Consider a solid sphere, of radius R, spinning about the z-axis. The mass densit
ID: 3643822 • 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=rho0 e(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 alpha. Perform the Montearlo 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 dphi d theta, can be reduced to dv = 2pir2 sin phi dr dphi.Explanation / Answer
its too long