{"id":2050,"date":"2023-03-13T14:33:49","date_gmt":"2023-03-13T13:33:49","guid":{"rendered":"https:\/\/technischemechanik.com\/?p=2050"},"modified":"2023-03-13T14:33:54","modified_gmt":"2023-03-13T13:33:54","slug":"kreisel-kollermuehle","status":"publish","type":"post","link":"https:\/\/technischemechanik.com\/en\/2023\/03\/13\/kreisel-kollermuehle\/","title":{"rendered":"Gyro: Roller mill"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Herzlich Willkommen!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Wir f\u00fcgen wieder einmal ein Kreiselbeispiel zu unserem Repertoire hinzu. Diesmal geht es um eine der klassischsten Anwendung der Kreiseldynamik, n\u00e4mlich eine Kollerm\u00fchle. Wie ihr wahrscheinlich wisst, wird dieses Ger\u00e4t in der Zerkleinerungstechnik (z.B. um Mehl zu mahlen) verwendet. Warum das \u00fcberhaupt funktioniert, sollte das heutige Beispiel sehr anschaulich zeigen. <\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Eine Kollerm\u00fchle besteht aus einer drehbar gelagerten, d\u00fcnnen Kreisscheibe (Masse m, Radius \u03c10), die \u00fcber einen masselosen Stab der L\u00e4nge l=2\u03c10 aus der Ruhelage mit konstanter Winkelbeschleunigung \u03b1 beschleunigt wird, wobei gilt \u03c90(t)=\u03b1t. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bestimme f\u00fcr reines Rollen zwischen Scheibe und Unterlage: <br>*das erforderliche \u00e4u\u00dfere Moment M im mit der Scheibe mitrotierenden k\u00f6rperfesten Koordinatensystem e\u20131-e\u20132-e\u20133. <br>*die Zeit t1, bei der die Anpresskraft zwischen Scheibe und Unterlage FN=2mg betr\u00e4gt. <br>*den erforderlichen minimalen Reibungskoeffizienten \u03bc zwischen Scheibe und Unterlage, sodass w\u00e4hrend des gesamten Beschleunigungsvorganges reines Rollen sichergestellt ist.<\/p>\n<\/blockquote>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"712\" height=\"420\" data-attachment-id=\"2052\" data-permalink=\"https:\/\/technischemechanik.com\/en\/2023\/03\/13\/kreisel-kollermuehle\/kreisel_2014_01_15\/\" data-orig-file=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2023\/03\/kreisel_2014_01_15.jpg?fit=759%2C448&amp;ssl=1\" data-orig-size=\"759,448\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"kreisel_2014_01_15\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2023\/03\/kreisel_2014_01_15.jpg?fit=712%2C420&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2023\/03\/kreisel_2014_01_15.jpg?resize=712%2C420&#038;ssl=1\" alt=\"\" class=\"wp-image-2052\" srcset=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2023\/03\/kreisel_2014_01_15.jpg?w=759&amp;ssl=1 759w, https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2023\/03\/kreisel_2014_01_15.jpg?resize=300%2C177&amp;ssl=1 300w\" sizes=\"auto, (max-width: 712px) 100vw, 712px\" \/><\/figure>\n<\/div><\/div><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Die Angabe zum Download gibt es wie gewohnt hier:<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2023\/03\/Kreisel-K04.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Kreisel-K04.\"><\/object><a id=\"wp-block-file--media-a5c71da8-b890-4293-9fe2-be887e6e3f39\" href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2023\/03\/Kreisel-K04.pdf\">Kreisel-K04<\/a><a href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2023\/03\/Kreisel-K04.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-a5c71da8-b890-4293-9fe2-be887e6e3f39\">Herunterladen<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Wir k\u00f6nnen hier laut Angabe davon ausgehen, dass die Stange masselos ist, weil sie als sehr leicht im Vergleich zur Kreisscheibe angenommen wird. Daher reicht es aus, die relevanten Gleichungen f\u00fcr die Scheibe &#8211; allerdings im gegebenen e1-e2-e3-Koordinatensystem &#8211; anzuschreiben. Wir ben\u00f6tigen also den Drehimpulssatz der Scheibe. Damit wir diesen aufstellen k\u00f6nnen, brauchen wir wiederum die Winkelgeschwindigkeit und den Tr\u00e4gheitstensor der Kreisscheibe. Aus dem fertigen Drehimpulssatz l\u00e4sst sich schlie\u00dflich sowohl die gesuchte Zeit t1, als auch der minimal notwendige Reibungskoeffizient zwischen Scheibe und Unterlage bestimmen, sodass wir jederzeit reines Rollen haben. Wie immer findest du alle Details im verlinkten Video. <\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-handler-einbetten wp-block-embed-handler-einbetten wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"712\" height=\"401\" src=\"https:\/\/www.youtube.com\/embed\/xl-c-NIMmI4?