9.3 Polar coordinates
Philosopher and mathematician René Descartes originated the idea of describing plane geometry using (x,y) coordinates measured from a pair of perpendicular coordinate axes. These rectangular coordinates are known as Cartesian coordinates, in his honor.
As a logical extension of Descartes' idea, one can find different ways of defining coordinates on the plane, such as the polar coordinates in figure c. In polar coordinates, the differential of area, figure d can be written as da=R dRd φ. The idea is that since dR and d φ are infinitesimally small, the shaded area in the figure is very nearly a rectangle, measuring dR is one dimension and Rd φ in the other. (The latter follows from the definition of radian measure.)
◊ A disk has mass M and radius b. Find its moment of inertia for rotation about the axis passing perpendicularly through its center.