Q:
# What Is the Moment of Inertia of a Sphere?

**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.

Learn more about Motion & Mechanics-
Q:
## Why Does a Ring Have a Higher Moment of Inertia Than a Solid Disc of Equal Mass and Outer Radius?

A: Northwestern University explains that a ring has a higher moment of inertia than a solid disk of equal mass and outer radius because it has less mass at it... Full Answer >Filed Under: -
Q:
## What Is the Parallel Axis Theorem?

A: The parallel axis theorem states that the "moment of inertia of any object about an axis through its center of mass is the minimum moment of inertia for an... Full Answer >Filed Under: -
Q:
## How Do You Calculate the Moment of Inertia of a Rod?

A: 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 r... Full Answer >Filed Under: -
Q:
## What Does the Law of Inertia Apply To?

A: The law of inertia is a fundamental physics principle used to describe how an object behaves in motion or at rest, particularly when forces are applied to ... Full Answer >Filed Under: