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ceiling fan with 16 -in. blades rotates at 40rpm. (a) Find the angular speed of the fan in rad/min. rad/min (b) Find the linear speed of the tips of the blades in in./min. in/min

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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

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