## College Physics (4th Edition)

The rotational speed of the lathe chuck is $9.05~rad/s$
We can find the time it takes the cutting tool to move one inch: $t = \frac{d}{v} = \frac{1~in}{0.080~in/s} = 12.5~s$ The lathe chuck must rotate 18 times in this time. We can find the angular speed: $\omega = \frac{18\times 2\pi~rad}{12.5~s} = 9.05~rad/s$ The rotational speed of the lathe chuck is $9.05~rad/s$