Two different flywheels, Flywheel A and Flywheel B, are mounted on separate, frictionless horizontal axles so that their centers of mass remain fixed. Each flywheel is spun up to the same constant angular speed ω.
• Flywheel A is a thin hoop of mass M and radius R.
• Flywheel B is a solid uniform disk of the same mass M and the same radius R.
Answer the following questions, neglecting all external torques once the flywheels have reached their final speed.
(a) Without performing a numerical calculation, state which flywheel has the greater rotational kinetic energy at speed ω. Provide a brief justification based on how mass is distributed in each flywheel.
(b) Derive an algebraic expression for the ratio KBKA of the rotational kinetic energies of flywheels A and B in terms of known constants.
(c) Suppose both flywheels are simultaneously brought to rest by identical braking torques applied to their axles. Which flywheel will take the longer time to stop? Justify your answer quantitatively using the result from part (b).
(d) Discuss one practical advantage and one disadvantage of using a thin-hoop flywheel instead of a solid-disk flywheel for energy storage applications.