Halliday, Resnick & Walker — Rotation: Problem 55

55 In Fig. 10-36a, an irregularly shaped plastic plate with uniform thickness and density (mass per unit volume) is to be rotated around an axle that is perpendicular to the plate face and through point $O$. The rotational inertia of the plate about that axle is measured with the following method. A circular disk of mass $0.500 \text{ kg}$ and radius $2.00 \text{ cm}$ is glued to the plate, with its center aligned with point $O$ (Fig. 10-36b). A string is wrapped around the edge of the disk the way a string is wrapped around a top. Then the string is pulled for $5.00 \text{ s}$. As a result, the disk and plate are rotated by a constant force of $0.400 \text{ N}$ that is applied by the string tangentially to the edge of the disk. The resulting angular speed is $114 \text{ rad/s}$. What is the rotational inertia of the plate about the axle?