Moment of Inertia: Sphere

The moment of inertia of a sphere about its central axis and a thin spherical shell are shown. For mass M = kg and radius R = cm the moment of inertia of a solid sphere is I(solid sphere) = kg m2 and the moment of inertia of a thin spherical shell is I(spherical shell) = kg m2 关于球体的转动惯量及其薄球壳的转动惯量如图所示。对于质量 M = kg 和半径 R = cm，实心球的转动惯量为 I(实心球) = kg m²，薄球壳的转动惯量为 I(薄球壳) = kg m² 中文译文中的待填/计算数值依次对应：1：m 2：R 3：i 4：i2。实际数值以上方原输入框为准。 Show development of expressions 展示表达式的推导

Moment of Inertia: Sphere

The expression for the moment of inertia of a sphere can be developed by summing the moments of infintesmally thin disks about the z axis. The moment of inertia of a thin disk is

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Sphere Details

Details about the moment of inertia of a sphere.

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Sphere Integral Details

The process involves integrating the moments of inertia of infinitesmally thin disks from the top to the bottom of the sphere. This involves polynomial form integrals.