{"id":1029,"date":"2021-09-09T13:32:45","date_gmt":"2021-09-09T13:32:45","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/eresmech\/?page_id=1029"},"modified":"2023-03-28T14:13:42","modified_gmt":"2023-03-28T14:13:42","slug":"4-1-1","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/eresmech\/mekanizma-teknigi\/ch4\/4-1-1\/","title":{"rendered":"4-1-1"},"content":{"rendered":"<div id=\"pl-gb1029-69d76067e6db2\"  class=\"panel-layout\" ><div id=\"pg-gb1029-69d76067e6db2-0\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-gb1029-69d76067e6db2-0-0\"  class=\"panel-grid-cell\" ><div id=\"panel-gb1029-69d76067e6db2-0-0-0\" 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 -1<\/h1>\n<p><span style=\"color: #cc0000\">D\u00fczlemde \u00fc\u00e7 de\u011fi\u015fik tipte hareketi ay\u0131rabiliriz:<\/span><\/p>\n<p><strong><span style=\"color: #cc0000\"><u>\u00d6teleme:<\/u><\/span><\/strong><\/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:550px\" 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_69d76067e83d1\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2023\/03\/Translation2_1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"548\" height=\"248\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2023\/03\/Translation2_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\/2023\/03\/Translation2_2.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"548\" height=\"248\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2023\/03\/Translation2_2.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d76067e83d1_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d76067e83d1\"))}, 0);}var su_image_carousel_69d76067e83d1_script=document.getElementById(\"su_image_carousel_69d76067e83d1_script\");if(su_image_carousel_69d76067e83d1_script){su_image_carousel_69d76067e83d1_script.parentNode.removeChild(su_image_carousel_69d76067e83d1_script);}<\/script><\/p>\n<p>Bir cisim \u00f6teleme yap\u0131yor ise, cismin \u00fczerinde her nokta birbirlerine paralel y\u00f6r\u00fcngeler \u00e7izecektir ve cisim \u00fczerinde bulunan bir do\u011fru, daima \u0131lk konumuna paralel olacak \u015fekilde hareket edecektir.Bu durumda A, B gibi her hangi iki nokta g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, birinci konumdan ikinci konuma belirli bir yer de\u011fi\u015fim oldu\u011funda,<\/p>\n<p style=\"text-align: center\"><strong>r<sub>A<\/sub><sub>1<\/sub>r<sub>B<\/sub><sub>1<\/sub><\/strong> = <strong>r<sub>A<\/sub><sub>2<\/sub>r<sub>B<\/sub><sub>2<\/sub><\/strong> = <strong>A<sub>1<\/sub>B<sub>1<\/sub><\/strong> = <strong>A<sub>2<\/sub>B<sub>2<\/sub><\/strong><\/p>\n<p>dir ve B noktas\u0131n\u0131n konum vekt\u00f6r\u00fc <strong>r<sub>B<\/sub><\/strong>:<\/p>\n<p style=\"text-align: