Problem 1.114

A horizontal disc of radius \(R\) rotates with a constant angular velocity \(\omega\) about a stationary vertical axis passing through its edge. Along the circumference of the disc a particle of mass \(m\) moves with a velocity that is constant relative to the disc. At the moment when the particle is at the maximum distance from the rotation axis, the resultant of the inertial forces \(F_{\text {in }}\) acting on the particle in the reference frame fixed to the disc turns into zero. Find: (a) the acceleration \(w^{\prime}\) of the particle relative to the disc; (b) the dependence of \(F_{\text {in }}\) on the distance from the rotation axis.