{"id":1860,"date":"2024-07-30T08:26:35","date_gmt":"2024-07-30T08:26:35","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=1860"},"modified":"2024-07-30T08:26:35","modified_gmt":"2024-07-30T08:26:35","slug":"centre-of-gravity-centre-of-mass-and-centroid-of-an-irregular-shape","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/07\/30\/centre-of-gravity-centre-of-mass-and-centroid-of-an-irregular-shape\/","title":{"rendered":"Centre of Gravity, Centre of Mass, and Centroid of an Irregular Shape"},"content":{"rendered":"\n<p id=\"para-003\">In\u00a0Figure 11.1,\u00a0an irregular shape is shown for which we want to calculate the centre of gravity, centre of mass, and centroid. Here, our purpose is to differentiate the concepts of these three different terms. It is assumed that the irregular shape, as shown in\u00a0Figure 11.1,\u00a0is of uniform thickness, density, and subjected to uniform gravitational field.<\/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\/page276.png\" alt=\"Figure 11.1\"\/><\/figure>\n\n\n\n<p id=\"para-004\"><strong>Figure 11.1<\/strong>&nbsp;Centre of Gravity, Centre of Mass, and Centroid<\/p>\n\n\n\n<p id=\"para-005\">Let&nbsp;<em>W<sub>i<\/sub><\/em>&nbsp;be the weight of an element in the given body.&nbsp;<em>W<\/em>&nbsp;be the total weight of the body. Let the coordinates of the element be&nbsp;<em>X<sub>i<\/sub>, Y<sub>i<\/sub>, Z<sub>i<\/sub><\/em>&nbsp;and that of centroid&nbsp;<em>G<\/em>&nbsp;be&nbsp;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/xbar.png\" alt=\"equation\" width=\"13\" height=\"17\">,&nbsp;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/ybar.png\" alt=\"equation\" width=\"10\" height=\"15\">, and&nbsp;<img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/zbar.png\" alt=\"Equation\" width=\"13\">. Since&nbsp;<em>W<\/em>&nbsp;is the resultant of&nbsp;<em>W<sub>i<\/sub><\/em>&nbsp;forces. Therefore,<\/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\/page276a.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-006\">Here,&nbsp;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/xbar.png\" alt=\"equation\" width=\"13\" height=\"17\">,&nbsp;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/ybar.png\" alt=\"equation\" width=\"10\" height=\"15\">, and&nbsp;<img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/zbar.png\" alt=\"Equation\" width=\"13\">&nbsp;are coordinates of centre of gravity,&nbsp;<em>G<\/em>. The resultant gravitational force acts through the point&nbsp;<em>G<\/em>.<\/p>\n\n\n\n<p id=\"para-007\">If gravitational field be uniform, the gravitational acceleration (<em>g<\/em>) will be same for all the points. Therefore, in of&nbsp;<em>W<sub>i<\/sub><\/em>, we can put&nbsp;<em>M<sub>i<\/sub>g<\/em>&nbsp;and the centre of mass can be expressed as<\/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\/page276b.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-008\">Here,&nbsp;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/xbar.png\" alt=\"equation\" width=\"13\" height=\"17\">,&nbsp;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/ybar.png\" alt=\"equation\" width=\"10\" height=\"15\">, and&nbsp;<img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/zbar.png\" alt=\"Equation\" width=\"13\">&nbsp;are coordinates of centre of mass,&nbsp;<em>G<\/em>. The resultant mass of the body is concentrated at the point,&nbsp;<em>G<\/em>.<\/p>\n\n\n\n<p id=\"para-009\">If the density of mass (<em>\u03b3<\/em>) and the thickness of the body (<em>t<\/em>) is uniform, the mass&nbsp;<em>M<sub>i<\/sub><\/em>&nbsp;can be represented as&nbsp;<em>\u03b3<\/em>&nbsp;\u00d7&nbsp;<em>A<sub>i<\/sub><\/em>&nbsp;\u00d7&nbsp;<em>t<\/em>. The centroid can be expressed as<\/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\/page277.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-010\">Here,&nbsp;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/xbar.png\" alt=\"equation\" width=\"13\" height=\"17\">,&nbsp;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/ybar.png\" alt=\"equation\" width=\"10\" height=\"15\">,&nbsp;<img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/zbar.png\" alt=\"Equation\" width=\"13\">&nbsp;and are coordinates of centroid,&nbsp;<em>G<\/em>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In\u00a0Figure 11.1,\u00a0an irregular shape is shown for which we want to calculate the centre of gravity, centre of mass, and centroid. Here, our purpose is to differentiate the concepts of these three different terms. It is assumed that the irregular shape, as shown in\u00a0Figure 11.1,\u00a0is of uniform thickness, density, and subjected to uniform gravitational field. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1861,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[343],"tags":[],"class_list":["post-1860","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-3.jpeg","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1860","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=1860"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1860\/revisions"}],"predecessor-version":[{"id":1862,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1860\/revisions\/1862"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/1861"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=1860"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=1860"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=1860"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}