center\"><strong>r<sub>B<\/sub><\/strong>\u00a0=\u00a0<strong>r<sub>A<\/sub><\/strong>\u00a0+\u00a0<strong>r<sub>AB<\/sub><\/strong><\/p>\n<p>olarak yaz\u0131labilir. Bu noktan\u0131n zamana g\u00f6re t\u00fcrevi, noktan\u0131n h\u0131z\u0131n\u0131 verecektir:<\/p>\n<p style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\frac{{\\text{d}{{\\mathbf{r}}_{\\mathbf{B}}}}}{{\\text{dt}}}=\\frac{{\\text{d}{{\\mathbf{r}}_{\\mathbf{A}}}}}{{\\text{dt}}}+\\frac{{\\text{d}{{\\mathbf{r}}_{{\\mathbf{AB}}}}}}{{\\text{dt}}} <\/span><\/p>\n<p><strong>r<sub>AB<\/sub><\/strong>\u00a0vekt\u00f6r\u00fcn\u00fcn \u015fiddeti ve a\u00e7\u0131sal y\u00f6n\u00fc de\u011fi\u015fmedi\u011finden ikinci terim s\u0131f\u0131ra e\u015fit olacak ve:<\/p>\n<p style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\frac{{\\text{d}{{\\mathbf{r}}_{\\mathbf{B}}}}}{{\\text{dt}}}=\\frac{{\\text{d}{{\\mathbf{r}}_{\\mathbf{A}}}}}{{\\text{dt}}} <\/span> veya <strong>V<sub>A<\/sub><\/strong>\u00a0= <strong>V<sub>B<\/sub><\/strong><\/p>\n<p>olacakt\u0131r. Ayn\u0131 de\u011ferlendirmeyi ikinci t\u00fcrev i\u00e7in yapabiliriz ve :<\/p>\n<p style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\frac{{{{\\text{d}}^{2}}{{\\mathbf{r}}_{\\mathbf{B}}}}}{{\\text{d}{{\\text{t}}^{2}}}}=\\frac{{{{\\text{d}}^{2}}{{\\mathbf{r}}_{\\mathbf{A}}}}}{{\\text{d}{{\\text{t}}^{2}}}} <\/span> veya\u00a0<strong>a<sub>A<\/sub><\/strong>\u00a0= <strong>a<sub>B<\/sub><\/strong><\/p>\n<p>olaca\u011f\u0131n\u0131 g\u00f6r\u00fcr\u00fcz. \u00d6yle ise:\u00a0<strong><span style=\"color: #cc0000\">\u00d6teleme yapan cisimlerde cisim \u00fczerinde bulunan her noktan\u0131n yer de\u011fi\u015fim, h\u0131z\u0131 ve ivmesi birbirlerine e\u015fittir<\/span><\/strong>.<\/p>\n<p><strong><span style=\"color: #cc0000\"><u>Sabit bir eksen etraf\u0131nda d\u00f6nme:<\/u><\/span><\/strong><\/p>\n<p>D\u00fczlemsel bir hareket i\u00e7in sabit eksen d\u00fczleme dik ve d\u00fczlemi A<sub>0<\/sub>\u00a0noktas\u0131nda kesen bir eksendir (bu noktaya d\u00fczlemsel hareket i\u00e7in d\u00f6nme merkezi diyece\u011fiz). Bu durumda rijit cisim \u00fczerinde bulunan her nokta ayn\u0131 merkezli daire yaylar\u0131 \u00fczerinde hareket edecektir. \u015eekilde cisim belirli bir yer de\u011fi\u015fim yapm\u0131\u015f olarak iki ayr\u0131 konumda g\u00f6r\u00fclmektedir ve:<\/p>\n<p style=\"text-align: center\">\u2220AA<sub>0<\/sub>A\u2032 = \u2220BB<sub>0<\/sub>B\u2032 =\u00a0\u0394\u03d5<\/p>\n<p>olacakt\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:330px\" 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_69d76067e8d31\"><div class=\"su-image-carousel-item\"><div class=\"su-image-carousel-item-content\"><a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/translation_1.