# Moment of Inertia of Compound Disk

## Homework Statement

A compound disk of outside diameter 152 cm is made up of a uniform solid disk of radius 41.0 cm and area density 3.30 g/cm2 surrounded by a concentric ring of inner radius 41.0 cm , outer radius 76.0 cm , and area density 2.10 g/cm2 .

Find the moment of inertia of this object about an axis perpendicular to the plane of the object and passing through its center (in kg*m2).

## Homework Equations

Moment of inertia of solid cylinder (a thin cylinder is a disk) = I = .5mr2

## The Attempt at a Solution

This object is basically one inner disk with mass mi surrounded by an outer disk with mass mo. Finding the moment of inertia of each of these and adding them together should give the solution.

mi in kg = (area * density)/1000 = (pi*412 *3.3)/1000 = 17.427

mo in kg = [(area - inner area) * density]/1000 = [(pi*712 - pi*412) * 2.1]/1000 = 22.1671

Using the moment of inertia for solid cylinder and adding yields:
.5mi*.412+.5mo*.762= 7.87 kg*m2

The answer given is 11.5 kg*m2. What am I doing wrong?

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