Final answer:
The question involves finding the area and the moment of inertia for a disk in physics. The area is found by integrating the formula for the area of a circle, while the moment of inertia formulas depend on whether the disk is alone or part of a compound object and could involve the parallel-axis theorem.
Step-by-step explanation:
The question seems to be pertaining to the calculation of the area of a disk and the moment of inertia in the context of physics. We calculate the full area of the disk by integrating from r = 0 to r = R to add up all the thin rings within that radius range, using the formula A = πr². For the moment of inertia of a solid disk about an axis through its center, the formula is I = MR², where M is the mass of the disk and R is its radius.
In a more complex scenario, involving a compound object like a disk at the end of a rod, one must use the parallel-axis theorem. The theorem states Iparallel-axis = Icenter of mass + md², where d is the distance from the new axis to the original axis through the center of mass, and Icenter of mass is the moment of inertia about the center of mass. For the disk mentioned in this problem, this would be computed as Iparallel-axis = maR² + ma(L + R)², where m represents mass and a is a constant.