Final answer:
The angular speed of the fan is 4.19 rad/min and the linear speed of the tips of the blades is 2008 in./min.
Step-by-step explanation:
(a) To find the angular speed of the fan in rad/min, we need to convert the given speed from rpm to rad/min. There are 2π radians in one revolution, so:
Angular speed (in rad/min) = (40 rpm) x (2π rad/1 rev) x (1 min/60 s) = 4.19 rad/min
(b) To find the linear speed of the tips of the blades in./min, we need to find the distance travelled by the tips of the blades in one minute. The distance traveled by a point on the edge of the blade in one revolution is equal to the circumference of the circle traced by that point. So:
Linear speed (in in./min) = (circumference of circle) x (40 rpm) = (π x diameter) x (40 rpm) = (π x 16 in.) x (40 rpm) = 2008 in./min