Question

Find the moment of inertia of a cone of total mass M, whose base

has a radius R, and that has a total height of h, about its
symmetry axis. Express your answer in terms of M, R, and h.
I=

Answer 1

The moment of inertia of a cone with mass M, base radius R, and height h around its symmetry axis is I = (3/10)MR².

Step-by-step explanation:

The question of finding the moment of inertia of a cone about its symmetry axis involves integrating the moment of inertia of infinitesimally thin disks that make up the cone. To solve this, we consider the moment of inertia of a disk with mass distribution and mass density. We integrate from the base to the tip of the cone, considering the varying radius of the disks. The formula for the moment of inertia I of a disk is I = (1/2)mR². For a cone, this becomes I = (3/10)MR² when calculating it about its symmetry axis.