{"id":26401,"date":"2025-06-19T13:44:54","date_gmt":"2025-06-19T13:44:54","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=26401"},"modified":"2025-06-19T13:45:07","modified_gmt":"2025-06-19T13:45:07","slug":"which-of-the-following-objects-has-the-largest-moment-of-inertia-assuming-they-all-have-the-same-mass-and-the-same-radius","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-of-the-following-objects-has-the-largest-moment-of-inertia-assuming-they-all-have-the-same-mass-and-the-same-radius\/","title":{"rendered":"Which of the following objects has the largest moment of inertia, assuming they all have the same mass and the same radius"},"content":{"rendered":"\n

Which of the following objects has the largest moment of inertia, assuming they all have the same mass and the same radius? solid sphere solid disk circular hoop a solid cylinder<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer: Circular hoop<\/strong><\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

The moment of inertia<\/strong> (denoted I<\/em>) measures an object’s resistance to rotational acceleration about an axis. It depends on both the mass<\/strong> of the object and how that mass is distributed<\/strong> relative to the axis of rotation. When comparing objects with the same mass<\/strong> and same radius<\/strong>, the distribution of mass becomes the key factor.<\/p>\n\n\n\n

Here are the standard formulas for the moment of inertia of each object rotating about its central axis:<\/p>\n\n\n\n

    \n
  1. Solid Sphere<\/strong>:
    I=25MR2I = \\frac{2}{5}MR^2I=52\u200bMR2<\/li>\n\n\n\n
  2. Solid Disk<\/strong>:
    I=12MR2I = \\frac{1}{2}MR^2I=21\u200bMR2<\/li>\n\n\n\n
  3. Circular Hoop<\/strong> (thin ring):
    I=MR2I = MR^2I=MR2<\/li>\n\n\n\n
  4. Solid Cylinder<\/strong>:
    I=12MR2I = \\frac{1}{2}MR^2I=21\u200bMR2<\/li>\n<\/ol>\n\n\n\n

    Where:<\/p>\n\n\n\n

      \n
    • M<\/em> is the mass of the object<\/li>\n\n\n\n
    • R<\/em> is the radius of the object<\/li>\n<\/ul>\n\n\n\n

      As seen from the formulas, the circular hoop<\/strong> has the largest moment of inertia, because all of its mass is located at the maximum possible distance from the axis<\/strong> (at radius R). This means the entire mass contributes maximally to the rotational inertia.<\/p>\n\n\n\n

      By contrast, the solid sphere<\/strong> has the smallest moment of inertia among the listed objects. In the solid sphere, most of the mass is concentrated closer to the center, which lowers the moment of inertia.<\/p>\n\n\n\n

      Thus, even if all the objects have equal mass and radius, the circular hoop resists rotational acceleration the most<\/strong> due to its greater moment of inertia.<\/p>\n\n\n\n

      Summary of Values:<\/h3>\n\n\n\n
        \n
      • Solid Sphere: 25MR2=0.4MR2\\frac{2}{5}MR^2 = 0.4MR^252\u200bMR2=0.4MR2<\/li>\n\n\n\n
      • Solid Disk: 12MR2=0.5MR2\\frac{1}{2}MR^2 = 0.5MR^221\u200bMR2=0.5MR2<\/li>\n\n\n\n
      • Solid Cylinder: 12MR2=0.5MR2\\frac{1}{2}MR^2 = 0.5MR^221\u200bMR2=0.5MR2<\/li>\n\n\n\n
      • Circular Hoop: 1MR2=1MR21MR^2 = 1MR^21MR2=1MR2<\/li>\n<\/ul>\n\n\n\n

        Conclusion<\/strong>: The circular hoop<\/strong> has the largest moment of inertia<\/strong>.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Which of the following objects has the largest moment of inertia, assuming they all have the same mass and the same radius? solid sphere solid disk circular hoop a solid cylinder The Correct Answer and Explanation is: Correct Answer: Circular hoop Explanation: The moment of inertia (denoted I) measures an object’s resistance to rotational acceleration […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-26401","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26401","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=26401"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26401\/revisions"}],"predecessor-version":[{"id":26404,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26401\/revisions\/26404"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26401"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26401"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}