Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_180

3/180 The small particle of mass \( m \) and its restraining cord are spinning with an angular velocity \( \omega \) on the horizontal surface of a smooth disk, shown in section. As the force \( F \) is slightly relaxed, \( r \) increases and \( \omega \) changes. Determine the rate of change of \( \omega \) 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.