{"id":40248,"date":"2025-01-14T13:50:18","date_gmt":"2025-01-14T13:50:18","guid":{"rendered":"https:\/\/idea.membrane.com\/songwriter\/?p=40248"},"modified":"2025-01-16T14:38:34","modified_gmt":"2025-01-16T14:38:34","slug":"velocity-accelerates-until","status":"publish","type":"post","link":"http:\/\/kingarthur.com\/songwriter\/2025\/01\/14\/velocity-accelerates-until\/","title":{"rendered":"Velocity Accelerates Until&#8230;."},"content":{"rendered":"<ul>\n<li><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/IX\/Velocity-Accelerates-Until-0.mp3\"> Velocity-Accelerates-Until-0.mp3<\/a><\/li>\n<li><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/IX\/Velocity-Accelerates-Until-0.mp4\"> Velocity-Accelerates-Until-0.mp4<\/a><\/li>\n<li><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/IX\/Velocity-Accelerates-Until-I.mp3\"> Velocity-Accelerates-Until-I.mp3<\/a><\/li>\n<li><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/IX\/Velocity-Accelerates-Until-I.mp4\"> Velocity-Accelerates-Until-I.mp4<\/a><\/li>\n<li><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/IX\/Velocity-Accelerates-Until-intro.mp3\"> Velocity-Accelerates-Until-intro.mp3<\/a><\/li>\n<\/ul>\n<p>[Intro]<br \/>Rollin&#8217; down a hill&#8230;<br \/>Velocity accelerates until&#8230;.<\/p>\n<p>[Bridge]<br \/>Exponential growth<br \/>Exponential velocity<br \/>(Indeed)<\/p>\n<p>[Verse 1]<br \/>Amass a mass<br \/>(Rolling past)<br \/>You know&#8230;<br \/>(Watch &#8216;er grow)<br \/>She&#8217;s gonna go<\/p>\n<p>[Bridge]<br \/>Rollin&#8217; down a hill&#8230;<br \/>Velocity accelerates until&#8230;<\/p>\n<p>[Chorus]<br \/>Rollin&#8217; down a hill<br \/>(Faster and faster until)<br \/>Rollin&#8217; down a hill<br \/>(Bigger, bigger, bigger still)<\/p>\n<p>[Verse 2]<br \/>Increase proportional<br \/>(to the cube of the radius)<br \/>Oh, please! Sensational<br \/>(amazing to all of us)<br \/>Exponential growth<br \/>Exponential velocity<br \/>(Indeed)<\/p>\n<p>[Bridge]<br \/>Rollin&#8217; down a hill&#8230;<br \/>Velocity accelerates until&#8230;<\/p>\n<p>[Verse]<br \/>&#8230;until external forces<br \/>(friction, resistance, or slope gradient)<br \/>&#8230;limit the growth&#8230; courses&#8230;<br \/>Reach the limit (that&#8217;s it)<\/p>\n<p>[Outro]<br \/>Rollin&#8217; (rollin&#8217;, rollin&#8217;)<br \/>Rollin&#8217;! (rollin&#8217;, rollin&#8217;)<\/p>\n<p>A SCIENCE NOTE<\/p>\n<p>As a snowball rolls down a snow-covered hill, its mass and velocity change due to the accumulation of snow and the forces acting on it. Here&#8217;s a breakdown of typical changes:<\/p>\n<h3><strong>1. Mass Increase:<\/strong><\/h3>\n<ul>\n<li><strong>Mechanism<\/strong>: The snowball picks up snow from the surface of the hill as it rolls, increasing its mass.<\/li>\n<li><strong>Rate of Growth<\/strong>:\n<ul>\n<li>The mass increase depends on factors such as the snowball&#8217;s surface area, the stickiness and density of the snow, and the snowball&#8217;s velocity.<\/li>\n<li>Snow density can range from <strong>200 to 500 kg\/m\u00b3<\/strong>, meaning the rate of mass growth varies significantly based on conditions.<\/li>\n<li>The increase is approximately proportional to the snowball&#8217;s surface area, which grows as the square of the radius.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3><strong>2. Velocity Increase:<\/strong><\/h3>\n<ul>\n<li><strong>Mechanism<\/strong>: Gravity accelerates the snowball as it moves downhill, increasing its velocity.<\/li>\n<li><strong>Rate of Acceleration<\/strong>:\n<ul>\n<li>The acceleration depends on the incline of the slope (<span class=\"katex\"><span class=\"katex-mathml\">\u03b8\\theta<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03b8<\/span><\/span><\/span><\/span>) and frictional forces.<\/li>\n<li>Friction decreases with steeper slopes or smoother snow surfaces.