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

Formula: Sphere (axis of rotation through the center)
Rotating sphere with an axis of rotation through the center point

Moment of inertia

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.


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.


Radius of the sphere. If the radius is doubled, the moment of inertia is quadrupled.

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