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"345\" height=\"306\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/translation_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\/translation3.gif\" target=\"_blank\" rel=\"noopener noreferrer\" data-caption=\"\"><img loading=\"lazy\" decoding=\"async\" width=\"329\" height=\"306\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/translation3.gif\" class=\"\" alt=\"\" \/><\/a><\/div><\/div><\/div><script id=\"su_image_carousel_69d76067e8d31_script\">if(window.SUImageCarousel){setTimeout(function() {window.SUImageCarousel.initGallery(document.getElementById(\"su_image_carousel_69d76067e8d31\"))}, 0);}var su_image_carousel_69d76067e8d31_script=document.getElementById(\"su_image_carousel_69d76067e8d31_script\");if(su_image_carousel_69d76067e8d31_script){su_image_carousel_69d76067e8d31_script.parentNode.removeChild(su_image_carousel_69d76067e8d31_script);}<\/script><\/p>\n<p>Her nokta A<sub>0<\/sub>\u00a0merkezli bir daire yay\u0131 \u00fczerinde hareket edece\u011finden o noktan\u0131n yer de\u011fi\u015fim miktar\u0131, o noktan\u0131n A<sub>0<\/sub>\u00a0merkezinden uzakl\u0131\u011f\u0131 ile (radyan olarak \u00f6l\u00e7\u00fclen) a\u00e7\u0131sal yer de\u011fi\u015fim miktar\u0131 \u00e7arp\u0131m\u0131na e\u015fittir. Yani:<\/p>\n<p style=\"text-align: center\">\u0394r<sub>A<\/sub> = r<sub>A<\/sub>\u0394\u03d5 \u00a0 \u00a0 \u0394r<sub>B<\/sub> = r<sub>B<\/sub>\u0394\u03d5<\/p>\n<p>bu yer de\u011fi\u015fimin belirli bir zaman aral\u0131\u011f\u0131nda d\u00fc\u015f\u00fcn\u00fcl\u00fcr ise,<\/p>\n<p style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{{\\text{\u0394}{{\\text{r}}_{\\text{A}}}}}{{\\text{\u0394t}}}={{\\text{r}}_{\\text{A}}}\\frac{{\\text{\u0394\u03d5}}}{{\\text{\u0394t}}}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{{\\text{\u0394}{{\\text{r}}_{\\text{B}}}}}{{\\text{\u0394t}}}={{\\text{r}}_{\\text{B}}}\\frac{{\\text{\u0394\u03d5}}}{{\\text{\u0394t}}}<\/span><\/p>\n<p>ve \u0394t\u00a0limitte s\u0131f\u0131ra gitti\u011fi d\u00fc\u015f\u00fcn\u00fclerek:<\/p>\n<p style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {\\text{v}}_{\\text{A}}={{\\text{r}}_{\\text{A}}}\\frac{{\\text{\u0394\u03d5}}}{{\\text{\u0394t}}}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {\\text{v}}_{\\text{B}}={{\\text{r}}_{\\text{B}}}\\frac{{\\text{\u0394\u03d5}}}{{\\text{\u0394t}}}<\/span><\/p>\n<p>Burada v<sub>A<\/sub>\u00a0and v<sub>B<\/sub>, A ve B noktalar\u0131n\u0131n h\u0131z vekt\u00f6rlerinin \u015fiddetidir ve \u03c9 = d\u03d5\/dt cismin a\u00e7\u0131sal h\u0131z\u0131d\u0131r. H\u0131z vekt\u00f6rlerinin y\u00f6n\u00fc mutlaka o noktay\u0131 merkeze ba\u011flayan do\u011fruya dik olacakt\u0131r. Vekt\u00f6rel olarak h\u0131z vekt\u00f6r\u00fc, <strong>\u03c9<\/strong>\u00a0ve\u00a0<strong>r<sub>A<\/sub><\/strong>\u00a0vekt\u00f6r olarak yaz\u0131l\u0131p vekt\u00f6rel \u00e7arp\u0131m yap\u0131larak:<\/p>\n<p style=\"text-align: center\"><strong>v<sub>A<\/sub><\/strong> = <strong>\u03c9<\/strong> \u00d7\u00a0<strong>r<sub>A<\/sub><\/strong><\/p>\n<p>Bu denklemde \u00d7\u00a0vekt\u00f6rel \u00e7arp\u0131m operat\u00f6r\u00fcd\u00fcr.