A coin of mass \(m=20 \mathrm{~g}\) is placed on top of a rotating disk at a radial distance \(R=20 \mathrm{~cm}\) from the axis. The coefficient of static friction between the two disks is \(\mu_{s}=0.55\). Determine the maximum angular frequency \(\omega_{\max }\) allowed for the coin to remain at rest. Evaluate the same magnitude in the case that \(m\) was subjected to an ingoing radial force of magnitude \(F_{1}=0.05\) \(\mathrm{N}\), or in the case that it was subjected to a tangential force of magnitude \(F_{2}=0.04 \mathrm{~N}\). Discuss why \(\omega_{\max }\) in one case increases and the other decreases.