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=en-GB&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><figcaption class=\"wp-element-caption\">F\u00fcr diejenigen unter euch die lieber lesen als ein Video anzuschauen gibt es das pdf der fertigen Rechnung hier zum Download.<\/figcaption><\/figure>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2023\/03\/K04.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of K04.\"><\/object><a id=\"wp-block-file--media-f3ff12f8-b9ba-49ff-907e-1bd1bbd29b9a\" href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2023\/03\/K04.pdf\">K04<\/a><a href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2023\/03\/K04.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-f3ff12f8-b9ba-49ff-907e-1bd1bbd29b9a\">Herunterladen<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Bei Fragen meldet euch sehr gerne jederzeit bei mir. Ich versuche alles schnellstm\u00f6glich zu beantworten.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hat euch das Video gefallen? Dann lasst bitte ein Like hier auf dem Blog und auf YouTube da. Abonniert auch unbedingt den Kanal um kein Video mehr zu verpassen. Vielen Dank!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bis bald,<br>Markus <\/p>\n\n\n<div class=\"crowdsignal-feedback-wrapper\" data-crowdsignal-feedback=\"{&quot;feedbackPlaceholder&quot;:&quot;Sag mir bitte was dir besonders gefallen hat und was ich verbessern soll! Vielen Dank!&quot;,&quot;submitText&quot;:&quot;Danke f\\u00fcr dein Feedback!&quot;,&quot;surveyId&quot;:2705235,&quot;title&quot;:&quot;Feedback&quot;,&quot;emailResponses&quot;:false,&quot;emailPlaceholder&quot;:&quot;Your Email&quot;,&quot;emailRequired&quot;:false,&quot;header&quot;:&quot;\\ud83d\\udc4b Hey there!&quot;,&quot;hideBranding&quot;:false,&quot;hideTriggerShadow&quot;:false,&quot;submitButtonLabel&quot;:&quot;Submit&quot;,&quot;toggleOn&quot;:&quot;click&quot;,&quot;triggerLabel&quot;:&quot;Feedback&quot;,&quot;x&quot;:&quot;left&quot;,&quot;y&quot;:&quot;bottom&quot;,&quot;status&quot;:&quot;open&quot;,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true},&quot;nonce&quot;:&quot;c466676e7e&quot;}\"><\/div>\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"crowdsignal-vote-wrapper\" data-crowdsignal-vote=\"{&quot;pollId&quot;:&quot;29311620-3302-4a28-8c62-34c614948b60&quot;,&quot;title&quot;:&quot;Unbenannte Abstimmung 20&quot;,&quot;hideBranding&quot;:false,&quot;pollStatus&quot;:&quot;open&quot;,&quot;size&quot;:&quot;medium&quot;,&quot;borderWidth&quot;:1,&quot;borderRadius&quot;:5,&quot;hideResults&quot;:false,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true},&quot;apiPollData&quot;:{&quot;id&quot;:11926210,&quot;question&quot;:&quot;&quot;,&quot;note&quot;:&quot;&quot;,&quot;settings&quot;:{&quot;title&quot;:&quot;Unbenannte Abstimmung 20&quot;,&quot;after_vote&quot;:&quot;results&quot;,&quot;after_message&quot;:&quot;&quot;,&quot;randomize_answers&quot;:false,&quot;restrict_vote_repeat&quot;:false,&quot;captcha&quot;:false,&quot;multiple_choice&quot;:false,&quot;redirect_url&quot;:&quot;&quot;,&quot;close_status&quot;:&quot;open&quot;,&quot;close_after&quot;:false},&quot;answers&quot;:[{&quot;answer_text&quot;:&quot;up&quot;,&quot;id&quot;:54279760,&quot;client_id&quot;:&quot;4ae8e890-5309-41a3-bae2-719a23a5da36&quot;},{&quot;answer_text&quot;:&quot;down&quot;,&quot;id&quot;:54279761,&quot;client_id&quot;:&quot;b583d8b0-1c19-492c-a781-9f4dfba236ce&quot;}],&quot;source_link&quot;:&quot;https:\\\/\\\/technischemechanik.com&quot;,&quot;client_id&quot;:&quot;29311620-3302-4a28-8c62-34c614948b60&quot;}}\">\n<div data-crowdsignal-vote-item=\"{&quot;answerId&quot;:&quot;4ae8e890-5309-41a3-bae2-719a23a5da36&quot;,&quot;type&quot;:&quot;up&quot;,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true}}\"><\/div>\n\n<div data-crowdsignal-vote-item=\"{&quot;answerId&quot;:&quot;b583d8b0-1c19-492c-a781-9f4dfba236ce&quot;,&quot;type&quot;:&quot;down&quot;,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true}}\"><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"crowdsignal-applause-wrapper\" data-crowdsignal-applause=\"{&quot;pollId&quot;:&quot;94052372-60ee-4246-bdb3-b44cfaeeec3b&quot;,&quot;title&quot;:&quot;Unbenannter