<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1086\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img221-3.gif\" alt=\"\" width=\"380\" height=\"295\" \/><\/p>\n<p>D\u00fczlemsel hareket i\u00e7in h\u0131z ve ivmenin g\u00f6steriminde karma\u015f\u0131k say\u0131lardan da kolayl\u0131kla faydalan\u0131labilir. \u00d6rne\u011fin, A noktas\u0131n\u0131n konum vekt\u00f6r\u00fc karma\u015f\u0131k say\u0131larla:<\/p>\n<p style=\"text-align: center\"><strong>r<sub>A<\/sub><\/strong>\u00a0= r<sub>A<\/sub>e<sup>i\u03b8<\/sup><\/p>\n<p>olacakt\u0131r. E\u011fer cisim sadece A<sub>0<\/sub> noktas\u0131ndan ge\u00e7en d\u00fczleme dik bir eksen etraf\u0131nda d\u00f6nme yap\u0131yor ise, bu denklemde \u03b8\u00a0de\u011fi\u015fken bir a\u00e7\u0131d\u0131r ve r<sub>A<\/sub>, A noktas\u0131n\u0131n merkezden uzakl\u0131\u011f\u0131n\u0131 g\u00f6steren parametre bir sabittir. e<sup>i\u03b8<\/sup>\u00a0terimi ise\u00a0<strong>A<sub>0<\/sub>A<\/strong>\u00a0y\u00f6n\u00fcnde bir birim vekt\u00f6rd\u00fcr. Konum vekt\u00f6r\u00fcn\u00fcn t\u00fcrevi bize o noktan\u0131n h\u0131z\u0131n\u0131 verecektir:<\/p>\n<p style=\"text-align: center\"><strong>v<sub>A<\/sub><\/strong> = ir<sub>A<\/sub>\u03c9e<sup>i\u03b8<\/sup><\/p>\n<p>Bu denklemde \u03c9 = d\u03b8\/dt dir. \u03c9a\u00e7\u0131sal h\u0131z\u0131 e\u011fer \u03b8\u00a0a\u00e7\u0131s\u0131n\u0131n zamana g\u00f6re de\u011fi\u015fimi saat yelkovan\u0131na ters y\u00f6nde art\u0131yor ise (veya saat yelkovan\u0131 y\u00f6n\u00fcnde azal\u0131yor ise), pozitifdir. Saat y\u00f6n\u00fcnde zamana g\u00f6re art\u0131\u015f ise negatif bir a\u00e7\u0131sal h\u0131zd\u0131r. H\u0131z vekt\u00f6r\u00fcn\u00fcn \u015fiddeti r<sub>A<\/sub>\u03c9 olup y\u00f6n\u00fc ise ie<sup>i\u03b8<\/sup> d\u0131r. i = e<sup>i\u03c0\/2<\/sup> oldu\u011funa g\u00f6re, ie<sup>i\u03b8<\/sup> = e<sup>i(\u03b8+\u03c0\/2)<\/sup> dir . Yani, bu yeni birim vekt\u00f6r <strong>A<sub>0<\/sub>A<\/strong> do\u011frusuna g\u00f6re 90\u00b0\u00a0saat yelkovan\u0131na ters y\u00f6nde d\u00f6nm\u00fc\u015f bir birim vekt\u00f6rd\u00fcr. H\u0131z vekt\u00f6r\u00fcn\u00fcn \u015fiddeti daima pozitif al\u0131nmas\u0131 durumunda e\u011fer \u03c9 negatif ise, A noktas\u0131n\u0131n h\u0131z vekt\u00f6r\u00fcn\u00fcn y\u00f6n\u00fc \u2212ie<sup>i\u03b8<\/sup>, yani e<sup>i(\u03b8\u2212\u03c0\/2)<\/sup> olacakt\u0131r. Bu