{"id":332858,"date":"2016-12-06T03:00:00","date_gmt":"2016-12-06T00:00:00","guid":{"rendered":"https:\/\/www.fyysika.ee\/?guid=8cc370909d52417a53b7fbdbfe656d13"},"modified":"2016-12-06T03:00:00","modified_gmt":"2016-12-06T00:00:00","slug":"the-bead-on-a-rotating-hoop-revisited-an-unexpected-resonance-2","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=332858","title":{"rendered":"The bead on a rotating hoop revisited: an unexpected resonance"},"content":{"rendered":"<p>The bead on a rotating hoop is a typical problem in mechanics, frequently posed to junior science<br \/>\nand engineering students in basic physics courses. Although this system has a rich dynamics, it is<br \/>\nusually not analysed beyond the point particle approximation in undergraduate textbooks, nor<br \/>\nempirically investigated. Advanced textbooks show the existence of bifurcations owing to the<br \/>\nsystem&#8217;s nonlinear nature, and some papers demonstrate, from a theoretical standpoint, its points of<br \/>\ncontact with phase transition phenomena. However, scarce experimental research has been conducted to<br \/>\nbetter understand its behaviour. We show in this paper that a minor modification to the problem<br \/>\nleads to appealing consequences that can be studied both theoretically and empirically with the<br \/>\nbasic conceptual tools and experimental skills available to junior students. In particular, we go<br \/>\nbeyond the point particle approximation by treating the bead as a rigid spherical body, and explore<br \/>\nthe effect of a sl&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The bead on a rotating hoop is a typical problem in mechanics, frequently posed to junior science<br \/>\nand engineering students in basic physics courses. Although this system has a rich dynamics, it is<br \/>\nusually not analysed beyond the point particle approx&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-332858","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/332858","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=332858"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/332858\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=332858"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=332858"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=332858"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}