Applaus&quot;,&quot;answerId&quot;:&quot;4951fcb8-b48f-428e-82e4-90330cd7aed6&quot;,&quot;hideBranding&quot;:false,&quot;size&quot;:&quot;medium&quot;,&quot;pollStatus&quot;:&quot;open&quot;,&quot;TrpContentRestriction&quot;:{&quot;restriction_type&quot;:&quot;exclude&quot;,&quot;selected_languages&quot;:[],&quot;panel_open&quot;:true},&quot;apiPollData&quot;:{&quot;id&quot;:11926211,&quot;question&quot;:&quot;&quot;,&quot;note&quot;:&quot;&quot;,&quot;settings&quot;:{&quot;title&quot;:&quot;Unbenannter Applaus&quot;,&quot;after_vote&quot;:&quot;results&quot;,&quot;after_message&quot;:&quot;&quot;,&quot;randomize_answers&quot;:false,&quot;restrict_vote_repeat&quot;:false,&quot;captcha&quot;:false,&quot;multiple_choice&quot;:false,&quot;redirect_url&quot;:&quot;&quot;,&quot;close_status&quot;:&quot;open&quot;,&quot;close_after&quot;:false},&quot;answers&quot;:[{&quot;answer_text&quot;:&quot;clap&quot;,&quot;id&quot;:54279762,&quot;client_id&quot;:&quot;4951fcb8-b48f-428e-82e4-90330cd7aed6&quot;}],&quot;source_link&quot;:&quot;https:\\\/\\\/technischemechanik.com&quot;,&quot;client_id&quot;:&quot;94052372-60ee-4246-bdb3-b44cfaeeec3b&quot;}}\"><\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Herzlich Willkommen! Wir f\u00fcgen wieder einmal ein Kreiselbeispiel zu unserem Repertoire hinzu. Diesmal geht es um eine der klassischsten Anwendung der Kreiseldynamik, n\u00e4mlich eine Kollerm\u00fchle. Wie ihr wahrscheinlich wisst, wird dieses Ger\u00e4t in der Zerkleinerungstechnik (z.B. um Mehl zu mahlen) verwendet. Warum das \u00fcberhaupt funktioniert, sollte das heutige Beispiel sehr anschaulich zeigen. Eine Kollerm\u00fchle besteht &hellip; <a href=\"https:\/\/technischemechanik.com\/en\/2023\/03\/13\/kreisel-kollermuehle\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Gyro: Roller mill<\/span><\/a><\/p>","protected":false},"author":110396568,"featured_media":2051,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_seo_schema_type":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[2602546,1145536,5004009],"tags":[129538,25466,2245662,7978,13261836,102130347,6886663,12237,750913297,35890,166867,3480,807373,40987001,2517859,750913303,947685,32590,5685069,727263877,662707,7091101,215605283,720191,10126,73726871,161115,172005,2411,122145655,3831784,14084,1121513,727213064,1097356,2722,33601,17744,21321],"class_list":["post-2050","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ubungsaufgaben","category-dynamik","category-kreisel","tag-aufgabe","tag-beispiel","tag-beschleunigung","tag-bildung","tag-digitale-bildung","tag-digitaler-unterricht","tag-drehzahl","tag-dynamics","tag-dynamik","tag-featured","tag-hochschule","tag-homeschooling","tag-ingenieur","tag-ingenieurwissenschaft","tag-krafte","tag-kreisel","tag-losung","tag-lehre","tag-lernhilfe","tag-markus-orthaber","tag-maschinenbau","tag-maschinenbauingenieur","tag-mathematik-lernen","tag-mechanik","tag-physik","tag-physik-nachhilfe","tag-screencast","tag-studieren","tag-studium","tag-studyhelp","tag-tachometer","tag-technik","tag-technische-mechanik","tag-technische-mechanik-1","tag-tm1","tag-uni","tag-universitat","tag-wissen","tag-wissenschaft"],"jetpack_publicize_connections":[],"jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7UJuu-x4","jetpack-related-posts":[],"amp_enabled":true,"jetpack_featured_media_url":"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2023\/03\/Kreisel-K04.png?fit=1280%2C720&ssl=1","_links":{"self":[{"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts\/2050","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/users\/110396568"}],"replies":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/comments?post=2050"}],"version-history":[{"count":3,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts\/2050\/revisions"}],"predecessor-version":[{"id":2057,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts\/2050\/revisions\/2057"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/media\/2051"}],"wp:attachment":[{"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/media?parent=2050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/categories?post=2050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/tags?post=2050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}