durumda h\u0131z vekt\u00f6r\u00fc\u00a0<strong>A<sub>0<\/sub>A<\/strong>\u00a0ya yine dik olup\u00a0<strong>A<sub>0<\/sub>A<\/strong>\u00a0do\u011frusuna g\u00f6re saat yelkovan\u0131 y\u00f6n\u00fcnde d\u00f6nm\u00fc\u015ft\u00fcr. \u00d6yle ise, A noktas\u0131n\u0131n h\u0131z\u0131n\u0131n \u015fiddeti r<sub>A<\/sub>\u03c9 olup <strong>A<sub>0<\/sub>A<\/strong> ya\u00a0diktir. Y\u00f6n\u00fc\u00a0<strong>A<sub>0<\/sub>A<\/strong> y\u00f6n\u00fcnde bir birim vekt\u00f6r\u00fcn a\u00e7\u0131sal h\u0131z\u0131n y\u00f6n\u00fcne g\u00f6re saat yelkovan\u0131 y\u00f6n\u00fcnde veya ters y\u00f6n\u00fcnde 90\u00b0\u00a0d\u00f6nd\u00fcr\u00fclmesi ile elde edilen bir birim vekt\u00f6r y\u00f6n\u00fcndedir.<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1087\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img221-4.gif\" alt=\"\" width=\"433\" height=\"265\" \/><\/p>\n<p>H\u0131z vekt\u00f6r\u00fcn\u00fcn t\u00fcrevi yerde\u011fi\u015fimin zamana g\u00f6re ikinci t\u00fcrevini verecektir:<\/p>\n<p style=\"text-align: center\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle {{\\text{a}}_{\\text{A}}}=\\frac{{\\text{d}{{\\text{v}}_{\\text{A}}}}}{{\\text{dt}}}=\\frac{\\text{d}}{{\\text{dt}}}\\left( {\\text{i}{{\\text{r}}_{\\text{A}}}{{\\text{e}}^{{\\text{i\u03b8}}}}} \\right)=\\text{i}\\frac{{\\text{d\u03c9}}}{{\\text{dt}}}{{\\text{r}}_{\\text{A}}}{{\\text{e}}^{{\\text{i\u03b8}}}}-{{\\text{r}}_{\\text{A}}}{{\\text{\u03c9}}^{2}}{{\\text{e}}^{{\\text{i\u03b8}}}}=\\text{i}\\text{\u03b1}{{\\text{r}}_{\\text{A}}}{{\\text{e}}^{{\\text{i\u03b8}}}}-{{\\text{r}}_{\\text{A}}}{{\\text{\u03c9}}^{2}}{{\\text{e}}^{{\\text{i\u03b8}}}} <\/span><\/p>\n<p>Burada \u03b1 = d\u03c9\/dt = d<sup>2<\/sup>\u03b8\/dt<sup>2<\/sup> cismin a\u00e7\u0131sal ivmesidir. A\u00e7\u0131sal ivme, \u03b8\u00a0konum a\u00e7\u0131s\u0131n\u0131n zamana g\u00f6re ikinci t\u00fcrevi; saat yelkovan\u0131na ters y\u00f6nde oldu\u011funda pozitif say\u0131lacakt\u0131r. Saat yelkovan\u0131 y\u00f6n\u00fcnde ise negatif a\u00e7\u0131sal ivmedir.<\/p>\n<p>Birinci terimin \u015fiddeti \u03b1r<sub>A<\/sub>, y\u00f6n\u00fc ie<sup>i\u03b8<\/sup>\u00a0olup\u00a0<strong>A<sub>0<\/sub>A<\/strong>\u00a0ya diktir. Bu vekt\u00f6r\u00fcn y\u00f6n\u00fc\u00a0<strong>A<sub>0<\/sub>A<\/strong> vekt\u00f6r\u00fcn\u00fcn a\u00e7\u0131sal ivme \u03b1&#8217;ya g\u00f6re 90\u00b0 d\u00f6nd\u00fcr\u00fclmesi ile elde edilir. Bu ivme bile\u015feni A noktas\u0131n\u0131n y\u00f6r\u00fcngesine te\u011fet oldu\u011fundan <strong><span style=\"color: #cc0000\">te\u011fetsel ivme bile\u015feni<\/span><\/strong>dir ve genellikle <strong>a<sub>A<\/sub><sup>t<\/sup><\/strong>\u00a0olarak g\u00f6sterilir. \u0130kinci terimin \u015fiddeti a\u00e7\u0131sal