Chapter 5.4, Problem 2P

As needed, use a computer to plot graphs of figures and to check values of integrals

Using polar coordinates:

1. Show that the equation of the circle sketched is $r=2a\text{ cos}\theta$. Hint: Use the right triangle OP Q.
2. By integration, find the area of the disk $r\le 2a\text{ cos}\theta$.
3. Find the centroid of the area of the first quadrant half disk
4. Find the moments of inertia of the disk about each of the three coordinate axes, assuming constant area density
5. Find the length and the centroid of the semicircular arc in the first quadrant.
6. Find the center of mass and the moments of inertia of the disk if the density is r.
7. Find the area common to the disk sketched and the disk $r\le a$.