Halliday, Resnick & Walker — Rotation: Problem 24

24 A vinyl record is played by rotating the record so that an approximately circular groove in the vinyl slides under a stylus. Bumps in the groove run into the stylus, causing it to oscillate. The equipment converts those oscillations to electrical signals and then to sound. Suppose that a record turns at the rate of \(33\frac{1}{3}\) rev/min, the groove being played is at a radius of \(10.0\text{ cm}\), and the bumps in the groove are uniformly separated by \(1.85\text{ mm}\). At what rate (hits per second) do the bumps hit the stylus?