## Fundamentals of Physics Extended (10th Edition)

$199\ hits/second$
Given: Angular velocity $\omega = 33\frac{1}{3}\ rev/min = \frac{100}{3}\ rev/min$ Then, we convert $rev/min$ into $rad/s$: Since one revolution is equal to $2\pi$ radians and one minute is equal to $60$ seconds; $\omega = \frac{100}{3}(\frac{2\pi\ rad}{60\ s})$ $\omega =3.49\ rad/s$ Also, The radius $r =10\ cm = 0.1\ m$ The separation $d=1.75\ mm=1.75\times 10^{-3}\ m$ Linear velocity is $v=r\omega$ Therefore; $v=(0.1\ m)(3.49\ rad/s) =0.349\ m/s$ Number of hits/second = $\frac{v}{d}$ Number of hits/second = $\frac{0.349\ m/s}{1.75\times 10^{-3}\ m}$ Number of hits/second = $199\ hits/s$