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## 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/cm

^{2}surrounded by a concentric ring of inner radius 41.0 cm , outer radius 76.0 cm , and area density 2.10 g/cm

^{2}.

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*m

^{2}).

## Homework Equations

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

^{2}

## The Attempt at a Solution

This object is basically one inner disk with mass m

_{i}surrounded by an outer disk with mass m

_{o}. Finding the moment of inertia of each of these and adding them together should give the solution.

m

_{i}in kg = (area * density)/1000 = (pi*41

^{2}*3.3)/1000 = 17.427

m

_{o}in kg = [(area - inner area) * density]/1000 = [(pi*71

^{2}- pi*41

^{2}) * 2.1]/1000 = 22.1671

Using the moment of inertia for solid cylinder and adding yields:

.5m

_{i}*.41

^{2}+.5m

_{o}*.76

^{2}= 7.87 kg*m

^{2}

The answer given is 11.5 kg*m

^{2}. What am I doing wrong?

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