{"id":17907,"date":"2022-12-03T17:45:15","date_gmt":"2022-12-03T22:45:15","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?page_id=17907"},"modified":"2024-10-05T18:09:20","modified_gmt":"2024-10-05T22:09:20","slug":"motion-on-a-curvy-track","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/motion-on-a-curvy-track\/","title":{"rendered":"Motion on a curvy track"},"content":{"rendered":"<p>BACKGROUND<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7652 aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2020\/06\/path-scaled-e1591548197809-271x300.jpg\" alt=\"\" width=\"241\" height=\"267\" \/><\/p>\n<p>The path kinematics description has taught us the following things:<\/p>\n<ul>\n<li style=\"list-style-type: none\">\n<ul style=\"list-style-type: circle\">\n<li style=\"list-style-type: none\">\n<ul style=\"list-style-type: square\">\n<li>Velocity is always TANGENT to the path.<\/li>\n<li>Acceleration, in general, has BOTH tangential and normal components.<\/li>\n<li>The normal component of acceleration always points INWARD to the path.<\/li>\n<li>The tangential component direction depends on how the point P is changing in speed. If the speed is INCREASING, angle \u03b8 between the velocity and acceleration vectors is in the range of: \u00a00 \u2264\u00a0\u03b8&lt; 90\u00b0; that is, the tangential component points forward of the motion.<\/li>\n<li>If the speed is DECREASING, angle \u03b8 between the velocity and acceleration vectors is in the range of: \u00a090\u00b0 &lt; \u03b8 \u2264 180\u00b0; that is, the tangential component points rearward of the motion.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>Shown below is an animation made from a simulation of an object moving along on a curvy path. The speed of the object goes through cycles of increasing and decreasing speed. The <span style=\"color: #0000ff\"><em><strong>velocity<\/strong><\/em><\/span> and <span style=\"color: #ff0000\"><em><strong>acceleration<\/strong><\/em><\/span> vectors for the object are shown in <span style=\"color: #0000ff\"><em><strong>blue<\/strong><\/em><\/span> and <span style=\"color: #ff0000\"><em><strong>red<\/strong><\/em><\/span>, respectively. Can you make the above observations on the motion shown below of this object?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2023\/01\/track.gif\" width=\"520\" height=\"403\" \/><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>BACKGROUND The path kinematics description has taught us the following things: Velocity is always TANGENT to the path. Acceleration, in general, has BOTH tangential and normal components. The normal component of acceleration always points INWARD to the path. The tangential component direction depends on how the point P is changing in speed. If the speed &hellip; <a href=\"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/motion-on-a-curvy-track\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Motion on a curvy track<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":14,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-17907","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/17907","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/comments?post=17907"}],"version-history":[{"count":4,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/17907\/revisions"}],"predecessor-version":[{"id":18025,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/17907\/revisions\/18025"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/14"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/media?parent=17907"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}