A compound disk of outside diameter 140.0 cm is made up of a uniform solid disk of radius 50.0 cm and area density 3.00 g/cm2 surrounded by a concentric ring of inner radius 50.0 cm, outer radius 70.0 cm, and area density 2.00 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.

Solution 37E Introduction We have to calculate the moment of inertia of the each section and then we can calculate the total moment of inertia by adding them. Step 1 At first let us calculate the moment of inertia of the inner disc. The moment of inertia of a thin disc is given by 2 Here, 1 3.00 g/cm is the area density and r =150 cm is the radius of the disc. Hence we have