Part A Two spherical shells have their mass uniformly distrubuted over the spher
ID: 1902815 • Letter: P
Question
Part A Two spherical shells have their mass uniformly distrubuted over the spherical surface. One of the shells has a diameter of 2 meters and a mass of 1 kilogram. The other shell has a diameter of 1 meter. What must the mass m of the 1-meter shell be for both shells to have the same moment of inertia about their centers of mass? Part B Consider the moment of inertia of a solid uniform disk, versus that of a solid sphere, about their respective centers of mass. Assume that they both have the same mass and outer radius, that they have uniform mass distributions, and that the disk is rotated about an axis perpendicular to its face. What is the relation between the moment of inertia of the disk I_disk and that of the sphere I_sphere?Explanation / Answer
spherical shell : I = 2/3 MR^2. for first sphere I = 2/3 *1*1^2 = 2/3. for sphere 2, 2/3 = 2/3 M (1/2)^2 1/4 M = 1 M = 4 kilograms b) A solid disk has I = 1/2 Mr^2 and a sphere 2/5 Mr^2. Thus the disk has 1.25 as more inertia as the sphere