# Find moment of inertia of a uniform hollow cylinder

We know that the moment of inertia for hoop with radius R is mR2. We can divide cylinder into thin concentric hoops of thickness dR.
Density = Mass per unit volume
Density = dm / dV

where:
þ; - Density
dm - Mass of a ring or radius R
dV - Volume of a ring or radius R
Lets assume height of the cylinder is h.

we have

We can obtain moment of inertia by integrating over all these hoops

Cylinder has uniform density, where þ = constant

Volume of this cylinder is

Mass M is

since

Moment of inertia for hollow cylinder is