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# What is the moment of inertia of a sphere?

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The moment of inertia of a sphere is I = 2/5 MR^2 for a solid sphere and I = 2/3 MR^2 for a thin spherical shell. This moment of inertia can be derived from the moment of inertia of a thin disk by summing the moments of inertia of a series of infinitely thin disks throughout the volume of the sphere.

## Keep Learning

The moment of inertia of an object is equivalent to its rotational inertia, or how likely it is to resist a change in velocity in rotational directions. In rotational dynamics problems, the rotational inertia takes the same basic position that mass does in linear dynamics problems. To convert it to a form that can be used in these types of mathematical problems, the moment of inertia can be considered as some proportion of the radius of the object multiplied by its mass.

The most basic moment of inertia is that for a point mass, which is I = MR^2, and all other moments of inertia can be calculated based on this equation. Although the moment of inertia of a sphere can be determined using integral calculus, most basic three-dimensional shapes have known moments of inertia that can be referenced from published lists.

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## Related Questions

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The moment of inertia of a solid cylinder is equal to one half of the mass multiplied by the square of the radius. This equation should be used to find the cylinder's moment of inertia with respect to the z-axis, or the plane parallel to the cylinder's height.

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Calculating the moment of inertia for a rod requires you to know the mass, length and location of the rotational axis. An estimation may be required with regards to the position of this axis.

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As explained by Hyperphysics, angular momentum is calculated by finding the product of the moment of inertia and the angular velocity of a rotating body or system. The moment of inertia with respect to an axis is the product of the mass times the distance from the axis squared, and angular velocity is the rate of change of angular displacement.