{"id":1906,"date":"2024-07-30T09:22:05","date_gmt":"2024-07-30T09:22:05","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=1906"},"modified":"2024-07-30T09:22:06","modified_gmt":"2024-07-30T09:22:06","slug":"centroid-of-semicircular-section-of-a-disc","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/07\/30\/centroid-of-semicircular-section-of-a-disc\/","title":{"rendered":"Centroid of Semicircular-Section of a Disc"},"content":{"rendered":"\n<p id=\"para-043\">Considering a semicircle of radius\u00a0<em>R<\/em>\u00a0as shown in\u00a0Figure 11.10.\u00a0Due to symmetry centroid must lie on\u00a0<em>y<\/em>-axis. Let its distance from the\u00a0<em>x<\/em>-axis be\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"10\" height=\"15\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/ybar.png\" alt=\"equation\">. To find\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"10\" height=\"15\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/ybar.png\" alt=\"equation\">, consider an element at a distance\u00a0<em>r<\/em>\u00a0from the centre\u00a0<em>O<\/em>\u00a0of the semicircle, radial width\u00a0<em>dr,<\/em>\u00a0and bound by radii at\u00a0<em>\u03b8<\/em>\u00a0and\u00a0<em>\u03b8 + d\u03b8<\/em>.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page280a.png\" alt=\"Figure 11.10\"\/><\/figure>\n\n\n\n<p id=\"para-049\"><strong>Figure 11.10<\/strong>&nbsp;Centroid of Circular Section of a Disc<\/p>\n\n\n\n<p id=\"para-044\">Area of the element =&nbsp;<em>rd\u03b8 dr<\/em>.<\/p>\n\n\n\n<p id=\"para-045\">Its moment about&nbsp;<em>x<\/em>-axis is given by,<\/p>\n\n\n\n<p id=\"para-046\">&nbsp;<\/p>\n\n\n\n<p><em>rd\u03b8<\/em>&nbsp;\u00d7&nbsp;<em>dr<\/em>&nbsp;\u00d7&nbsp;<em>r<\/em>&nbsp;sin&nbsp;<em>\u03b8<\/em>&nbsp;=&nbsp;<em>r<\/em><sup>2<\/sup>&nbsp;sin&nbsp;<em>\u03b8 dr d\u03b8<\/em><\/p>\n\n\n\n<p id=\"para-047\">&nbsp;<\/p>\n\n\n\n<p id=\"para-048\">Total moment of area about&nbsp;<em>x<\/em>-axis,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page280b.png\" alt=\"equation\"\/><\/figure>\n\n\n\n<p id=\"para-050\">Thus, the centroid lies on\u00a0<em>y<\/em>-axis at a distance of\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"20\" height=\"33\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page280c.png\" alt=\"equation\">\u00a0from the diametric axis.<\/p>\n\n\n\n<p id=\"para-043\">Considering a semicircle of radius\u00a0<em>R<\/em>\u00a0as shown in\u00a0Figure 11.10.\u00a0Due to symmetry centroid must lie on\u00a0<em>y<\/em>-axis. Let its distance from the\u00a0<em>x<\/em>-axis be\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"10\" height=\"15\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/ybar.png\" alt=\"equation\">. To find\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"10\" height=\"15\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/ybar.png\" alt=\"equation\">, consider an element at a distance\u00a0<em>r<\/em>\u00a0from the centre\u00a0<em>O<\/em>\u00a0of the semicircle, radial width\u00a0<em>dr,<\/em>\u00a0and bound by radii at\u00a0<em>\u03b8<\/em>\u00a0and\u00a0<em>\u03b8 + d\u03b8<\/em>.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page280a.png\" alt=\"Figure 11.10\"\/><\/figure>\n\n\n\n<p id=\"para-049\"><strong>Figure 11.10<\/strong>&nbsp;Centroid of Circular Section of a Disc<\/p>\n\n\n\n<p id=\"para-044\">Area of the element =&nbsp;<em>rd\u03b8 dr<\/em>.<\/p>\n\n\n\n<p id=\"para-045\">Its moment about&nbsp;<em>x<\/em>-axis is given by,<\/p>\n\n\n\n<p id=\"para-046\">&nbsp;<\/p>\n\n\n\n<p><em>rd\u03b8<\/em>&nbsp;\u00d7&nbsp;<em>dr<\/em>&nbsp;\u00d7&nbsp;<em>r<\/em>&nbsp;sin&nbsp;<em>\u03b8<\/em>&nbsp;=&nbsp;<em>r<\/em><sup>2<\/sup>&nbsp;sin&nbsp;<em>\u03b8 dr d\u03b8<\/em><\/p>\n\n\n\n<p id=\"para-047\">&nbsp;<\/p>\n\n\n\n<p id=\"para-048\">Total moment of area about&nbsp;<em>x<\/em>-axis,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page280b.png\" alt=\"equation\"\/><\/figure>\n\n\n\n<p id=\"para-050\">Thus, the centroid lies on&nbsp;<em>y<\/em>-axis at a distance of&nbsp;<img loading=\"lazy\" decoding=\"async\" alt=\"equation\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page280c.png\" width=\"20\" height=\"33\">&nbsp;from the diametric axis.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Considering a semicircle of radius\u00a0R\u00a0as shown in\u00a0Figure 11.10.\u00a0Due to symmetry centroid must lie on\u00a0y-axis. Let its distance from the\u00a0x-axis be\u00a0. To find\u00a0, consider an element at a distance\u00a0r\u00a0from the centre\u00a0O\u00a0of the semicircle, radial width\u00a0dr,\u00a0and bound by radii at\u00a0\u03b8\u00a0and\u00a0\u03b8 + d\u03b8. Figure 11.10&nbsp;Centroid of Circular Section of a Disc Area of the element =&nbsp;rd\u03b8 dr. Its [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1907,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[343],"tags":[],"class_list":["post-1906","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-centroid-and-moment-of-inertia"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/07\/download-7-1.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1906","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=1906"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1906\/revisions"}],"predecessor-version":[{"id":1908,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1906\/revisions\/1908"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/1907"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=1906"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=1906"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=1906"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}