{"id":22922,"date":"2012-09-22T23:10:04","date_gmt":"2012-09-22T23:10:04","guid":{"rendered":"http:\/\/rafaelfajardo.com\/portfolio\/dataanxiety-quantumaniac-simple-and-circular\/"},"modified":"2018-12-05T21:43:27","modified_gmt":"2018-12-06T04:43:27","slug":"dataanxiety-quantumaniac-simple-and-circular","status":"publish","type":"post","link":"https:\/\/rafaelfajardo.com\/portfolio\/dataanxiety-quantumaniac-simple-and-circular\/","title":{"rendered":""},"content":{"rendered":"<div id='gallery-1' class='gallery galleryid-22922 gallery-columns-3 gallery-size-thumbnail'><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/rafaelfajardo.com\/portfolio\/dataanxiety-quantumaniac-simple-and-circular\/attachment\/22923\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/rafaelfajardo.com\/portfolio\/wp-content\/uploads\/tumblr_m257xelTm91r2h5u7o1_500-100x100.gif\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" \/><\/a>\n\t\t\t<\/div><\/figure>\n\t\t<\/div>\n\n<p><a href=\"http:\/\/dataanxiety.tumblr.com\/post\/23859662252\/quantumaniac-simple-and-circular-motion\" class=\"tumblr_blog\">dataanxiety<\/a>:<\/p>\n<blockquote>\n<p><strong><a class=\"tumblr_blog\" href=\"http:\/\/quantumaniac.tumblr.com\/post\/20730300861\/simple-and-circular-motion-although-it-may\">quantumaniac<\/a><\/strong>:<\/p>\n<blockquote>\n<p><strong>Simple and Circular Motion<\/strong><\/p>\n<p>Although it may seem\u00a0counterintuitive, simple harmonic motion (left) and simple circular motion (right) have a great deal in common. If one looks at an object undergoing simple circular motion, it is clear that there are two scales to which an extreme can be reached &#8211; a polarized left\/right, and an equally polarized up\/down. However, looking from the side &#8211; only the top and bottom can be seen, and by looking at circular motion from the side it looks exactly like simple harmonic motion.\u00a0<\/p>\n<p>The physical equations governing these bodies are also quite similar.<\/p>\n<p><strong>Angular Velocity<\/strong><\/p>\n<ul>\n<li>A spring in (simple harmonic) motion: \u00a0<img decoding=\"async\" alt=\"sqrt{frac{k}{m}}\" class=\"tex\" src=\"http:\/\/upload.wikimedia.org\/wikibooks\/en\/math\/e\/b\/d\/ebdc7597a4b90fb00f8c2ef5f7d7a0a0.png\" \/><\/li>\n<li>A pendulum: \u00a0\u00a0<img decoding=\"async\" alt=\"sqrt{frac{g}{l}}\" class=\"tex\" src=\"http:\/\/upload.wikimedia.org\/wikibooks\/en\/math\/8\/d\/c\/8dc2de4c241fbb0e5e5a6ebe8359d792.png\" \/><\/li>\n<\/ul>\n<p><strong>Time Period<\/strong><\/p>\n<ul>\n<li>Spring: \u00a0 \u00a0 \u00a0<img decoding=\"async\" alt=\"2pi sqrt{frac{m}{k}}\" class=\"tex\" src=\"http:\/\/upload.wikimedia.org\/wikibooks\/en\/math\/3\/5\/f\/35fd8f024aee7e2949f1b9a066d66e5b.png\" \/><\/li>\n<li>Pendulum:\u00a0<img decoding=\"async\" alt=\"2pi sqrt{frac{l}{g}}\" class=\"tex\" src=\"http:\/\/upload.wikimedia.org\/wikibooks\/en\/math\/3\/b\/1\/3b11c211a0498eb8c03549cda0cfce82.png\" \/><\/li>\n<\/ul>\n<p><em>where k is the spring constant, m is the object\u2019s mass, g is gravity, l is the length of the pendulum arm<\/em><\/p>\n<\/blockquote>\n<p>Given the similarities, it seems reasonable that the product of angular velocity and time period would also be the same. It is: 2 * pi. (Intuition now swings in favor of simple circular motion, rather than the simple harmonic motion of a mass on a spring.)<\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>dataanxiety: quantumaniac: Simple and Circular Motion Although it may seem\u00a0counterintuitive, simple harmonic motion (left) and simple circular motion (right) have a great deal in common. If one looks at an object undergoing simple circular motion, it is clear that there are two scales to which an extreme can be reached &#8211; a polarized left\/right, and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"gallery","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":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":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":[10],"tags":[],"class_list":["post-22922","post","type-post","status-publish","format-gallery","hentry","category-words","post_format-post-format-gallery"],"jetpack_publicize_connections":[],"jetpack_shortlink":"https:\/\/wp.me\/p6PWot-5XI","jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/posts\/22922","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/comments?post=22922"}],"version-history":[{"count":1,"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/posts\/22922\/revisions"}],"predecessor-version":[{"id":22924,"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/posts\/22922\/revisions\/22924"}],"wp:attachment":[{"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/media?parent=22922"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/categories?post=22922"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/tags?post=22922"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}