A small solid sphere, with radius 0.25 cm and mass 0.41 g rolls without slipping on the inside of a large fixed hemisphere with radius 16 cm and a vertical axis of symmetry. The sphere starts at the top from rest.
1. What is its kinetic energy at the bottom?
2. What fraction of its kinetic energy at the bottom is related with rotation about an axis through its center of mass?
3. What is the magnitude of the normal force on the hemisphere from the sphere when the sphere reaches the bottom?