e7\u0131sal h\u0131z ile ba\u011f\u0131l h\u0131z\u0131n \u00e7arp\u0131m\u0131n\u0131n iki kat\u0131 olup y\u00f6n\u00fc ise ba\u011f\u0131l h\u0131z vekt\u00f6r\u00fcn\u00fcn a\u00e7\u0131sal h\u0131z y\u00f6n\u00fcnde 90\u00b0\u00a0d\u00f6nd\u00fcr\u00fclmesi ile elde edilir B\u00f6ylece B<sub>3<\/sub> noktas\u0131n\u0131n ivmesi:<\/p>\n<p style=\"text-align: center\"><strong>a<\/strong><sub>B3<\/sub> = ir\u03b1e<sup>i\u03b8<\/sup> \u2212 r\u03c9<sup>2<\/sup>e<sup>i\u03b8<\/sup> + (dr<sup>2<\/sup>\/dt<sup>2<\/sup>)e<sup>i\u03b8<\/sup> + 2i(dr\/dt)\u03c9e<sup>i\u03b8<\/sup><\/p>\n<p style=\"text-align: center\" align=\"center\"><strong>a<\/strong><sub>B3<\/sub> = <strong><b>a<sup>t<\/sup><\/b><\/strong><sub>B<\/sub><sub>2<\/sub> + <strong><b>a<sup>n<\/sup><\/b><\/strong><sub>B<\/sub><sub>2<\/sub>\u00a0+ <strong> <b>a<sup>t<\/sup><\/b><\/strong><sub>B<\/sub><sub>3\/2<\/sub> + <strong>a<sup>c<\/sup><\/strong><sub>B<\/sub><sub>3\/2<\/sub><\/p>\n<p><strong><span style=\"color: #cc0000\">KAYAR \u00c7\u0130FT EKSEN\u0130N\u0130N RADYAL Y\u00d6NDE OLMADI\u011eI DURUM<\/span><\/strong><\/p>\n<p>Yukar\u0131da ele al\u0131nan durumda kayar \u00e7ift eksen y\u00f6n\u00fc B<sub>0<\/sub>B radyal y\u00f6n ile \u00e7ak\u0131\u015ft\u0131\u011f\u0131ndan, B<sub>2<\/sub>\u00a0noktas\u0131n\u0131n normal ivmesi (<strong>a<sup>n<\/sup><\/strong><sub>B<\/sub><sub>2<\/sub>) ile ba\u011f\u0131l te\u011fetsel ivme (<strong>a<sup>t<\/sup><\/strong><sub>B<\/sub><sub>3\/2<\/sub>) ve B<sub>2<\/sub> noktas\u0131n\u0131n te\u011fetsel ivmesi ile Coriolis ivmesi y\u00f6nleri (<strong>a<sup>c<\/sup><\/strong><sub>B<\/sub><sub>3\/2<\/sub>\u00a0ve\u00a0<strong>a<sup>t<\/sup><\/strong><sub>B<\/sub><sub>2<\/sub>)ayn\u0131 bulunmaktad\u0131r. Daha genel bir durum i\u00e7in a\u015fa\u011f\u0131da g\u00f6sterilen durumu ele alal\u0131m. Bu \u015fekilde g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi 2 ve 3 uzuvlar\u0131 aras\u0131nda bulunan kayar \u00e7ift genel bir y\u00f6ndedir. B<sub>3<\/sub>\u00a0konum vekt\u00f6r\u00fc:<\/p>\n<p style=\"text-align: center\" align=\"center\">\u00a0 \u00a0 \u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1104\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-12.gif\" alt=\"\" width=\"361\" height=\"324\" \/><\/p>\n<p style=\"text-align: center\"><strong>r<\/strong><sub>B<\/sub><sub>3<\/sub> = ae<sup>i\u03b8<\/sup> + se<sup>i(\u03b8+\u03b2)<\/sup><\/p>\n<p>dir. Bu denklemde \u03b2 ve a (= |A<sub>0<\/sub>A|), 2 uzvunun sabit boyutlar\u0131 olup, s ise B<sub>2<\/sub>\u00a0i\u00e7in sabit, B<sub>3<\/sub>\u00a0i\u00e7in de\u011fi\u015fkendir. T\u00fcrev al\u0131nd\u0131\u011f\u0131nda:<\/p>\n<p style=\"text-align: center\"><strong>v<\/strong><sub>B<\/sub><sub>3<\/sub> = ia\u03c9e<sup>i\u03b8<\/sup> + is\u03c9e<sup>i(\u03b8+\u03b2)<\/sup> + (ds\/dt)e<sup>i(\u03b8+\u03b2)<\/sup><\/p>\n<p>Bu denklem:<\/p>\n<p style=\"text-align: center\"><strong>v<\/strong><sub>B<\/sub><sub>3<\/sub> = i\u03c9e<sup>i\u03b8<\/sup>(a + se<sup>i\u03b2<\/sup>) + (ds\/dt)e<sup>i(\u03b8+\u03b2)<\/sup><\/p>\n<p>\u015feklinde yaz\u0131labilir. Dikkat edilir ise:<\/p>\n<p style=\"text-align: center\">a + se<sup>i\u03b2<\/sup> = be<sup>i\u03b3<\/sup><\/p>\n<p>d\u0131r. Burada b = |A<sub>0<\/sub>B| olup de\u011fi\u015fkendir. \u03b3 ise 2 uzvu \u00fczerinde bulunan A<sub>0<\/sub>A ile A<sub>0<\/sub>B do\u011frular\u0131 aras\u0131nda kalan de\u011fi\u015fken a\u00e7\u0131d\u0131r. Ancak 2 uzvu \u00fczerinde sabit B<sub>2<\/sub> noktas\u0131 g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, bu nokta i\u00e7in b ve \u03b3\u00a0sabit de\u011ferlerdir. Bu durumda B<sub>3<\/sub>\u00a0noktas\u0131n\u0131n h\u0131z\u0131:<\/p>\n<p style=\"text-align: center\"><strong>v<\/strong><sub>B<\/sub><sub>3<\/sub> = i\u03c9be<sup>i(\u03b8+\u03b3)<\/sup>\u00a0+ (ds\/dt)e<sup>i(\u03b8+\u03b2)<\/sup><\/p>\n<p>veya<\/p>\n<p style=\"text-align: center\"><strong>v<\/strong><sub>B<\/sub><sub>3<\/sub>\u00a0=\u00a0<strong>v<\/strong><sub>B<\/sub><sub>2<\/sub> +\u00a0<strong>v<\/strong><sub>B<\/sub><sub>3\/2<\/sub><\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1105 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-13.gif\" alt=\"\" width=\"675\" height=\"372\" \/><\/p>\n<p>Birinci terimin \u015fiddeti \u03c9|A<sub>0<\/sub>B| = \u03c9b olup y\u00f6n\u00fc B noktas\u0131n\u0131 d\u00f6nme merkezine ba\u011flayan A<sub>0<\/sub>B do\u011frusuna diktir (ie<sup>i(\u03b8+\u03b3)<\/sup> y\u00f6n\u00fc). \u0130kinci terimin \u015fiddeti (ds\/dt) olup B<sub>3<\/sub> noktas\u0131n\u0131n 2 uzvuna g\u00f6re ba\u011f\u0131l h\u0131z\u0131d\u0131r. Bu ba\u011f\u0131l h\u0131z vekt\u00f6r\u00fcn\u00fcn y\u00f6n\u00fc ise kayar \u00e7ift ekseni y\u00f6n\u00fc olan AB y\u00f6n\u00fcd\u00fcr ve e<sup>i(\u03b8+\u03b2)<\/sup>\u00a0birim vekt\u00f6rle g\u00f6sterilir.<\/p>\n<p>H\u0131z denkleminin t\u00fcrevi al\u0131nd\u0131\u011f\u0131nda B<sub>3<\/sub>\u00a0noktas\u0131n\u0131n ivmesi elde edilecektir:<\/p>\n<p style=\"text-align: center\"><strong>a<\/strong><sub>B<\/sub><sub>3<\/sub> = ia\u03b1e<sup>i\u03b8<\/sup> \u2212 a\u03c9<sup>2<\/sup>e<sup>i\u03b8<\/sup> + is\u03b1e<sup>i(\u03b8+\u03b2)<\/sup> + i(ds\/dt)\u03c9e<sup>i(\u03b8+\u03b2)<\/sup> \u2212 s\u03c9<sup>2<\/sup>e<sup>i(\u03b8+\u03b2)<\/sup> + (d<sup>2<\/sup>s\/dt<sup>2<\/sup>)e<sup>i(\u03b8+\u03b2)<\/sup> + i(ds\/dt)\u03c9e<sup>i(\u03b8+\u03b2)<\/sup><\/p>\n<p>Terimler gruplan\u0131r ise:<\/p>\n<p style=\"text-align: center\"><strong>a<\/strong><sub>B<\/sub><sub>3<\/sub> = i\u03b1(a + se<sup>i\u03b2<\/sup>)e<sup>i\u03b8<\/sup> \u2212 \u03c9<sup>2<\/sup>(a + se<sup>i\u03b2<\/sup>)e<sup>i\u03b8<\/sup> + 2i(ds\/dt)\u03c9e<sup>i(\u03b8+\u03b2)<\/sup>+ (d<sup>2<\/sup>s\/dt<sup>2<\/sup>)e<sup>i(\u03b8+\u03b2)<\/sup><\/p>\n<p>veya h\u0131z denkleminde oldu\u011fu gibi, a + se<sup>i\u03b2<\/sup> = be<sup>i\u03b3<\/sup> dersek:<\/p>\n<p style=\"text-align: center\"><strong>a<\/strong><sub>B<\/sub><sub>3<\/sub> = i\u03b1be<sup>i(\u03b8+\u03b3)<\/sup> \u2212 \u03c9<sup>2<\/sup>be<sup>i(\u03b8+\u03b3)<\/sup> + 2i(ds\/dt)\u03c9e<sup>i(\u03b8+\u03b2)<\/sup>+ (d<sup>2<\/sup>s\/dt<sup>2<\/sup>)e<sup>i(\u03b8+\u03b2)<\/sup><\/p>\n<p>\u0130lk iki terim B<sub>2<\/sub>\u00a0noktas\u0131n\u0131n te\u011fetsel ve normal ivmeleridir ve bu ivmelerin y\u00f6n\u00fc s\u0131ras\u0131 ile A<sub>0<\/sub>B do\u011frusuna dik ve paraleldir (A<sub>0<\/sub>&#8216;a do\u011fru). \u00dc\u00e7\u00fcnc\u00fc terim ise ba\u011f\u0131l Coriolis ivmesi olup 2 ve 3 uzuvlar\u0131 aras\u0131nda bulunan kayar mafsal eksenine (AB do\u011frusuna) diktir (birim vekt\u00f6r\u00fc ie<sup>i(\u03b8<sub>\u00a0<\/sub>+<sub>\u00a0<\/sub>\u03b2)<\/sup> d\u0131r). Sonuncu terim ise ba\u011f\u0131l te\u011fetsel ivme olup \u015fiddeti d<sup>2<\/sup>s\/dt<sup>2<\/sup>\u00a0y\u00f6n\u00fc ise e<sup>i(\u03b8<sub>\u00a0<\/sub>+<sub>\u00a0<\/sub>\u03b2)<\/sup>\u00a0birim vekt\u00f6r\u00fc