Two wheels, X and Y, are made of the same material and have the same mass M and radius R. Wheel X is a thin circular ring (hoop) while wheel Y is a uniform solid disc. Both rotate about their central axes.
(i) Define moment of inertia and explain its physical significance in rotational motion.
(ii) For an identical angular speed, which wheel possesses greater rotational kinetic energy? Give a reason based on the distribution of mass.
(iii) If both wheels are required to store the same rotational kinetic energy, which one must rotate faster? Support your answer with an appropriate mathematical relation.