h\u0131z\u0131n karesi ile A<sub>0<\/sub>A uzakl\u0131\u011f\u0131n\u0131n \u00e7arp\u0131m\u0131d\u0131r (r\u03c9<sup>2<\/sup>), y\u00f6n\u00fc ise \u2212e<sup>i\u03b8<\/sup>\u00a0birim vekt\u00f6rd\u00fcr, yani\u00a0<strong>r<sub>A<\/sub><\/strong>\u00a0konum vekt\u00f6r\u00fcne ters y\u00f6nde bir vekt\u00f6rd\u00fcr. Ayr\u0131ca a\u00e7\u0131sal h\u0131z\u0131n karesi oldu\u011fundan y\u00f6n a\u00e7\u0131sal h\u0131z veya ivmeden daima ba\u011f\u0131ms\u0131z olacakt\u0131r. Bu ivmeye\u00a0<strong><span style=\"color: #cc0000\">normal ivme<\/span><\/strong>\u00a0diyece\u011fiz ve <strong>a<sub>A<\/sub><sup>n<\/sup><\/strong> ile g\u00f6sterece\u011fiz (baz\u0131 kitaplarda bu ivmeye merkezka\u00e7 ivmesi dense de bu terimin kullan\u0131lmas\u0131 yanl\u0131\u015f anlamalara neden oldu\u011fundan burada kullan\u0131lmayacakt\u0131r). Normal ivme A noktas\u0131n\u0131n y\u00f6r\u00fcngesine daima dik olup her zaman y\u00f6r\u00fcngenin e\u011frilik merkezine do\u011frudur. Sabit bir eksen etraf\u0131nda d\u00f6nen cisimlerin \u00fczerinde bulunan her hangi bir noktan\u0131n h\u0131z ve te\u011fetsel ivme y\u00f6n\u00fc a\u00e7\u0131sal h\u0131z ve ivmeye ba\u011fl\u0131 iken normal ivmenin y\u00f6n\u00fc a\u00e7\u0131sal h\u0131z ve ivmenin y\u00f6n\u00fcnden ba\u011f\u0131ms\u0131zd\u0131r.<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1088 aligncenter\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/09\/img221-5.gif\" alt=\"\" width=\"304\" height=\"234\" \/><\/p>\n<p>Bu a\u00e7\u0131klamalar\u0131n \u0131\u015f\u0131\u011f\u0131nda A noktas\u0131n\u0131n ivmesi iki bile\u015fenle:<\/p>\n<p style=\"text-align: center\"><strong>a<sub>A<\/sub><\/strong>\u00a0=\u00a0<strong>a<sub>A<\/sub><sup>t<\/sup><\/strong>\u00a0+\u00a0<strong>a<sub>A<\/sub><sup>n<\/sup><\/strong><\/p>\n<p>g\u00f6sterilebilecektir.<\/p>\n<p>t ve n \u00fcst indisleri te\u011fetsel ve normal ivme bile\u015fenlerini g\u00f6stermek i\u00e7indir. Bir cismin sabit bir eksen etraf\u0131nda d\u00f6nmesi s\u0131ras\u0131nda, d\u00f6nme ekseninin ge\u00e7ti\u011fi A<sub>0<\/sub>\u00a0merkez noktas\u0131 cisim \u00fczerinde bulunan h\u0131z\u0131 ve ivmesi s\u0131f\u0131r olan tek noktad\u0131r.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.metu.edu.tr\/eresmech\/files\/2021\/04\/important.gif\" title=\"\" alt=\"\" \/> \u00a0 \u00a0 \u00a0<b>Cismin sabit bir eksen etraf\u0131nda d\u00f6nmesi s\u0131ras\u0131nda hareket \u00f6zelliklerini \u015fu \u015fekilde \u00f6zetleyebiliriz:<\/b><\/p>\n<ol>\n<li><span style=\"color: #cc0000\">Cisim \u00fczerinde her noktan\u0131n h\u0131z\u0131, cismin a\u00e7\u0131sal h\u0131z\u0131 ile o noktan\u0131n d\u00f6nme eksenine uzakl\u0131\u011f\u0131n\u0131n \u00e7arp\u0131m\u0131na e\u015fittir. Yani eksenden uzakla\u015ft\u0131k\u00e7a h\u0131z artacakt\u0131r. H\u0131z vekt\u00f6r\u00fc daima o noktay\u0131 d\u00f6nme eksenine birle\u015ftiren do\u011fruya dik olup y\u00f6n\u00fc a\u00e7\u0131sal h\u0131z y\u00f6n\u00fcne g\u00f6re belirlidir.