{"id":9090,"date":"2023-10-03T15:28:58","date_gmt":"2023-10-03T09:58:58","guid":{"rendered":"https:\/\/acejee.com\/blog\/?p=9090"},"modified":"2024-09-30T08:10:10","modified_gmt":"2024-09-30T02:40:10","slug":"center-of-mass-of-a-uniform-i-shaped-lamina","status":"publish","type":"post","link":"https:\/\/acejee.com\/blog\/center-of-mass-of-a-uniform-i-shaped-lamina\/","title":{"rendered":"Center of Mass of a Uniform &#8216;I&#8217; Shaped Lamina"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/acejee.com\/blog\/wp-content\/uploads\/2021\/09\/Uniform_I_Shaped_Lamina-1024x576.jpg\" alt=\"Center of mass of uniform I shaped lamina\" class=\"wp-image-4506\" srcset=\"https:\/\/acejee.com\/blog\/wp-content\/uploads\/2021\/09\/Uniform_I_Shaped_Lamina-1024x576.jpg 1024w, https:\/\/acejee.com\/blog\/wp-content\/uploads\/2021\/09\/Uniform_I_Shaped_Lamina-300x169.jpg 300w, https:\/\/acejee.com\/blog\/wp-content\/uploads\/2021\/09\/Uniform_I_Shaped_Lamina-768x432.jpg 768w, https:\/\/acejee.com\/blog\/wp-content\/uploads\/2021\/09\/Uniform_I_Shaped_Lamina-1536x864.jpg 1536w, https:\/\/acejee.com\/blog\/wp-content\/uploads\/2021\/09\/Uniform_I_Shaped_Lamina-2048x1152.jpg 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Center of mass of uniform I shaped lamina<\/figcaption><\/figure>\n\n\n\n<p>Center of mass of $I$ shaped lamina (of uniform surface density $\\sigma$):<\/p>\n\n\n\n<p>$x_{CM} = \\cfrac{ab\\cfrac{a}{2}+cd\\cfrac{a}{2}+ef\\cfrac{a}{2}}{ab+cd+ef}$<br>$y_{CM} = \\cfrac{ab\\cfrac{b}{2}+cd\\cfrac{2b+c}{2}+ef\\cfrac{2b+2c+f}{2}}{ab+cd+ef}$<\/p>\n\n\n\n<p>To continue to explore center of mass of other commonly encountered shapes, <a href=\"https:\/\/acejee.com\/blog\/center-of-mass-formula-list-for-different-shapes-jee-main\/\" title=\"\">click here<\/a>&#8230; <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-two-or-more-particle-systems\" title=\"\">Two Particle System<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-two-or-more-particle-systems\" title=\"\">System of Three Particles<\/a><\/li>\n\n\n\n<li>A group of simple rigid bodies (for example a uniform $I$ shaped lamina<\/li>\n\n\n\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-a-non-uniform-rod-of-length-l\/\" title=\"\">Non uniform rod of length $L$<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-an-arc-of-a-ring\/\" title=\"\">Arc<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-a-uniform-circular-arc\/\" title=\"\">Uniform Circular arc<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-an-arc-of-a-ring\/\" title=\"\">Semicircular ring<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-semicircular-and-annular-semicircular-discs\/\" title=\"\">Semicircular disc<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-semicircular-and-annular-semicircular-discs\/\" title=\"\">Annular semicircular disc<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-a-triangle-triangular-lamina\/\" title=\"\">Triangle<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-solid-and-hollow-hemispheres\/\" title=\"\">Solid hemisphere<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-solid-and-hollow-hemispheres\/\" title=\"\">Hollow hemisphere<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-a-solid-and-a-hollow-cone\/\" title=\"\">Hollow cone<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/acejee.com\/blog\/center-of-mass-of-a-solid-and-a-hollow-cone\/\" title=\"\">Solid cone<\/a><\/li>\n<\/ul>\n\n\n\n<a href=\"https:\/\/acejee.com\/jee-main-advanced-physics-online-classes\/\" class=\"floating-button-JEE-Phy-Online-Classes-GutenbergPosts\">JEE Physics Online Classes<\/a>\n","protected":false},"excerpt":{"rendered":"<p>Here is the center of mass of an I shaped lamina along with its derivation<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ocean_post_layout":"full-width","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"on","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"off","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"off","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"","cybocfi_hide_featured_image":"yes","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"on","ocean_gallery_id":[],"footnotes":""},"categories":[1],"tags":[],"class_list":["post-9090","post","type-post","status-publish","format-standard","hentry","category-uncategorized","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/posts\/9090","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/comments?post=9090"}],"version-history":[{"count":5,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/posts\/9090\/revisions"}],"predecessor-version":[{"id":9407,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/posts\/9090\/revisions\/9407"}],"wp:attachment":[{"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/media?parent=9090"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/categories?post=9090"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/tags?post=9090"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}