Answer
Angular speed: $5 \pi \space rad./s$
Linear speed: $40 \pi \space in./s$
Work Step by Step
$1 \space min = 60 \space s$
$1 \space rev. = 2\pi \space rad.$
$$\theta = 150 \space rev. \times \frac{2 \pi \space rad.}{1 \space rev.} = 300 \pi \space rad.$$
$$\omega = \frac{\theta}{t} = \frac{300 \pi \space rad.}{60 \space s} = 5\pi \space rad./s$$
$$v = r \omega = (8 \space in.)(5 \pi \space rad./s) = 40 \pi \space in./s$$