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3><strong>Momentum<\/strong>:<\/h3>\n<ul>\n<li><strong>Formula<\/strong>: Momentum is given by <span class=\"katex\"><span class=\"katex-mathml\">p=mv<\/span><\/span>, where <span class=\"katex\"><span class=\"katex-mathml\">m<\/span><\/span> is the mass and <span class=\"katex\"><span class=\"katex-mathml\">v<\/span><\/span> is the velocity.<\/li>\n<li><strong>Changes<\/strong>:\n<ul>\n<li>As mass (<span class=\"katex\"><span class=\"katex-mathml\">m<\/span><\/span>) increases, momentum increases.<\/li>\n<li>As velocity (<span class=\"katex\"><span class=\"katex-mathml\">v)<\/span><\/span> increases due to acceleration, momentum increases further.<\/li>\n<li>Momentum grows at a rate combining both mass accumulation and acceleration, making it nonlinear over time.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3><strong>3. Typical Observations<\/strong>:<\/h3>\n<ul>\n<li>A small snowball might double in size (diameter) in a short distance on a sticky snow-covered hill.<\/li>\n<li>Its mass (<span class=\"katex\"><span class=\"katex-mathml\">m<\/span><\/span>) could increase proportional to the cube of its radius.<\/li>\n<li>Its velocity (<span class=\"katex\"><span class=\"katex-mathml\">v<\/span><\/span>) increases with the slope but may plateau if friction or air resistance becomes significant.<\/li>\n<\/ul>\n<p>In short, as a snowball gains size, its mass increases significantly, and its velocity accelerates until external forces like friction, air resistance, or slope gradient limit the growth.<\/p>\n<h3>From the album &#8220;<a href=\"http:\/\/idea.membrane.com\/songwriter\/tag\/snowball-effect\/\">Snowball Effect<\/a>&#8221; by <a href=\"http:\/\/membrane.com\/change\/\">\u0394 To Cause a Change<\/a><\/h3>\n<h2><a href=\"http:\/\/membrane.com\/global_warming\/\">The Human Induced Climate Change Experiment<\/a><\/h2>\n<h2><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/IX\/\">MegaEpix Enormous<\/a><\/h2>\n","protected":false},"excerpt":{"rendered":"<p>Velocity-Accelerates-Until-0.mp3 Velocity-Accelerates-Until-0.mp4 Velocity-Accelerates-Until-I.mp3 Velocity-Accelerates-Until-I.mp4 Velocity-Accelerates-Until-intro.mp3 [Intro]Rollin&#8217; down a hill&#8230;Velocity accelerates until&#8230;. [Bridge]Exponential growthExponential velocity(Indeed) [Verse 1]Amass a mass(Rolling past)You know&#8230;(Watch &#8216;er grow)She&#8217;s gonna go [Bridge]Rollin&#8217; down a hill&#8230;Velocity accelerates until&#8230; [Chorus]Rollin&#8217; down a hill(Faster and faster until)Rollin&#8217; down a hill(Bigger, bigger, bigger still) [Verse 2]Increase proportional(to the cube of the radius)Oh, please! Sensational(amazing to all [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","footnotes":""},"categories":[3,3945,5,9,14,3955],"tags":[163,546,563,4082],"class_list":["post-40248","post","type-post","status-publish","format-standard","hentry","category-4d-music","category-change","category-chaos-theory","category-daniel","category-lyrics","category-megaepix-enormous","tag-climate-change","tag-mp4","tag-music-videos","tag-snowball-effect"],"_links":{"self":[{"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/40248","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/comments?post=40248"}],"version-history":[{"count":6,"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/40248\/revisions"}],"predecessor-version":[{"id":40423,"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/40248\/revisions\/40423"}],"wp:attachment":[{"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/media?parent=40248"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/categories?post=40248"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/tags?post=40248"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}