Three uniform objects, each of mass 2.0kg and radius 0.20m, rotate about their central axes.
• Object X is a thin hoop spinning at 10rads−1.
• Object Y is a solid cylinder spinning at 14rads−1.
• Object Z is a solid sphere spinning at 19rads−1.
Assume each object’s mass is uniformly distributed according to its stated shape. Use reasoning based on moment of inertia and angular speed to compare their rotational kinetic energies.
(a) Rank the three objects from greatest to least rotational kinetic energy. If any are equal, state so explicitly.
(b) Provide a qualitative justification for your ranking. In your explanation, refer to the relative distribution of mass and the given angular speeds rather than performing an explicit numerical calculation.