{"id":1992,"date":"2023-02-10T14:00:00","date_gmt":"2023-02-10T13:00:00","guid":{"rendered":"https:\/\/technischemechanik.com\/?p=1992"},"modified":"2023-02-15T16:34:29","modified_gmt":"2023-02-15T15:34:29","slug":"kreisel-rotierender-stab-mit-drehfeder-2","status":"publish","type":"post","link":"https:\/\/technischemechanik.com\/en\/2023\/02\/10\/kreisel-rotierender-stab-mit-drehfeder-2\/","title":{"rendered":"Kreisel: Rotor in rotierender Gabel"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Herzlich Willkommen!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Kreiseldynamik ist derzeit noch eine recht unterrepr\u00e4sentierte Spezies hier auf der Website. Dies soll sich im Laufe der Zeit \u00e4ndern, daher gibt es heute wieder einmal ein Kreiselbeispiel mit folgender Angabe.<\/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\">In einer Gabel, die mit der konstanten Winkelgeschwindigkeit \u03a9 rotiert, ist ein Rotor gelagert, der sich seinerseits mit der konstanten Winkelgeschwindigkeit \u03c9r relativ zur Gabel dreht. Der Rotor besitzt die Haupttr\u00e4gheitsmomente: I<sub>x<\/sub> = I<sub>y<\/sub> = I<sub>z<\/sub> = I und das Gewicht G. F\u00fcr die Gabel sind die Abmessungen l<sub>1<\/sub>, l<sub>2<\/sub> und l gegeben. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Errechne im gabelfesten xyz\u2212System: <br>*den Drehimpuls des Rotors bez\u00fcglich S. <br>*die Auflagerkr\u00e4fte in C und D. <br>*die Auflagerkr\u00e4fte in A und B zufolge des Rotors.<\/p>\n<cite>Quelle: Aufgabe 4.4.1 (S. 41) aus P. Lugner et al., Technische Mechanik, 1992 Springer-Verlag, Wien<\/cite><\/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=\"558\" height=\"860\" data-attachment-id=\"1994\" data-permalink=\"https:\/\/technischemechanik.com\/en\/2023\/02\/10\/kreisel-rotierender-stab-mit-drehfeder-2\/beispiel_2_10-6\/\" data-orig-file=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2023\/02\/Beispiel_2_10-6.jpg?fit=558%2C860&amp;ssl=1\" data-orig-size=\"558,860\" 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=\"Beispiel_2_10-6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2023\/02\/Beispiel_2_10-6.jpg?fit=558%2C860&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2023\/02\/Beispiel_2_10-6.jpg?resize=558%2C860&#038;ssl=1\" alt=\"\" class=\"wp-image-1994\" srcset=\"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2023\/02\/Beispiel_2_10-6.jpg?w=558&amp;ssl=1 558w, https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2023\/02\/Beispiel_2_10-6.jpg?resize=195%2C300&amp;ssl=1 195w\" sizes=\"auto, (max-width: 558px) 100vw, 558px\" \/><\/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\/02\/Kreisel-K01.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Kreisel-K01.\"><\/object><a id=\"wp-block-file--media-a5c71da8-b890-4293-9fe2-be887e6e3f39\" href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2023\/02\/Kreisel-K01.pdf\">Kreisel-K01<\/a><a href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2023\/02\/Kreisel-K01.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\">Es handelt sich in diesem Fall um ein relativ simples Kreiselbeispiel. Nachdem die Rotationen von Rotor und Gabel normal zueinander stehen ergibt sich ein kompakter Drehimpulsvektor, der wiederum zu einem sehr kompakten Drehimpulssatz f\u00fchrt. Anschlie\u00dfend ben\u00f6tigen wir noch den Schwerpunktsatz als zweite Gleichung, der allerdings auch zum Kr\u00e4ftegleichgewicht wird, weil es keine Schwerpunktsbewegung gibt. Damit lassen sich schon alle vier Lagerreaktionen berechnen. Die Schritt-f\u00fcr-Schritt Erkl\u00e4rung findet ihr im Video. Viel Spa\u00df damit.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube 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\/U1TzOZRA_5Y?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 wieder lieber lesen als ein Video zu schauen gibt es das pdf der fertigen Rechnung.<\/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\/02\/K01.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of K01.\"><\/object><a id=\"wp-block-file--media-f3ff12f8-b9ba-49ff-907e-1bd1bbd29b9a\" href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2023\/02\/K01.pdf\">K01<\/a><a href=\"https:\/\/technischemechanik.com\/wp-content\/uploads\/2023\/02\/K01.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\">S\u00e4mtliche Fragen beantworte ich wie immer sehr gerne &#8211; schreibt sie mir bitte einfach hier oder auf YouTube als Kommentar.<\/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;bc2d822b24&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;:11585415,&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;:52803617,&quot;client_id&quot;:&quot;4ae8e890-5309-41a3-bae2-719a23a5da36&quot;},{&quot;answer_text&quot;:&quot;down&quot;,&quot;id&quot;:52803618,&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;:11585416,&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;:52803619,&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! Kreiseldynamik ist derzeit noch eine recht unterrepr\u00e4sentierte Spezies hier auf der Website. Dies soll sich im Laufe der Zeit \u00e4ndern, daher gibt es heute wieder einmal ein Kreiselbeispiel mit folgender Angabe. In einer Gabel, die mit der konstanten Winkelgeschwindigkeit \u03a9 rotiert, ist ein Rotor gelagert, der sich seinerseits mit der konstanten Winkelgeschwindigkeit \u03c9r &hellip; <a href=\"https:\/\/technischemechanik.com\/en\/2023\/02\/10\/kreisel-rotierender-stab-mit-drehfeder-2\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Kreisel: Rotor in rotierender Gabel<\/span><\/a><\/p>","protected":false},"author":110396568,"featured_media":1999,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_crdt_document":"","advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"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-1992","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_featured_media_url":"https:\/\/i0.wp.com\/technischemechanik.com\/wp-content\/uploads\/2023\/02\/Kreisel-K01.png?fit=1280%2C720&ssl=1","jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7UJuu-w8","jetpack-related-posts":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts\/1992","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=1992"}],"version-history":[{"count":5,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts\/1992\/revisions"}],"predecessor-version":[{"id":2003,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/posts\/1992\/revisions\/2003"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/media\/1999"}],"wp:attachment":[{"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/media?parent=1992"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/categories?post=1992"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/technischemechanik.com\/en\/wp-json\/wp\/v2\/tags?post=1992"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}