Answer
$199\ hits/second$
Work Step by Step
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 = $199\ hits/s$
