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.
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.