Answer:
The moment of inertia of the sphere about a parallel axis that is tangent to the surface of the sphere is [tex]I_{O} = \frac{7}{5}\cdot M\cdot R^{2}[/tex].
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:
[tex]I_{O} = I_{g} + M\cdot d^{2}[/tex] (Eq. 1)
Where:
[tex]I_{g}[/tex] - Moment of inertia of the sphere about an axis passing through center of mass, measured in kilogram-square meters.
[tex]M[/tex] - Mass of the sphere, measured in kilograms.
[tex]d[/tex] - Distance between axes, measured in meters.
If we know that [tex]I_{g} = \frac{2}{5} \cdot M\cdot R^{2}[/tex] and [tex]d = R[/tex], the moment of inertia of the sphere about a parallel axis that is tangent to the surface of the sphere is:
[tex]I_{O} = \frac{2}{5}\cdot M\cdot R^{2}+M\cdot R^{2}[/tex]
Where [tex]R[/tex] is the radius of the sphere, measured in meters.
[tex]I_{O} = \frac{7}{5}\cdot M\cdot R^{2}[/tex]
The moment of inertia of the sphere about a parallel axis that is tangent to the surface of the sphere is [tex]I_{O} = \frac{7}{5}\cdot M\cdot R^{2}[/tex].
