A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is ______ J. ($g = 10\ \text{m/s}^2$)
Numerical value type. Enter your answer.
Answer: 30
Treat the flywheel as a uniform disc: $I = \frac12MR^2$. With no slipping, $v = \omega R$.
Energy conservation:
$$mgh = \frac12mv^2 + \frac12I\omega^2 = \frac12mv^2 + \frac14Mv^2$$
$$3\times10\times3 = \frac12(3)v^2 + \frac14(3)v^2 = \frac94v^2 \Rightarrow v^2 = 40\ \text{m}^2/\text{s}^2$$
Kinetic energy of the wheel:
$$K = \frac14Mv^2 = \frac14\times3\times40 = 30\ \text{J}$$
Solution by Sreeraj P, M.Sc Physics