Randall D. Knight — Dynamics II: Motion in a Plane: Problem 69

The 10 mg bead in FIGURE CP8.69 is free to slide on a frictionless wire loop. The loop rotates about a vertical axis with angular velocity \(\omega\). If \(\omega\) is less than some critical value \(\omega_c\), the bead sits at the bottom of the spinning loop. When \(\omega > \omega_c\), the bead moves out to some angle \(\theta\). a. What is \(\omega_c\) in rpm for the loop shown in the figure? b. At what value of \(\omega\), in rpm, is \(\theta = 30^\circ\)?