**Moment of Inertia**

The angular momentum in a moving coordinate system is given by:

where I is the moment of inertia with respect to a central axis, which is given by:

or, in the continuous case:

Further holds:

Steinerâ€™s theorem is: if axis C axis D.

Object | Moment of Inertia | Object | Moment of Inertia |
---|---|---|---|

Cavern cylinder | Massive cylinder | ||

Disc, axis in plane disc through m | Halter | ||

Cavern sphere | Massive sphere | ||

Bar, axis through c.o.m. | Bar, axis through end | ||

Rectangle, axis plane thr. c.o.m. | Rectangle, axis b thr. m |

**Principal axes**

Each rigid body has (at least) 3 principal axes which stand to each other. For a principal axis holds:

The following holds: with

**Time dependence**

For torque of force holds:

The torque is defined by: