Question #42556

A refrigerator is powered entirely by a decelerating flywheel-generator system. The flywheel has a moment of inertia $I = 2 \text{ kg m}^2$ and an initial angular velocity $\omega_0 = 10 \text{ rad s}^{-1}$. The generator experiences a magnetic damping torque due to eddy currents given by $\tau = -k\omega$, where $k = 0.5 \text{ N m s rad}^{-1}$ and $\omega$ is the instantaneous angular velocity. The mechanical power dissipated by this damping is converted entirely into electrical power to drive the refrigerator. The coefficient of performance (COP) of the refrigerator varies with the instantaneous angular velocity and is given by $\text{COP} = c\omega$, where $c = 0.03 \text{ s rad}^{-1}$. What is the total heat extracted from the cold reservoir as the flywheel comes to a complete stop?