(A) Find the moment of inertia of a uniform plate shaped like a quarter of a circle of radius R, made to rotate around the square corner (with the rotation axis perpendicular to the plate). Suggestion: have the plate be in the first quadrant (that is, the square corner is the origin) and do the integral in polar coordinates. Express this both in terms of its radius and mass density, and its radius and mass.
(B) The same uniform quarter-circle plate, now made to rotate around an axis that is along one of its straight sides. This one is easier in polar coordinates, but can be done in rectangular coordinates as well. Again, express this both in terms of radius and mass density, and in terms of radius and mass.