Mass of a thin shell, moments and center of mass.

- 1.
__Mass:__

- 2.
__First moments about the coordinate planes:__

- 3.
__Coordinates of the center of mass:__

- 4.
__Moments of inertia:__

where*L*is any line in the space and*r*is the distance from the point (*x*,*y*,*z*) to the line*L*.- 5.
__Radius of gyration about the line__*L*:

- 1.
- The mass: by the same way as in Example 8.27, we have:

- 2.
- First moments:
- about the
*xy*-plane:

- about the
*yz*-plane:

- about the
*xz*-plane:

The fact that this last is equal to the previous one result could be foreseen, as the settings are totally symmetric in*x*and*y*.

- about the
- 3.
- The coordinates of the center of mass: