Consider a solid hemisphere of radius R. The density is constant, and the mass of the hemi- sphere is equal to m. a) Calculate the moment of inertia of the hemisphere about its symmetry axis. b) Compute the position of the centre-of-mass of the hemisphere. c) What are the principal axes of the system? Is there an ambiguity in defining them?

Consider a solid hemisphere of radius R. The density is constant, and the mass of the hemi- sphere is equal to m. a) Calculate the moment of inertia of the hemisphere about its symmetry axis. b) Compute the position of the centre-of-mass of the hemisphere. c) What are the principal axes of the system? Is there an ambiguity in defining them?