# Formula Hollow cylinder - rotation around the symmetry axis Moment of inertia    Mass    Outer radius    Inner radius

## Moment of inertia

Unit
According to $$M ~=~ I \, \alpha$$ ($$\alpha$$: angular acceleration), the moment of inertia determines how hard it is to exert 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 we calculate the moment of inertia of a homogeneously hollow cylinder whose axis of rotation passes through the center, perpendicular to the diameter, i.e. through the axis of symmetry of the cylinder.

## Mass

Unit
Total mass of the cylinder homogeneously distributed on the shell of the hollow cylinder. The greater the mass, the greater the moment of inertia.

The "e" in the index stands for "external". The hollow cylinder can have a certain thickness. Here $$r_{\text e}$$ indicates the distance to the outer wall of the cylinder.
The "i" in the index stands for "internal". Here $$r_{\text i}$$ indicates the distance to the inner wall of the cylinder.