Randall D. Knight — Dynamics II: Motion in a Plane: Problem 44

A 2.00-m-diameter horizontal turntable rotates on a laboratory table. A 1.00-m-tall vertical post is attached to the rim of the turntable. A 75.0-cm-long string with a 50.0 g mass at the end is tied to the top of the post. What is the turntable’s angular velocity in rpm if the string makes a 7.00° angle with vertical? Hint: For angles smaller than 10°, you can use the small-angle approximation \tan \theta \approx \sin \theta.