Question

A uniform solid sphere has a mass M and radius R. The moment of inertia about an axis through its center is 25MR225MR2. What is the moment of inertia of the sphere about a parallel axis that is tangent to the surface of the sphere

Answer 1

The moment of inertia of the sphere about a parallel axis that is tangent to the surface of the sphere is
`I_(O) = (7)/(5)\cdot M\cdot R^(2)`.

Step-by-step explanation:

To know the moment of inertia of the sphere about a parallel axis that is tangent to the surface of the sphere, we must use the Theorem of Parallel Axis, which states that:

`I_(O) = I_(g) + M\cdot d^(2)` (Eq. 1)

Where:

`I_(g)` - Moment of inertia of the sphere about an axis passing through center of mass, measured in kilogram-square meters.

`M` - Mass of the sphere, measured in kilograms.

`d` - Distance between axes, measured in meters.

If we know that
`I_(g) = (2)/(5) \cdot M\cdot R^(2)` and
`d = R`, the moment of inertia of the sphere about a parallel axis that is tangent to the surface of the sphere is:

`I_(O) = (2)/(5)\cdot M\cdot R^(2)+M\cdot R^(2)`

Where
`R` is the radius of the sphere, measured in meters.

`I_(O) = (7)/(5)\cdot M\cdot R^(2)`

The moment of inertia of the sphere about a parallel axis that is tangent to the surface of the sphere is
`I_(O) = (7)/(5)\cdot M\cdot R^(2)`.