A cylindrical bucket partially filled with dry sand spins steadily about its vertical symmetry axis on a low-friction bearing. As the bucket rotates, a small hatch at the bottom is opened so that sand trickles vertically downward out of the bucket into a container that is fixed to the Earth beneath it. Neglect air resistance.
(a) Qualitatively describe how, if at all, the rotation rate of the bucket changes as sand leaves. Provide a clear explanation based on external interactions.
(b) Is the angular momentum of the bucket–remaining-sand system conserved while the sand is escaping? Justify your answer.
(c) Identify a larger system for which angular momentum is conserved during the sand-release process, and explain why conservation applies to that choice of system.