Consider a solid cone with uniform density \rho, height h, and circular base with radius r (mass hr ). let the vertex of the cone be the origin of the body frame. by symmetry, choose basis vectors \mathbf{e}_{i} for the body frame such that the inertia tensor i_{ij} is diagonal.
(a) will this rigid body with this body origin be an asymmetric top, a symmetric top, or a spherical top? calculate the inertia tensor in this basis.
(b) how will the inertia tensor change if we change the body origin to the center of mass while the basis vectors remain fixed? hint: steiner’s parallel axis theorem might with this part of the problem.