Problems

01

Center of mass, moment of inertia

Consider the region of the $xy$-plane that is bounded above by $y=1-x^2$ and bounded below by the $x$-axis. Suppose the mass density is $\rho (x,y)=y$. Find:

• (a) the center of mass of this region,
• (b) the moment of inertia of this region, supposing it is rotated about the $y$-axis.