# Moment of inertia

1. Apr 5, 2004

### Antares

I need help finding the moment of inertia for a hollow cylinder with a closed bottom (like a glass of water). My strategy is to add the moments of inertia of the cylinder and the disk but I only have the total mass of the whole object. Is there a way to find the mass of each part or is there another approach to this problem?

2. Apr 5, 2004

### Kurdt

Staff Emeritus
Just sum the mass as an integral as follows.

$$I=\int r^2 dm$$

3. Apr 6, 2004

### Staff: Mentor

If the thickness is uniform then you can find the masses of the cylinder and bottom by comparing their relative areas. The surface area of the cylinder is Lx2πr; the area of the bottom is πr2.