{"id":393,"date":"2023-06-19T18:46:32","date_gmt":"2023-06-19T18:46:32","guid":{"rendered":"https:\/\/physigeek.com\/nl\/hoekversnelling\/"},"modified":"2023-06-19T18:46:32","modified_gmt":"2023-06-19T18:46:32","slug":"hoekversnelling","status":"publish","type":"post","link":"https:\/\/physigeek.com\/nl\/hoekversnelling\/","title":{"rendered":"Hoekversnelling"},"content":{"rendered":"<p>In dit artikel wordt uitgelegd wat hoekversnelling in de natuurkunde is. Zo ontdek je hoe je de hoekversnelling berekent, een opgeloste oefening en wat de relatie is tussen hoekversnelling en tangenti\u00eble versnelling. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-la-aceleracion-angular\"><\/span> Wat is hoekversnelling?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Hoekversnelling<\/strong> is een maatstaf die de rotatieversnelling van een lichaam definieert. Daarom geeft hoekversnelling de verandering in de hoeksnelheid van een lichaam aan. Met andere woorden: de hoekversnelling vertegenwoordigt de snelheid waarmee de hoeksnelheid verandert.<\/p>\n<p> De eenheid van hoekversnelling in het Internationale Systeem (SI) is de radiaal per seconde in het kwadraat (rad\/s <sup>2<\/sup> ). Op dezelfde manier wordt de hoekversnelling ook uitgedrukt in eenheden van s <sup>-2<\/sup> , aangezien de radiaal feitelijk dimensieloos is.<\/p>\n<p> Hoekversnelling wordt meestal weergegeven door het symbool voor de Griekse letter \u03b1 (alfa). <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/acceleration-angulaire.png\" alt=\"hoekversnelling\" class=\"wp-image-7362\" width=\"357\" height=\"249\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/acceleration-angulaire-300x210.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/acceleration-angulaire.png 493w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<p> De hoekversnelling wordt weergegeven door een axiale vector evenwijdig aan de rotatieas. De norm van de vector is de waarde van de hoekversnelling en de richting van de vector wordt bepaald door de rechterhandregel. Als het object in het vlak met de klok mee draait, zal de hoekversnellingsvector binnen het vlak gaan. Als het object daarentegen tegen de klok in draait, zal de hoekversnellingsvector buiten het vlak gaan. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Zie:<\/strong> <a href=\"https:\/\/physigeek.com\/nl\/hoeksnelheid\/\">Hoeksnelheid vinden<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-de-la-aceleracion-angular\"><\/span> Formule voor hoekversnelling<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> De gemiddelde hoekversnelling is gelijk aan de toename van de hoeksnelheid (\u0394\u03c9) gedeeld door de toename in de tijd (\u0394t). Om de hoekversnelling te berekenen, moet het verschil tussen de eind- en beginhoeksnelheid dus worden gedeeld door het verschil tussen het eind- en beginmoment (\u03b1 = \u0394\u03c9\/\u0394t).<\/p>\n<p> Daarom is de <strong>formule voor het berekenen van de gemiddelde versnelling<\/strong> : <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/formule-dacceleration-angulaire.png\" alt=\"formule voor hoekversnelling\" class=\"wp-image-7365\" width=\"232\" height=\"231\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/formule-dacceleration-angulaire-300x300.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/formule-dacceleration-angulaire-150x150.png 150w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/formule-dacceleration-angulaire.png 414w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<p style=\"margin-bottom:5px\"> Goud: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-5f44d9bbc8046069be4aa2989bff19aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> is de hoekversnelling. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-94f4e26a511e85d1ab00d3f1686bf7e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Delta \\omega\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: 0px;\"><\/p>\n<p> is de verandering in hoeksnelheid. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-819ab50990df5adf82bea9dfa75ffff2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Delta t\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\"><\/p>\n<p> is de temporele variatie. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-562a49afd4fa3e0e36dd810290074f64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega_f\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"19\" style=\"vertical-align: -6px;\"><\/p>\n<p> is de uiteindelijke hoeksnelheid. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-90b8586302c2fbf8bfa7a04162507ebd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> is de initi\u00eble hoeksnelheid. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-82d36af17e232807e56da9ccdbbda0d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t_f\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"14\" style=\"vertical-align: -6px;\"><\/p>\n<p> is het laatste moment. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-bf289b768173104db12fe7044c723db4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t_i\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"11\" style=\"vertical-align: -3px;\"><\/p>\n<p> is het eerste moment.<\/span><\/li>\n<\/ul>\n<p> Houd er rekening mee dat aan deze formule alleen wordt voldaan als de mobiel een uniform versnelde cirkelbeweging beschrijft, dat wil zeggen als de hoekversnelling over het hele pad constant is. Gebruik anders de volgende formule om de <strong>momentane hoekversnelling<\/strong> te vinden:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-9ca4f14fe6b21fc84c313375224fb893_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\alpha=\\lim_{\\Delta t\\to0}\\frac{\\Delta\\omega}{\\Delta t}=\\frac{d\\omega}{dt}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"152\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Na het berekenen van de waarde van de hoekversnelling moet het resultaat worden ge\u00efnterpreteerd volgens het teken van de hoekversnelling:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u03b1&gt;0<\/strong> : als de hoekversnelling positief is, betekent dit dat de waarde van de hoeksnelheid met de tijd toeneemt. Het is dus een eenparig versnelde cirkelvormige beweging.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u03b1&lt;0<\/strong> : als de hoekversnelling negatief is, betekent dit dat de waarde van de hoeksnelheid afneemt met de tijd. Het is dus een gelijkmatig vertraagde cirkelvormige beweging.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u03b1=0<\/strong> : als de hoekversnelling gelijk is aan nul, betekent dit dat de waarde van de hoeksnelheid constant is. Het is dus een uniforme cirkelvormige beweging.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplo-del-calculo-de-la-aceleracion-angular\"><\/span> Voorbeeld van het berekenen van hoekversnelling<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Nadat we de definitie van hoekversnelling en de formule ervan hebben gezien, zullen we in deze sectie een concreet voorbeeld zien van hoe hoekversnelling wordt berekend.<\/p>\n<ul>\n<li> Een lichaam in cirkelvormige beweging roteert met een hoeksnelheid van 80 rpm. Als het lichaam na 6 seconden volledig stopt met draaien, wat is dan de gemiddelde hoekversnelling van het lichaam gedurende deze periode?<\/li>\n<\/ul>\n<p> Eerst zullen we de hoeksnelheid omzetten in radialen per seconde om met eenheden van Syst\u00e8me International te werken. E\u00e9n winding is gelijk aan 2\u03c0 radialen, dus:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-84da1ead9b143fa4e97b6539717d9788_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"80 \\ \\cfrac{tours}{min} \\cdot \\cfrac{2\\pi \\ rad}{1 \\ tour}\\cdot \\cfrac{1 \\ min}{60 \\ s}=8,38 \\ \\cfrac {rad }{s}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"291\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> We passen nu de hoekversnellingsformule toe:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fedefe7f3708477dc61b93a792509ab6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha=\\cfrac{\\Delta\\omega}{\\Delta t}=\\cfrac{\\omega_f-\\omega_i}{t_f-t_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"148\" style=\"vertical-align: -18px;\"><\/p>\n<\/p>\n<p> Als het lichaam uiteindelijk tot stilstand komt, zal de uiteindelijke hoeksnelheid nul zijn. Bovendien kennen we de waarde van het eindmoment of het beginmoment niet, maar we weten wel dat het verschil tussen de twee 6 s is. De hoekversnelling is daarom:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fde4a41d03c719f8f5fd9b007a0f2387_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha=\\cfrac{0-8.38}{6}=-1.40 \\ \\cfrac{rad}{s^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"204\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Merk op dat in dit geval de hoekversnelling negatief is, wat betekent dat het lichaam met steeds lagere hoeksnelheid draait totdat het volledig tot stilstand komt. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Aceleracion-angular-y-aceleracion-tangencial\"><\/span> Hoekversnelling en tangenti\u00eble versnelling<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Hoekversnelling en tangenti\u00eble versnelling zijn wiskundig gerelateerd, dus tangenti\u00eble versnelling kan worden berekend op basis van hoekversnelling (of omgekeerd).<\/p>\n<p> Tangenti\u00eble versnelling (of lineaire versnelling) wordt berekend door de hoekversnelling te vermenigvuldigen met de straal van het cirkelvormige bewegingspad. Daarom zijn hoekversnelling en tangenti\u00eble versnelling gerelateerd aan de straal van het cirkelvormige bewegingspad.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-dcadf85fe24bbd678ca72ce3e1f0e582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_t=\\alpha\\cdot r\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"71\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Goud: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-ab56b4b3337ead2a6dab40b537d0ba6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_t\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"14\" style=\"vertical-align: -3px;\"><\/p>\n<p> is de tangenti\u00eble versnelling. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-5f44d9bbc8046069be4aa2989bff19aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> is de hoekversnelling. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> is de straal van het pad van cirkelvormige beweging. <\/span><\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Zie:<\/strong> <a href=\"https:\/\/physigeek.com\/nl\/tangentiele-versnelling-of-lineaire-versnelling\/\">Wat is tangenti\u00eble versnelling?<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>In dit artikel wordt uitgelegd wat hoekversnelling in de natuurkunde is. Zo ontdek je hoe je de hoekversnelling berekent, een opgeloste oefening en wat de relatie is tussen hoekversnelling en tangenti\u00eble versnelling. Wat is hoekversnelling? Hoekversnelling is een maatstaf die de rotatieversnelling van een lichaam definieert. Daarom geeft hoekversnelling de verandering in de hoeksnelheid van &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/nl\/hoekversnelling\/\"> <span class=\"screen-reader-text\">Hoekversnelling<\/span> Weiterlesen &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-393","post","type-post","status-publish","format-standard","hentry","category-filmisch"],"yoast_head":"<!-- This site is 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