## Essential University Physics: Volume 1 (4th Edition)

a) $M=\frac{2\pi\rho_0wR^2}{3}$ b) $I=\frac{3MR^2}{5}$
a) We know that the mass is equal to the integral of the quantity of the density times the volume. Thus, we find: $M = 2\int_0^R \frac{\rho_0r}{R}\pi r^2 w dr$ $M=\frac{2\pi\rho_0wR^2}{3}$ b) Using the definition of moment of inertia, we find: $I=\frac{3MR^2}{5}$