The small particle of mass m and its restraining cord are spinning with an angular veloc...

The small particle of mass m and its restraining cord are spinning with an angular velocity ω on the horizontal surface of a smooth disk, shown in section. As the force F is slightly relaxed, r increases and ω changes. Determine the rate of change ω of with respect to r and show that the work done by F during a movement dr equals the change in kinetic energy of the particle.