# Formula Sphere (axis of rotation through the center) Moment of inertia    Mass    Radius

## Moment of inertia

Unit
According to $$M ~=~ I \, \alpha$$ ($$\alpha$$: angular acceleration), the moment of inertia determines how hard it is to generate a torque $$M$$ on the body. Moment of inertia $$I$$ depends on the mass distribution and on the choice of the axis of rotation. Here the moment of inertia of a homogeneous rotating sphere is calculated, whose axis of rotation passes through the center.

## Mass

Unit
Total mass of the sphere that is homogeneously distributed within the sphere. The greater the mass, the greater the moment of inertia of the sphere.