Consider a solid sphere, of radius R, spinning about the z-axis. The mass densit
ID: 3643823 • Letter: C
Question
Consider a solid sphere, of radius R, spinning about the z-axis. The mass density of the sphere is given by rho = rho0e(r-0.5R)2 / 4R2. Show that the moment of inertia of the solid cylinder about the spinning axis is of the form I=alphaMR2 and use Monte-Carlo to find the numerical value (with uncertainties) of a. Perform the Mont-Carlo integration for a sample size of 100 000 000. This will take a long time so do not wait till the last minute. Note that for spherical coordinates r is not =r sin phi where phi is the angle r makes with the z-axis. Also note that for spherical coordinates, with no dependence on the angle in the xy-plane (the azimuthal angle), general infinitesimal volume element dV= r2 sin phi dr d phi d theta, can be reduced to dV=2pi r2 sin phi dr dphi.Explanation / Answer
its too long