<\/span><\/li>\n<li><span style=\"color: #cc0000\">Cisim \u00fczerinde her noktan\u0131n normal ivmesi, a\u00e7\u0131sal h\u0131z\u0131n karesi ile o noktan\u0131n d\u00f6nme eksenine uzakl\u0131\u011f\u0131n\u0131n \u00e7arp\u0131m\u0131d\u0131r. Normal ivme daima o noktadan d\u00f6nme ekseni merkezine do\u011frudur.<\/span><\/li>\n<li><span style=\"color: #cc0000\">Cisim \u00fczerinde her noktan\u0131n te\u011fetsel ivmesi, a\u00e7\u0131sal ivme ile o noktan\u0131n d\u00f6nme eksenine uzakl\u0131\u011f\u0131n\u0131n \u00e7arp\u0131m\u0131na e\u015fittir. Te\u011fetsel ivme vekt\u00f6r\u00fc, o noktay\u0131 d\u00f6nme ekseni merkezine birle\u015ftiren do\u011fruya dik olup y\u00f6n\u00fc a\u00e7\u0131sal ivme y\u00f6n\u00fcne g\u00f6re belirlenir.<\/span><\/li>\n<li><span style=\"color: #cc0000\">Cisim \u00fczerinde bulunan bir noktan\u0131n ivmesi te\u011fetsel ve normal ivmelerin vekt\u00f6rel toplam\u0131d\u0131r.<\/span><\/li>\n<li><span style=\"color: #cc0000\">Cisim belirli bir a\u00e7\u0131sal h\u0131z ile d\u00f6nerken sadece d\u00f6nme merkezinin a\u00e7\u0131sal h\u0131z\u0131 ve ivmesi s\u0131f\u0131rd\u0131r.<\/span><\/li>\n<\/ol>\n<p>Ayr\u0131ca dikkat edilir ise, a\u00e7\u0131sal h\u0131z ve ivme bir cisme ait de\u011ferlerdir (cismin \u00fczerinde bir noktaya ait de\u011fer de\u011fildirler).<\/p>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div>\n\n\n<p> <a href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mekanizma-teknigi\/ch4\/\" 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\/4-1-2\/\" 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 -1 D\u00fczlemde \u00fc\u00e7 de\u011fi\u015fik tipte hareketi ay\u0131rabiliriz: \u00d6teleme: Bir cisim \u00f6teleme yap\u0131yor ise, cismin \u00fczerinde her nokta birbirlerine paralel y\u00f6r\u00fcngeler \u00e7izecektir ve cisim \u00fczerinde bulunan bir do\u011fru, daima \u0131lk konumuna paralel olacak \u015fekilde hareket edecektir.Bu &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/blog.metu.edu.tr\/eresmech\/mekanizma-teknigi\/ch4\/4-1-1\/\"> <span class=\"screen-reader-text\">4-1-1<\/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-1029","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1029","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=1029"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/eresmech\/wp-json\/wp\/v2\/pages\/1029\/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=1029"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}