y\u00f6n\u00fcnde, yani AB do\u011frusu y\u00f6n\u00fcndedir. Bu durumda B<sub>3<\/sub>\u00a0noktas\u0131n\u0131n ivmesi:<\/p>\n<p style=\"text-align: center\"><strong>a<\/strong><sub>B<\/sub><sub>3<\/sub> = <strong><b>a<sup>t<\/sup><\/b><\/strong><sub>B<\/sub><sub>2<\/sub> + <strong><b>a<sup>n<\/sup><\/b><\/strong><sub>B<\/sub><sub>2<\/sub>\u00a0+ <strong> <b>a<sup>c<\/sup><\/b><\/strong><sub>B<\/sub><sub>3\/2<\/sub> + <strong>a<sup>t<\/sup><\/strong><sub>B<\/sub><sub>3\/2<\/sub><\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1106 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img222-14.gif\" alt=\"\" width=\"674\" height=\"303\" \/><\/p>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div>\n\n\n<p> <a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mekanizma-teknigi\/ch4\/4-1-1\/\" data-type=\"page\"><img loading=\"lazy\" decoding=\"async\" width=\"38\" height=\"38\" class=\"wp-image-16\" style=\"width: 38px\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/04\/back_button.gif\" alt=\"\" \/><\/a><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mekanizma-teknigi\/ch4\/\" data-type=\"page\" data-id=\"52\"><img loading=\"lazy\" decoding=\"async\" width=\"38\" height=\"38\" class=\"wp-image-17\" style=\"width: 38px\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/04\/contents_button.gif\" alt=\"\" \/><\/a><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mekanizma-teknigi\/\" data-type=\"page\" data-id=\"47\"><img loading=\"lazy\" decoding=\"async\" width=\"38\" height=\"38\" class=\"wp-image-18\" style=\"width: 38px\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/04\/home_button.gif\" alt=\"\" \/><\/a><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mekanizma-teknigi\/ch4\/4-2-1\/\" data-type=\"page\" data-id=\"92\"><img loading=\"lazy\" decoding=\"async\" width=\"38\" height=\"38\" class=\"wp-image-20\" style=\"width: 38px\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/04\/next_button.gif\" alt=\"\" \/><\/a><img loading=\"lazy\" decoding=\"async\" width=\"119\" height=\"40\" class=\"wp-image-15\" style=\"width: 119px\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/04\/ceres.gif\" alt=\"\" \/>        <\/p>\n","protected":false},"excerpt":{"rendered":"<p>4.1 H\u0131z ve \u0130vme Analizi -2 Genel D\u00fczlemsel Hareket: D\u00fczlemde d\u00f6nme veya \u00f6teleme hareketi olarak tan\u0131mlanmayan hareket genel d\u00fczlemsel harekettir. Genel d\u00fczlemsel hareket d\u00f6nme ve \u00f6teleme hareketlerinin birle\u015fimi olan\u00a0ba\u011f\u0131l hareket\u00a0kavram\u0131 kullan\u0131larak ele al\u0131nabilir. AB konumundan A\u2032B\u2033 konumuna \u00f6teleme, A\u2032B\u2032 konumuna &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mekanizma-teknigi\/ch4\/4-1-2\/\"> <span class=\"screen-reader-text\">4-1-2<\/span> Devam\u0131n\u0131 Oku &raquo;<\/a><\/p>\n","protected":false},"author":7747,"featured_media":0,"parent":1027,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-1030","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1030","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/users\/7747"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/comments?post=1030"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1030\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1027"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/media?parent=1030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}