Randall D. Knight — Dynamics II: Motion in a Plane: Problem 52

Suppose you swing a ball of mass \( m \) in a vertical circle on a string of length \( L \). As you probably know from experience, there is a minimum angular velocity \( \omega_{min} \) you must maintain if you want the ball to complete the full circle without the string going slack at the top. a. Find an expression for \( \omega_{min} \). b. Evaluate \( \omega_{min} \) in rpm for a 120 g ball tied to a 1.7-m-long string.